heat transport of the quasionedimensional alternat

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2013职称英语理工类阅读理解原文答案译文之17

2013职称英语理工类阅读理解原文答案译文之17A Sunshade for the PlanetEven with the best will1 in the world, reducing our carbon emissions is not going prevent global warming. It has become clear that even if we take the most strong measures to control emissions, the uncertainties in our climate models still leave open the possibility of extreme warming and rises in sea level. At the same time, resistance by governments and special interest groups makes it quite possible that the actions suggested by climate scientists might not be implemented soon enough.Fortunately, if the worst comes to the worse2, scientists still have a few tricks up their sleeves3. For the most part they have strongly resisted discussing these options for fear of inviting a sense of complacency that might thwart efforts to tackle the root of the problem. Until now, that is. A growing number of researchers are taking a fresh look at large-scale “geoengineering” projects that might b e used to counteract global warming. “I use the analogy of methadone4,” says Stephen Schneider, a climate researcher at Stanford University in California who was among the first to draw attention to global warming. “If you have a heroin addict, the correct treatment is hospitalization, and a long rehab. But if they absolutely refuse, methadone is better than heroin.Basically the idea is to apply “sunscreen” to the whole planet. One astronomer has come up with a radical plan to cool Earth: launch trillions of feather-light discs into space, where they would form a vast cloud that would block the sun’s rays.It’s controversial, but recent studies suggest there are ways to deflect just enough of the sunlight reaching the Earth’s surface tocounteract the warming produced by the greenhouse effect. Global climate models show that blocking just 1. 8 per cent of t he incident energy in the sun’s rays would cancel out the warming effects produced by a doubling of greenhouse gases in the atmosphere. That could be crucial, because even the most severe emissions-control measures being proposed would leave us with a doubling of carbon dioxide by the end of this century, and that would last for at least a century more.注释:1. the best will:昀好的愿望2. if the worst comes to the worst:如果昀昀糟糕的事情发生了。

Heat conduction in one dimensional nonintegrable systems

a r X i v :c o n d -m at/0002192v 1 14 F e b 2000Heat conduction in one dimensional nonintegrable systemsBambi Hu 1,2,Baowen Li 1,3∗,and Hong Zhao 1,41Department of Physics and Centre for Nonlinear Studies,Hong Kong Baptist University,China2Department of Physics,University of Houston,Houston TX 77204-55063Department of Physics,National University of Singapore,119260Singapore 4Department of Physics,Lanzhou University,730000Lanzhou,China(Received 17June 1999)Two classes of 1D nonintegrable systems represented by the Fermi-Pasta-Ulam (FPU)model and the discrete φ4model are studied to seek a generic mechanism of energy transport in microscopic level sustaining macroscopic behaviors.The results enable us to understand why the class represented by the φ4model has a normal thermal conductivity and the class represented by the FPU model does not even though the temperature gradient can be established.PACS numbers:44.10.+i,05.70.Ln,05.45.-a,66.70.+fHeat conduction in one-dimensional (1D)noninte-grable Hamiltonian systems is a vivid example for study-ing microscopic origin of the macroscopic irreversibility in terms of deterministic chaos.It is one of the oldest but a rather fundamental problem in nonequilibrium statisti-cal mechanics [1].Intended to understand the underlying mechanism of the Fourier heat conduction law,the study of heat conduction has attracted increasing attention in recent years [2–11].Based on previous studies,we can classify the 1D lat-tices into three categories.The ﬁrst one consists of inte-grable systems such as the harmonic chain.It was rig-orously shown [12]that,in this category no tempera-ture gradient can be formed,and the thermal conductiv-ity is divergent.The second category includes a num-ber of nonintegrable systems such as the Lorentz gas model [2,10],the ding-a-ling and alike models [3],and the Frenkel-Kontorova (FK)model [5]and etc..In this category,the heat current is proportional to N −1and the temperature gradient dT/dx ∼N −1,thus the ther-mal conductivity κis a constant independent of system size N .The Fourier heat conduction law (J =−κdT/dx )is justiﬁed.The third category also includes some non-integrable systems such as the FPU [4,6]chain,the di-atomic Toda chain [7],the (mass)disorder chain [8],and the Heisenberg spin chain [9]and so on.In this cate-gory,although the temperature gradient can be set up with dT/dx ∼N −1,the heat current is proportional to N α−1with α∼0.43,the thermal conductivity κ∼N αwhich is divergent as one goes to the thermodynamic limit N →∞.These facts suggest that the nonintegrability is neces-sary to have a temperature gradient,but it is not suﬃ-cient to guarantee the normal thermal conductivity in a 1D lattice.This picture brings us to ask two questionsof fundamental importance:(i)Why do some noninte-grable systems have normal thermal conductivity,while the others fail?(ii)How can the temperature gradient be established in those nonintegrable systems having di-vergent thermal conductivity?The reason for the divergent thermal conductivity in integrable system is that the energy transports freely along the chain without any loss so that no temperature gradient can be established.The set up of temperature gradient in nonintegrable systems implies the existence of scattering.However,the diﬀerent heat conduction be-havior in the two categories of nonintegrable systems in-dicates that the underlying mechanism must be diﬀerent.To get the point,let’s write the Hamiltonian of a generic 1D lattice as H =iH i ,H i =p 2i∗To whom correspondence should be addressed.Email:bwli@.hk1models are the simplest anharmonic approximation of a monoatomic solid.In theφ4model,V takes the harmonic form,and the external potential U(x)=mx2/2+βx4/4, with mﬁxed to be zero in this paper.In the FPU model,U vanishes and V takes the anharmonic form of (x i−x i−1)2/2+β(x i−x i−1)4/4,andβ=1throughout this paper.In the case ofβ=0,the FPU model reduces to the harmonic chain.In our numerical simulations the Nos´e-Hoover ther-mostates[14]are put on theﬁrst and the last particles, keeping them at temperature T+and T−,respectively. The motion of these two particles are governed by¨x1=−ζ+˙x1+f1−f2,˙ζ+=˙x21/T+−1¨x N=−ζ−˙x N+f N−f N+1,˙ζ−=˙x21/T−−1.(2) where f i=−(V′+U′)is the force acting on the i’th particle.The equation of motion of other particle is ¨x i=f i−f i+1.The eighth-order Runge-Kutta algorithm was used.All computations are carried out in double ually the stationary state set in after107 time units.We should point out that we have performed computations by using other types of thermostate,and no qualitative diﬀerence has been found.thethehar-ofthe Fig.1(a)shows temperature proﬁles.In all noninte-grable systems,the temperature scales as T=T(i/N). However,in the FPU case there is a singular behavior near the two ends,which is a typical character of1D nonlinear lattices having divergent thermal conductivity. In the sameﬁgure we also show the temperature pro-ﬁles for two integrable lattices:the harmonic and the monoatomic Toda models.In these two cases no temper-ature gradient could be set up and the stationary state corresponds to T=(T++T−)/2,which is consistent with the rigorous result[12].In Fig.1(b),we plot the quantity J×N versus N for the FPU model and theφ4model.The inset shows the same quantity for the harmonic chain and the monoatomic Toda chain.The local heatﬂux is deﬁned by J i=˙x i∂Vφ4model,the head part of the proﬁle becomes weaker and weaker.The reason is that in theﬁrst three cases (a-c)both the total energy and the total momentum are conserved,whereas in theφ4model the momentum con-servation breaks down due to the external potential.The inset in Fig.2(d)shows that the total momentum in theφ4model decreases at least exponentially with time. The decay of the momentum with time indicates a loss of correlation.It is thus reasonable to envisage the en-ergy transport along theφ4chain as a random walk-like scattering.The solitary waves in the FPU chain exchange energy and momentum when colliding with each other.It causes the energy loss,and the heat current decreases when the system size is increased.To show this,we start two ex-citations at the two ends of the chain with diﬀerent mo-mentum,one moves to the right and another left.Let p1=6,p N=3and p i=0,i=1and N as our initial excitations.We calculate the momentums of the solitary waves(by simply summing up momentums of several lat-tices around the peaks)and investigate its change before and after the interaction.Weﬁnd that the bigger one generally transfers part of its momentum and energy to the smaller one,as is shown in Fig.3(a).The collision takes place at t=850,where a peak is shown up.of athemo-de-tail).The horizontal line is the momentum before collision.(c)The maximal momentum gain∆p max versus initial mo-mentum p0.(d)The ratio of the heatﬂux of J(400)/J(800) versus the average temperature T=(T++T−)/2in the semi-logarithmic scale.The results shown here are for the FPU model.Moreover,the interaction between solitary waves is found to depend closely on a“phase”diﬀerence.Here the“phase”diﬀerence is deﬁned as a time lag betweenthe excitations of two solitary waves.For instance,if we excite a solitary wave from the left end at time t,and another one from the right end at time t+δ,thenδis the“phase”diﬀerence.These two solitary waves,trav-eling through the chain in opposite directions,will col-lide with each other after a certain time.Although the physical meaning of the“phase”is not obvious,it is an important and good quantity to describe the interaction.We show p a L versusδfor two diﬀerent kinds of collision in Fig3(b),where p a L is the momentum of the solitary wave from the left after collision.In theﬁrst case both left and right solitary waves have the same initial mo-mentum p L=p R=6.27,which is excited by an initial condition of p1=p N=6and p i=0for other i.In the second case,the left one has p L=6.27and the right one p R=3.28,excited by an initial condition of p1=6, p N=3and p i=0for i=1and N.Theﬁgure shows that P a L depends on the“phase”sinusoidally.Other interesting features of the collision of solitary waves are shown in Fig.3(c),where we plot the maxi-mum momentum gain∆p max versus the initial momen-tum p0for the FPU model.∆p max is measured by sub-tracting the initial momentum p0from the maximum p L in Fig.3b.First of all,this picture tells us that the ex-change of momentum and energy depends on the initial momentum and energy.Secondly,there exists a criti-cal momentum below which no energy exchange can take place.The critical p c0∼1.8is clearly seen in theﬁgure.For p0<p c0,∆p max is zero.This result is very signiﬁcant, it indicates that there exists a threshold for the solitary wave interaction,below this threshold the interaction ceases,i.e.no momentum and energy exchanges between the solitary waves.A direct consequence of this fact is the existence of a threshold temperature below which the FPU chain should behave like a harmonic chain,namely, the excited waves travel freely along the chain without any energy loss,no temperature gradient can be set up, and the heat current remains a constant even though the size of the chain is changed.To testify this argument,we show the quantity J(400)/J(800)versus T=(T++T−)/2 in Fig.3(d),where J(N)is the heat currentﬂux for the system of size N.In the case of a size-independent J(N)one should get J(400)/J(800)=1,otherwise one would get J(400)/J(800)>1.Fig.3(d)captures this transition nicely for the FPU chain.The corresponding temperature threshold is about T c∼0.01.In the region of T∼0.001the numerical calculations do show that no temperature gradient is formed.The diﬀerent scattering mechanism in the FPU chain and those chains having normal thermal conductivity leads to a diﬀerent temperature dependence of ther-mal conductivityκ(T).In Fig.4we plotκ(T)for a FPU chain with an external potential of form U(x)=−γcos(2πx)for four diﬀerent values ofγ=0,0.01,0.05 and0.1.The chain size isﬁxed at N=100.As pointed out above,in smallγregime such asγ=0and0.01,the 3energy transport is assisted by the solitary waves,the system has a largeκwhich decreases as the temperature is increased.However,in the opposite regime(γ=0.05 and0.1),the energy transport is diﬀusive and obeys the Forier law,κincreases with temperature,because more phonons are excited.transport process can be reached,and the heat conduc-tion obeys the Fourier law;(ii)Although the interaction of solitary waves makes it possible to set up temperature gradient in the FPU and alike nonintegrable models,the momentum conservation prohibits the diﬀusive transport and consequently leading to the divergent thermal con-ductivity.In addition,we have uncovered an important fact in the FPU model,namely,the existence of a thresh-old temperature,below which the FPU mode behaves like a harmonic chain.BL would like to thank G.Casati for useful discus-sions.This work was supported in part by Hong Kong Research Grant Council and the Hong Kong Baptist Uni-versity Faculty Research Grant.Note added in proof.–After submission of this pa-per we get to know the following results.Prosen and Campbell[15]proved in a more rigorous way that for a1D classical many-body lattice total momentum con-servation implies anomalous conductivity.The normal thermal conductivity in theφ4lattice has also been ob-served by Aoki and Kusnezov[16].The role of the exter-nal potential has been further studied by Tsironis et al [17].。

高二英语海洋科学单选题40题

高二英语海洋科学单选题40题1. The ______ of the whale is one of the most amazing spectacles in the ocean.A. migrationB. hibernationC. reproductionD. digestion答案：A。

本题考查海洋生物的行为。

选项A“migration”意思是迁徙，鲸鱼的迁徙是海洋中令人惊叹的景象之一。

选项B“hibernation”指冬眠，鲸鱼通常不冬眠。

选项C“reproduction”是繁殖，虽然鲸鱼繁殖也是重要的生命活动，但不如迁徙具有壮观的景象。

选项D“digestion”是消化，与题干描述的壮观景象不符。

2. Some species of sea turtles can live up to 100 years. The underlined part means ______.A. kindsB. groupsC. numbersD. qualities答案：A。

“species”常见释义为“物种；种类”。

选项A“kinds”有“种类”的意思，符合。

选项B“groups”是“组；群”。

选项C“numbers”是“数量”。

选项D“qualities”是“质量；品质”。

3. The color of the octopus can change to blend in with its ______.A. environmentB. companionC. predatorD. competitor答案：A。

本题考查海洋生物的生存策略。

“blend in with”表示与......融合。

选项A“environment”环境，章鱼能变色与环境融合。

选项B“companion”同伴。

选项C“predator”捕食者。

选项D“competitor”竞争者。

章鱼变色主要是为了适应环境，而非同伴、捕食者或竞争者。

2024年06版小学第二次英语第2单元真题

2024年06版小学英语第2单元真题考试时间：80分钟（总分:120）A卷考试人：_________题号一二三总分得分一、选择题(共计20题，共40分)1、What do you call a young flamingo?A. ChickB. KitC. PupD. Calf2、What is the capital city of France?A. LyonB. ParisC. MarseilleD. Bordeaux3、What do we call a person who studies plants?A. BiologistB. BotanistC. ZoologistD. Ecologist4、Which one is a type of bird?A. LizardB. SparrowC. FrogD. Crab5、选择题：What is the largest organ in the human body?A. HeartB. SkinC. LiverD. Brain6、What do we call the process of heat transfer through direct contact?A. ConvectionB. ConductionD. Insulation7、What do you call a person who plays music?A. PainterB. MusicianC. ActorD. Writer8、选择题：What do you call a written message sent electronically?A. LetterB. EmailC. TextD. Note9、What do we use to write on a board?A. PencilB. MarkerC. CrayonD. Paint10、选择题：What do we call the place where you can see many plants?A. GardenB. ForestC. ParkD. Field11、选择题：What type of animal is a frog?A. MammalB. ReptileC. AmphibianD. Bird12、What do we call the outermost layer of the Earth?A. MantleB. CrustC. CoreD. Lithosphere13、What is the first month of the year?A. FebruaryB. MarchD. April14、选择题：What is the capital of Malta?A. VallettaB. MdinaC. SliemaD. Birkirkara15、选择题：What do you call the person who fixes cars?A. BakerB. MechanicC. TeacherD. Artist16、选择题：What do you call a baby otter?A. PupB. KitC. CalfD. Cub17、Which of these is a vegetable?A. AppleB. CarrotC. BananaD. Grape18、选择题：What is the name of the large body of salt water that covers most of the Earth?A. SeaB. OceanC. LakeD. River19、选择题：What is the main ingredient in guacamole?A. TomatoB. AvocadoC. PepperD. Onion20、选择题：Which instrument has keys and is played by pressing them?B. DrumsC. PianoD. Flute二、听力题(共计20题，共40分)1、听力题：We enjoy _____ (hiking) in the mountains.2、听力题：A ____ is a tiny animal with whiskers that likes to explore.3、听力题：The Earth's atmosphere is essential for regulating temperature and protecting against ______.4、听力题：The temperature at which a substance boils is its ______.5、听力题：She is ___ her lunchbox. (packing)6、听力题：There are ______ (five) birds in the tree.7、听力题：A __________ is a natural harbor.8、听力题：A __________ is crucial for the development of civilizations.9、听力题：The chemical formula for acetic acid is ________.10、听力题：A physical property of water is that it is ______.11、听力题：Oxidizing agents accept _____ during a chemical reaction.12、听力题：A mineral’s ______ refers to its shiny or dull appearance.The _______ of a wave can be visualized through a ripple effect.14、听力题：A solar eclipse occurs when the moon passes in front of the ______.15、听力题：The ______ is known for his bravery.16、听力题：The chemical formula for sodium bicarbonate is _______.17、听力题：Metals are usually _______ conductors of electricity.18、听力题：A __________ is a mixture where the components can be easily separated.19、听力题：Chemical reactions can be affected by _____, concentration, and surface area.20、听力题：The capital of Nigeria is ________.三、填空题(共计20题，共10分)1、填空题：The ______ (鲸鱼) is a majestic creature of the sea.2、填空题：I imagine my __________ (玩具名) can __________ (动词).3、填空题：I can ______ (自我提升) through feedback.4、填空题：The ________ is strong and sturdy.5、填空题：An octopus has ______ (触手) and lives in the sea.6、填空题：I want to learn how to _______ (骑马).Many plants have _____ (香味) that attract insects.8、填空题：I saw a _______ (蝴蝶) in my garden.9、填空题：The ______ (海豚) is very social and intelligent.10、填空题：A ________ (植物保护措施) is essential for survival.11、填空题：The squirrel has a bushy ______ (尾巴).12、填空题：The monkey loves to eat ______.13、填空题：The ________ was a major event in the history of Latin America.14、填空题：A _____ (果实) can contain many seeds.15、填空题：The puppy is very _______ (小狗非常_______).16、填空题：I want to grow a ________ that attracts bees.17、填空题：In PE class, we play many sports like ________ (篮球) and ________ (排球). It helps us stay ________ (健康).18、填空题：A ________ (航空港) is where planes take off and land.19、填空题：The ________ (公路) connects different cities.20、填空题：The __________ (野生动植物) rely on plants for food.。

Coherent phonon scattering effects on thermal transport in thin semiconductor nanowires

PACS numbers: 74.50+r 74.72-h
I.
Iof heat by phonons in quasi-onedimensional structures is sensitive to quantum conﬁnement eﬀects once the phonon wavelengths that dominate thermal transport are comparable to the structure dimensions. Strong quantum conﬁnement in thermal transport has been demonstrated in the observation1 of the thermal conductance quantum2,3,4 at temperatures T ≤ 1 K and also in recent experiments on semiconductor nanowires5,6 and nanotubes7 at higher temperatures (down to ∼ 10 K). Experiments on the thinnest nanowires are not well explained by current models of independent scattering events at the boundary8 , even though such models describe thicker wires quite well (see ﬁgure 1). In particular, data on a 22 nm Si nanowire5 shows thermal conductivity scaling with temperature up to temperatures of order 200 K, well above the temperature where higher transverse modes should be occupied; linear temperature dependence1 is expected when only the four gapless modes are occupied. This paper studies the eﬀect of coherence between diﬀerent scattering events in quasi-onedimensional systems of variable transverse dimension, using a large-scale numerical transfer matrix approach to check simple analytic models. The diﬀerences between bulk and boundary disorder are studied9,10,11 , and linear temperature dependence at high temperature is found to depend on having boundary disorder rather than bulk disorder. The study of quantum eﬀects on electrons in quasione-dimensional systems has developed steadily since the observation in 1988 of quantized electrical conductance in ballistic quantum point contacts12 . The electrical conductance as a function of gate voltage shows plateaus at multiples of Ge = 2e2 /h, where h is Planck’s constant and e the electron charge, and the factor of 2 results

Dispersion relations at finite temperature and density for nucleons and pions

a rXiv:h ep-ph/9911451v123Nov1999FIUN-CP-99/2Dispersion relations at ﬁnite temperature and density for nucleons and pions R.Hurtado 1Department of Physics,University of Wales Singleton Park,Swansea,SA28PP,United Kingdom J.Morales 1and C.Quimbay 1Departamento de F´ısica,Universidad Nacional de Colombia Ciudad Universitaria,Santaf´e de Bogot´a ,D.C.,Colombia November 21,1999To be published in Heavy Ion Physics Abstract We calculate the nucleonic and pionic dispersion relations at ﬁnite tem-perature (T )and non-vanishing chemical potentials (µf )in the context of an eﬀective chiral theory that describes the strong and electromagnetic interac-tions for nucleons and pions.The dispersion relations are calculated in thebroken chiral symmetry phase,where the nucleons are massive and pions are taken as massless.The calculation is performed at lowest order in the energy expansion,working in the framework of the real time formalism of thermal ﬁeld theory in the Feynman gauge.These one-loop dispersion relations are ob-tained at leading order with respect to T and µf .We also evaluate the eﬀective masses of the quasi-nucleon and quasi-pion excitations in thermal and chemical conditions as the ones of a neutron star.Keywords:Chiral Lagrangians,Dispersion Relations,Finite Temperature,Chemical Potentials,Nucleons,Pions.1IntroductionEﬀective chiral theories have become a major conceptual and analytical tool in par-ticle physics driven by the need of a theory to describe the low–energy phenomenology of QCD.The foundations were formulated originally by Weinberg[1]to characterise the most general S-matrix elements for soft pion interactions and later it was further developed by Gasser and Leutwyler[2].Eﬀective chiral theories have shown to be an adequate framework to treat low–energy phenomenology[3]-[6],as they reproduce,at lowest order in the chiral expansion,the most important results from current algebras including the low–energy theorems,and at next-to-leading order,they give precise corrections to these results[3].They have been widely applied to diﬀerent problems as meson–meson,meson–baryon,photon–photon,photon–meson and photon–baryon scattering,photoproduction processes and rare kaon decays[7,18].The propagation properties of relativistic particles in plasmas atﬁnite tempera-ture is also a subject of increasing interest.It is well known that the interaction of a particle with a plasma in thermal equilibrium at temperature T modiﬁes the Disper-sion Relations(DR)with respect to the zero temperature situation.This phenomenon has been extensively investigated for the non-dense plasma case[19]-[30],i.e.when the chemical potential(µf)associated to the fermions of the thermal plasma is equal to zero:µf=0and T=0.In this case the Fermionic Dispersion Relations(FDR) have been studied for massless fermions in[19]-[22]and massive fermions in[23]-[30]. The FDR describe the propagation of the fermionic excitations of the plasma(quasi-fermions and quasi-holes)through the thermal background.These excitations are originated in the collective behaviour of the plasma system at low momentum.On the other hand,DR describing the propagation of the fermionic excitations of a dense plasma atﬁnite temperature can be found in literature[31]-[35].For the dense plasma case atﬁnite temperature,i.e.µf=0and T=0,the FDR have been calculated both for massless fermions in[31]-[34]and for massive fermions in[35]. These FDR have been calculated in the context of realistic physical models,as for instance,the Minimal Standard Model[29,34].In the present work we calculate the DR for quasi–nucleons and quasi–pions prop-agating in a plasma atﬁnite temperature and non–vanishing chemical potentials. The calculation is performed for a SU(2)L×SU(2)R eﬀective chiral Lagrangian with the chiral symmetry broken into SU(2)L+R.This Lagrangian,which we introduce in section2,describe the strong and electromagnetic interactions of massive nucleons and massless pions.The calculation is performed using the real time formalism of the thermalﬁeld theory[36]-[38]in the Feynman gauge.The one–loop DR are calculated at lowest order in the energy expansion and obtained taking the T2andµ2f terms from the self–energy,as shown in section3.As an application of the DR obtained,we evaluate the eﬀective masses of the quasi–nucleon and quasi–pion excitations takingthe following values:T=150MeV,µp=100MeV andµn=2µp,beingµp(µn)the chemical potential for protons(neutrons)[43].This evaluation is shown in section4, as well as the discussion of the main results and conclusions.2Eﬀective chiral Lagrangian at leading order in the energy expansionEﬀective chiral theories are founded in the existence of an energy scaleΛχat which chiral symmetry SU(N f)L×SU(N f)R,with N f the number ofﬂavours,breaks into SU(N f)L+R leading to N2f−1Goldstone bosons associated to the N f broken generators.These Goldstone bosons are identiﬁed with the meson ground state octet for N f=3,and with the triplet of pions[2,6]in the case of N f=2.The chiral symmetry of the Lagrangian is broken through the introduction of an explicit mass term for the nucleons.A general form for a Lagrangian with SU(2)L+R symmetry describing the strong and electromagnetic interactions for massive nucleons and massless pions is[39,40]:L=F2π4FµνFµν,(2.1)whereLπN=¯Niγµ∂µN−ie¯NγµAµ 1+τ32FπN+Mg2A¯N τ·πFπ,(2.4) where the covariant derivative and electromagnetic charge are deﬁned asDµΣ=∂µΣ+ieAµ[Q,Σ],(2.5)Q= 23 .(2.6)Hereπ,N and Aµrepresent the pion,nucleon and electromagneticﬁelds,Fπ=93MeV is the pion decay constant,e is the electromagnetic coupling constant,g A=1.26is the axial coupling constant,and M is the average nucleon mass.3Dispersion relations for nucleons and pionsIn this section we calculate the DR for nucleons and pions in the framework of the Lagrangian given by(2.1).We consider the propagation of the nucleonic and pionic excitations in a dense thermal plasma constituted by protons,neutrons,charged pions,=0,where f i neutral pions and photons,being this plasma characterised byµfirepresents the diﬀerent fermion species.The calculation is performed in the real time formalism of the thermalﬁeld theory in the Feynman gauge.The real part of the nucleonic and pionic self-energies are evaluated at lowest order in the energy expansion and at one-loop order(g A/Fπ)2,considering only the leading contributions in T andµf.The Feynman rules for the vertices atﬁnite temperature and density(Fig.1)are the same as those at T=0andµf=0,while the propagators in the Feynman gauge for photons Dµν(p),pions D(p)and massive nucleons S(p)are[41]:Dµν(p)=−gµν 1−iΓb(p),(3.2)p2+iǫp/S(p)=,(3.6)e(p·u)/T−1n f(p)=θ(p·u)n−f(p)+θ(−p·u)n+f(p),(3.7) being n b(p)the Bose–Einstein distribution function,and the Fermi–Dirac distribution functions for fermions(n−f(p))and anti-fermions(n+f(p))are:1n∓f(p)=3.1Nucleonic Dispersion RelationUsing the Feynman diagrams given in Fig.(2),we calculate the FDR for quasi–protons and quasi–neutrons.In order to apply a similar procedure to that followed in[21,29,34],weﬁrst consider the hypothetical case of massless nucleons.In this case,we obtain two solutions:one describing the propagation of quasi-fermionsw(k)=M p,n+k3M p,n+O(k3),(3.9)and another one describing the propagation of quasi-holesw(k)=M p,n−k3M p,n+O(k3).(3.10)We observe that if k=0,w(k)=M p,n.Then M p(M n)can be interpreted as the eﬀective mass of the quasi-protons(quasi-neutrons),and their expressions are: M2p= 3g2A M28 T2+g2A M22 +e2µ2p64F2πT2+g2A M22+µ2p .(3.12)For the limit k>>M p,n the FDR are:w(k)=k+M2p,n2k3Log(2k2of the chiral phase transition in non–zero hadronic density [42].We observe that m p,n>Mp,n ,where m p (m n )is the rest mass of the proton (neutron)and M p,n aregiven by (3.11)and (3.12).In the limit m 2p,n >>M 2p,n the FDR become [24]:w (k )2=k 2+m 2p,n +M 2p,n .(3.15)Starting from relation (3.15)and equations (3.11),(3.12),we obtain a generalexpression for the nucleon eﬀective mass splitting ∆M 2N :∆M 2N =m 2p −m 2n +e 2T 28π2 g 2A M 2µ2n 8F 2π+e 2µ2p .(3.16)3.2Pionic Dispersion RelationUsing the Feynman rules given in Fig.(1),we obtain the following DR for quasi-pions:w (k )2=k 2+M 2π±,π0,(3.17)where M π±(M π0)is the eﬀective mass for charged (neutral)quasi–pions,and their expressions are:M 2π±=T 2F 2π+e2 +g 2A M 28π2F 2π2π2T 212.(3.20)4Results and conclusionsWe now give the results of the calculation for the eﬀective masses of quasi–nucleons and quasi–pions.We have used the following values m p =938.271MeV,m n =939.566MeV,M =938.919MeV,T =150MeV,µp =100MeV,µn =200MeV,e 2=0.095.The temperature and chemical potential values are of the order of those in a neutron star [43].The results for the eﬀective masses are:M p=1036.5133MeV M n=1033.8394MeV M π±=637.2312MeV M π0=637.0914MeVwhere M p,M n,Mπ±and Mπ0are the eﬀective masses for the proton,neutron,charged pions and the neutral pion,including the strong and electromagnetic interactions.The eﬀective mass splitting for nucleons and pions are:∆(M p−M n)=2.6740MeV∆(Mπ±−Mπ0)=0.1398MeVwhere∆(Mπ±−Mπ0)is due exclusively to the combined electromagnetic interaction and temperature eﬀects,as shown at(3.20).For the nucleons,from the total eﬀective mass splitting∆(M p−M n),the combined electromagnetic and temperature contribute is∆em(M p−M n)=0.0058MeV.In conclusion,temperature eﬀects enter into the eﬀective mass splitting relations (3.16)and(3.20)exclusively in the electromagnetic interaction term,which at T=0vanishes.Also,in the framework of our model we found that,for the chemical potentials and temperature used,the eﬀective mass on the proton is bigger than the one of the neutron.Our results should be improved by considering massive pions and introducing the weak interaction,as well as using a realistic model for neutron stars, to be presented in short.AcknowledgementsThis work was supported by COLCIENCIAS(Colombia),Universidad Nacional de Colombia and Centro Internacional de F´ısica.We want also to thank to Fernando Cristancho by invitation to participate in the Third Latinamerican Workshop on Nuclear and Heavy Ion Physics,San Andr´e s,Colombia.References[1]Weinberg,Physica A96(1979)327.[2]J.Gasser and Leutwyler,Ann.Phys(N.Y)(1984)158;Nucl.Phys.B250(1985)465.[3]J.F.Donoghue,E.Golowich and B.R.Holstein,“Dynamics of the StandardModel”,Cambridge University Press,1992.[4]U.G.Meissner,Rep.Prog.Phys.56(1993)903.[5]A.Pich,Rep.Prog.Phys.58(1995)563.[6]G.Ecker,Prog.Part.Nucl.Phys.35(1995)1;G.Ecker and M.Mojzis,Phys.Lett.B365(1996)312.[7]M.Wise,Phys.Rev.D45(1992)R2188.[8]G.Bardman and J.Donoghue,Phys.Lett.B280(1992)287.[9]T.M.Yan,H.Y.Chang and C.Y.Cheung,Phys.Rev.D46(1992)1148.[10]P.Cho,Phys.Lett.B285(1992)145.[11]Chungsik Song,Phys.Rev.D49(1994)1556.[12]E.Oset,J.A.Oller,J.R.Pelaez and A.Ramos,Acta Phys.Polon.B29(1998)3101.[13]J.A.Oller and E.Oset,Nucl.Phys.A620(1997)438.[14]N.Kaiser and P.B.Siegel,Nucl.Phys.A594(1995)325.[15]N.Kaiser and T.Waas,Nucl Phys A612(1997)297.[16]T.S.Park and D.P.Min,Phys.Rep.233(1993)341.[17]V.Bernard and N.Kaiser.Phys.Rep.246(1994)315;J.Modern of Physics E4(1995)193.[18]U.Mosel,“Fields,Symmetries,and Quarks”.Springer(1998).[19]O.K.Kalashnikov and V.V.Klimov,Sov.J.Nucl.Phys.31(1980)699.[20]V.V.Klimov,Sov.J.Nucl.Phys.33(1981)934;Sov.Phys.JETP55(1982)199.[21]H.A.Weldon,Phys.Rev.D26,2789(1982);Physica A158(1989)169;Phys.Rev.D40(1989)2410.[22]G.Gatoﬀand J.Kapusta,Phys.Rev.D41(1990)611.[23]R.Pisarski,Nucl.Phys.A498(1989)423c.[24]T.Altherr and P.Aurenche,Phys.Rev.D40(1989)4171.[25]V.V.Lebedev and A.V.Smilga,Ann.Phys.(NY)202(1980)229.[26]G.Baym,J.P.Blaizot and B.Svetitsky,Phys.Rev.D46(1992)4043.[27]E.Petitgirard,Z.Phys.C54(1992)673.[28]K.Enqvist,P.Elmforms and I.Vilja,Nucl.Phys.B412(1994)459.[29]C.Quimbay and S.Vargas-Castrillon,Nucl.Phys.B451(1995)265.[30]A.Riotto and I.Vilja,Phys.Lett.B402(1997)314.[31]E.J.Levinson and D.H.Boal,Phys.Rev.D31(1985)3280.[32]J.P.Blaizot and J.Y.Ollitrault,Phys.Rev.D48(1993)1390.[33]A.Erdas,C.W.Kim and J.A.Lee,Phys.Rev.D48(1993)3901.[34]J.Morales,C.Quimbay and F.Fonseca,Nucl.Phys.B560(1999)601.[35]O.K.Kalashnikov,Mod.Phys.Lett.A12(1997)347;JETP Lett.67(1998)1;Phys.Scripta58(1998)310;Mod.Phys.Lett.A13(1998)1719.[36]S.L.Dolan and R.Jackiw,Phys.Rev.D9(1974)3320.[37]A.J.Niemi and G.W.Semenoﬀ,Ann.Phys.(N.Y.)152(1984)105.[38]ndsman and Ch.G.van Weert,Phys.Rep.145(1987)141.[39]M.K.Volkov and V.N.Pervushin,Yad.Fiz.22(1975)346[40]P.Chang and F.Gursey,Phys.Rev.164(1967)1752.[41]R.L.Kobes,G.W.Semenoﬀand N.Weiss,Z.Phys.C29(1985)371.[42]L.D.McLerran and B.Svetitsky,Phys.Lett.B98(1981)195;J.Kogut at al.,Phys.Rev.Lett.48(1982)1140;J.Polonyi et al.,Phys.Rev.Lett.53(1984), 664.[43]J.Byrne,”Neutrons,Nuclei and Matter and Exploration of the Physics of SlowNeutrons”,Institute of Physics Publishing,Bristol and Philadelphia,1996.Figure1:Feynman Rules of the LπN.Figure2:Self–energy contributions for the calculation of FDR for:(a)Protons(b) Neutrons.。

高二英语地理现象单选题40题

高二英语地理现象单选题40题1.The process by which water changes from a liquid to a gas is called_____.A.evaporationB.condensationC.precipitationD.sublimation答案：A。

evaporation 是蒸发，水从液态变为气态的过程叫蒸发。

condensation 是冷凝，是气态变为液态。

precipitation 是降水。

sublimation 是升华，是固态直接变为气态。

2.The movement of air from an area of high pressure to an area of low pressure is known as_____.A.windB.cycloneC.anticycloneD.tornado答案：A。

wind 是风，空气从高压区向低压区的流动叫风。

cyclone 是气旋。

anticyclone 是反气旋。

tornado 是龙卷风。

3.The phenomenon where the sun appears to rise in the east and set in the west is due to_____.A.the rotation of the EarthB.the revolution of the EarthC.the tilt of the EarthD.the size of the Earth答案：A。

the rotation of the Earth 是地球自转，太阳从东边升起西边落下是由于地球自转。

the revolution of the Earth 是地球公转。

the tilt of the Earth 是地球倾斜。

the size of the Earth 是地球大小。

4.The layer of the atmosphere closest to the Earth's surface is called_____.A.troposphereB.stratosphereC.mesosphereD.thermosphere答案：A。

2022年考研考博-考博英语-厦门大学考试全真模拟易错、难点剖析AB卷(带答案)试题号：51

2022年考研考博-考博英语-厦门大学考试全真模拟易错、难点剖析AB卷（带答案）一.综合题(共15题)1.单选题Changing from solid to liquid, water takes in heat from all substances near it and this_______produces artificial cold surrounding it.问题1选项A.absorptionB.transitionC.consumptionD.interaction【答案】A【解析】absorption吸收; transition过渡, 转变; consumption消费, 消耗; interaction相互作用。

句意：水从固体变成液体, 会吸收附近所有物质的热量, 这种吸收会在周围产生人工寒潮。

选项A符合句意。

2.单选题The British historian Niall Ferguson speculated that the end of American_______might not fuel an orderly shift to a multipolar system.问题1选项A.domainB.hegemonyC.sovereigntyD.preference【答案】B【解析】domain领地,领域; hegemony霸权; sovereignty主权,君主; preference偏爱, 优先权。

句意：英国历史学家Niall Ferguson推测, 美国霸权主义的终结可能不会推动美国向多极体系的有序转变。

选项B符合句意。

3.翻译题(1). When we talk about the danger of romantic love, we don't mean danger in the obvious heartbreak way—the cheap betrayals, the broken promises—we mean the dark danger that lurks when sensible, educated women fall for the dogmatic idea that romantic love is the ultimate goal for the modern female. Every day, thousands of films, books, articles and TV programs hammer home this message—that without romance, life is somehow barren.However, there are women who entertain the subversive notion, like an intellectual mouse scratching behind the skirting board, that perhaps this higher love is not necessarily the celestial highway to absolute happiness. (2). Their empirical side kicks in. and they observe that couples who marry in a haze of adoration and sex are, ten years later, throwing china and fight bitterly over who gets the dog.(3). But the women who notice these contradictions are often afraid to speak them in case they should be labeled cynics. Surely only the most jaded and damaged would challenge the orthodoxy of romantic love. The received wisdom that there is not something wrong with the modern idea of sexual love as ultimate panacea, but (hat if you don't get it, there is something wrong with you. You freak, go back and read the label. (4).We say the privileging of romantic love over all others, the insistence that it is the one essential, incontrovertible element of human happiness, traced all the way back to the caves, is a trap and a snare. The idea that every human heart, since the invention of the wheel, was yearning for its other half is a myth.(5). Love is a human constant: it is the interpretation of it that changes. The way that love has been expressed, its significance in daily life, have never been immutable or constant. The different kinds of love and what they signify are not fixed, whatever the traditionalists may like to tell you.So the modern idea that romantic love is a woman's highest calling, that she is somehow only half a person without it, that if she questions it she is going against all human history, does not stand up to scrutiny. It is not an imperative carved in stone; it is a human idea, and human beings are frail and suggestible, and sometimes get the wrong end of the stick.Read the passage carefully and translate the underlined sentences into Chinese.【答案】1.当说到浪漫爱情的危险时, 我们并不是指显而易见令人心碎的危险一可耻的背叛、破碎的誓言——而是指当明智的知识女性对教条主义思想信以为真, 即浪漫的爱情是现代女性的终极目标时, 潜伏着的隐秘危险。

2017 年 05 月 13 日托福考试真题解析

2017 年05 月13 日托福考试真题解析托福阅读Passage one主题：Body temperature 内容回忆：本文共8 段。

第 1 段动物需要保持体温，还需要将热量传输到表面皮肤。

表面的温度低于内部才会产生热量的传输。

第 2 段产生热量的是少部分器官，比如人体中的chest，abdomen，brain 产生的热量就占所有热量的72%。

第3 段运动的时候，会产生更多的热量，要比平时多上十多倍的热量，主要是肌肉产生。

第4 段说的内部温度也不是都一样的，inner 的温度保持恒定，但是器官直接也有温度差，可能会有0.5 度的差别。

第5，6 段主要讲热量是怎么传输到表面的。

最后两段主要内容讲到，体温会根据日常的活动调节，不同的动物会不一样。

比如夜行动物在夜间体温高，白天低。

词汇题：1.uniform = constant2.considerably = greatly3.significance = importance4.roughly = approximatelyPassage two主题：The north long-neck turtle 内容回忆：第1 段介绍了生活在澳洲热带的long-neck turtle，它们的栖息地非常地特殊，会随着干湿两季的不同，改变栖息地；第 2 段讲到研究者们找了两年也没有找到这种龟的栖息地，但是当地的土著人知道，他们知道这种龟会将蛋产在水下。

为了验证这个说法，研究者在水下放了很多radio transmitter，turtle 下蛋的时候，transmitter 会附在蛋上，结果真的发现，long-neck turtle 会在水下14-17 米的泥下下蛋；第3 段讲为什么turtle 会选这里下蛋，这和它们生存的环境有关，它们生存的环境没有稳定的水，干湿两季是主要原因。

第 4 段讲到为什么这种龟下蛋在水下，蛋可以生存下来，不同于别的蛋，它们的蛋特别抗压。

EG Test 1 Passage 1 阅读译文

Making senseRecent research suggests that gender affects how we see the world and how we operate within it.最近研究表明，性别会影响我们的世界观以及处世之道。

A According to the results of new research into vision carried out at the City University of New York (CUNY), there are marked differences in the way that men's and women's brains process visual data. Israel Abramov of CUNY stated that the experiments relate to specific sets of thalamic neurons in the brain's primary visual cortex, which appear to be gender related. The development of these neurons is influenced by the male sex hormones during foetal growth early in pregnancy. Although Abramov can successfully explain the process that leads to the difference, he is at a loss to know what evolutionary motive there might be for the variance.一项最近在纽约市立大学进行的视觉研究结果显示，男性大脑和女性大脑在处理可视化数据的方式上具有明显的差异。

海龟喜欢吃海藻的作文英语

Sea turtles are among the most iconic and beloved creatures in the ocean,known for their gentle demeanor and majestic presence.One of the fascinating aspects of their diet is their preference for seaweed,a staple that provides them with essential nutrients and energy.This essay delves into the dietary habits of sea turtles,particularly their fondness for algae, and the ecological implications of this preference.Sea turtles are ectothermic reptiles,meaning they rely on external sources to regulate their body temperature.Their diet is diverse,ranging from seagrasses to mollusks,but algae play a significant role in their nutritional intake.Algae,being rich in vitamins,minerals,and fiber,offer a balanced diet that supports the growth and health of these marine reptiles.In the warm,shallow waters where sea turtles often forage,a variety of algae thrive.These marine plants sway gently with the current,creating an underwater landscape that is both visually stunning and rich in nutrients. Sea turtles have evolved to take advantage of this abundance,using their strong,beaklike jaws to tear off and consume large quantities of algae.One of the most striking examples of this dietary preference can be observed in the green sea turtle,a species that has developed a unique taste for seagrasses and algae.The green sea turtles digestive system is adapted to process these plant materials efficiently,extracting the necessary nutrients and energy to fuel their long migrations and reproductive cycles.The preference for algae among sea turtles is not just a matter of taste italso has ecological implications.By consuming large quantities of algae, sea turtles help to maintain the balance of marine ecosystems.Algae,while essential for the health of coral reefs and seagrass beds,can also become overgrown if not kept in check.Sea turtles,through their feeding habits, act as natural regulators,preventing algal blooms that could otherwise harm marine life.Moreover,the consumption of algae by sea turtles contributes to the recycling of nutrients within the marine environment.As they feed,sea turtles ingest not only the algae but also the microorganisms and detritus that cling to the plant surfaces.This material is then processed within the turtles digestive system and excreted back into the ocean,enriching the waters and providing a valuable source of nutrients for other marine organisms.However,the relationship between sea turtles and algae is not without its challenges.Climate change,pollution,and habitat destruction have led to shifts in the distribution and abundance of algae,impacting the availability of food for sea turtles.Additionally,the increasing prevalence of plastic waste in the ocean has resulted in sea turtles mistaking plastic debris for food,leading to ingestion and entanglement that can be fatal.Conservation efforts are crucial to protect both sea turtles and the algae they rely on for sustenance.By preserving marine habitats,reducing pollution,and addressing the impacts of climate change,we can help ensure that sea turtles continue to thrive and play their vital role in maintaining the health of our oceans.In conclusion,the dietary preference of sea turtles for algae is a testament to the intricate and delicate balance of marine ecosystems.As apex consumers,sea turtles contribute to the wellbeing of the ocean,and their survival is intrinsically linked to the health of the algae they consume.By understanding and appreciating this relationship,we can better appreciate the importance of protecting these magnificent creatures and the habitats they call home.。

Heat Transfer Analysis of boreholes in vertical ground heat exchangers

Heat transfer analysis of boreholes in vertical groundheat exchangersHeyi Zeng,Nairen Diao,Zhaohong Fang*The Ground Source Heat Pump Research Center,Shandong Institute of Architecture and Engineering,47Heping Road,Jinan 250014,ChinaReceived 1October 2002;received in revised form 25April 2003AbstractA ground heat exchanger (GHE)is devised for extraction or injection of thermal energy from/into the ground.Bearing strong impact on GHE performance,the borehole thermal resistance is deﬁned by the thermal properties of the construction materials and the arrangement of ﬂow channels of the GHEs.Taking the ﬂuid axial convective heat transfer and thermal ‘‘short-circuiting’’among U-tube legs into account,a new quasi-three-dimensional model for vertical GHEs is established in this paper,which provides a better understanding of the heat transfer processes in the GHEs.Analytical solutions of the ﬂuid temperature proﬁles along the borehole depth have been obtained.On this basis analytical expressions of the borehole resistance have been derived for diﬀerent conﬁgurations of single and double U-tube boreholes.Then,diﬀerent borehole conﬁgurations and ﬂow circuit arrangements are assessed in regard to their borehole resistance.Calculations show that the double U-tubes boreholes are superior to those of the single U-tube with reduction in borehole resistance of 30–90%.And double U-tubes in parallel demonstrate better performance than those in series.Ó2003Elsevier Ltd.All rights reserved.Keywords:Ground source heat pump;Ground heat exchanger;Model;Thermal resistance;Analytical solution1.IntroductionUtilizing the ground as a heat source/sink,ground-coupled heat pump (GCHP)systems have been gaining increasing popularity for space conditioning in residential and commercial buildings due to their reduced energy and maintenance costs as compared to conventional systems.This system is environment-friendly,causing less carbon dioxide emission than their conventional alternatives.The GCHP system features its ground,or geothermal,heat exchanger (ground heat exchanger,GHE),whether it is horizontally installed in trenches or as U-tubes in vertical boreholes.The ad-vantages of vertical GHEs are that they require smaller plots of land areas,and can yield the most eﬃcient ground source heat pump system performance.The vertical GHEs are usually constructed by inserting one or two high-density polyethylene U-tubes in vertical boreholes to serve as the ground loops,which are referred to as single U-tube or double U-tube GHEs,respectively.The boreholes should be grouted to provide better thermal conductance and prevent groundwater from possible contamination.The single U-tube conﬁguration has been widely used in the North American [1,2].Being popular mainly in Europe [3],the basic construction of the double U-tube GHE consists of two U-tubes installed in one borehole and piped in either a series or parallel ﬂow circuit.Borehole depths usually range from 40to 200m with diameter of 75–150mm.A schematic diagram of a borehole with U-tubes in vertical GHEs is illustrated in Fig.1.*Corresponding author.Tel.:+86-531-6401003;fax:+86-531-6952404.E-mail address:fangzh@ (Z.Fang).0017-9310/$-see front matter Ó2003Elsevier Ltd.All rights reserved.doi:10.1016/S0017-9310(03)00270-9International Journal of Heat and Mass Transfer 46(2003)4467–4481/locate/ijhmtDespite all the advantages of the GCHP system,commercial growth of the technology has been hindered by higher capital cost of the system,of which a signiﬁcant portion is attributed to GHE.In consequence,the borehole thermal resistance is critical for the economical competitiveness of GCHP systems in the heating and air-conditioning market.It is evident that the double U-tube conﬁguration provides more heat transfer area between the ﬂuid and the ground than the single U-tube GHE does,and will reduce the borehole thermal resistance.On the other hand,however,it may require more pipes and consume more pumping power in operation for a certain demand.Due to complexity of the analysis few studies on comparison among the diﬀerent GHE conﬁgurations have ever reported in literature so far.Thus,it remains a task for scholars and engineers to assess performances and costs of the diﬀerent GHE conﬁgurations by means of analyses and practical observations.2.Background of borehole heat transfer modelingHeat transfer between a GHE and its surrounding soil/rock is diﬃcult to model for the purpose of sizing the ex-changer or energy analysis of the system.Besides the structural and geometrical conﬁguration of the exchanger a lot of factors inﬂuence the exchanger performance,such as the ground temperature distribution,soil moisture content andits 4468H.Zeng et al./International Journal of Heat and Mass Transfer 46(2003)4467–4481thermal properties,groundwater movement and possible freezing and thawing in soil.Thus,it is crucial to work out appropriate and validated tools,by which the thermal behavior of GCHP systems can be assessed and then,optimized in technical and economical aspects.In the GHEs the heat carrierﬂuidﬂows along the borehole in one channel down to the bottom of the borehole and back upward in another channel.In cooling mode,for instance,the warmﬂuid induces conductive heatﬂow in the surrounding cooler soil.The borehole may be conceived as a hot rod,from which heatﬂows to the surrounding ground.A fundamental task for application of the GCHP technology is to grasp the heat conduction process of a single borehole in the GHE.Heat transfer in aﬁeld with multiple boreholes may be analyzed on this basis by means of the superimposition principle.The design goal is to control the temperature rise of the ground and the circulatingﬂuid within acceptable limits over the life of the system.Involving a time span of months or even years,the heat transfer process in the GHE is rather complicated,and should be treated,on the whole,as a transient one.Because of all the complications of this problem and its long time scale,the heat transfer process may usually be analyzed in two separated regions.One is the solid soil/rock outside the borehole,where the heat conduction has to be treated as a transient process.Since the borehole depth is much larger than its diameter,this process is often formulated by the one-dimensional line-source or cylindrical-source theory[4].A two-dimensional model of theﬁnite line-source[5]has also been presented by the authors to consider the axial heatﬂow in the ground for longer durations.Variation in load and on-oﬀcycling of the GHE can be considered by superim-position of a series of heating pulses[6].The temperature on the borehole wall can then be determined for any instant on speciﬁed operational conditions.Another sector isolated for analysis is the region inside the borehole,including the backﬁlling,the U-tubes and the circulatingﬂuid inside the pipes.The main objective of this analysis is to determine the entering and leaving tem-peratures of the circulatingﬂuid in the exchanger according to the borehole wall temperature and its heatﬂow. Compared with the inﬁnite ground outside it,both the dimensional scale and thermal mass of the borehole are much smaller.Moreover,the temperature variation inside the borehole is usually slow and minor.Thus,it is a common practice that the heat transfer in this region is approximated as a steady-state process.Such simpliﬁcation has been proved appropriate and convenient for most engineering practices except for analysis dealing with dynamic responses within a few hours[7].The borehole thermal resistance is determined by a number of parameters,including the composition andﬂow rate of the circulatingﬂuid,borehole diameter,grout and U-tube material as well as arrangement ofﬂow channels.A few models of varying complexity have been established to describe the heat transfer in the GHE boreholes. Models for practical engineering designs are often oversimpliﬁed in dealing with the complicated geometry inside the boreholes.A one-dimensional model[1]has been recommended,conceiving the legs of the U-tubes as a single ‘‘equivalent pipe’’inside the borehole,which leads to a simple expressionR b¼1b lnr bﬃﬃﬃﬃNpr p!þR pð1ÞAnother eﬀort to describe the borehole resistance has used the concept of the shape factor of conduction and re-sulted in an expressionR b¼k b b0r br p b1"#À1ð2Þwhere parameters b0and b1were obtained by means of curveﬁtting of eﬀective borehole resistance determined in laboratory measurements[8].In this approach only a limited number of inﬂuencing factors were considered,and all the pipes were assumed to be of identical temperature as a precondition.By a diﬀerent approach Hellstrom[9]has derived two-dimensional analytical solutions of the borehole thermal resistances in the cross-section perpendicular to the borehole with arbitrary numbers of pipes,which are superior to empirical expressions.Also on assumptions of identical temperatures and heatﬂuxes of all the pipes in it the borehole resistance has been worked out for symmetrically disposed double U-tubes asR b¼12p k blnr br p"À34þDr b2À14ln1ÀD8r8bÀ12lnﬃﬃﬃ2pDr p!À14ln2Dr p#þR p4ð3ÞExchanging heat with the surrounding ground,theﬂuid circulating through diﬀerent legs of the U-tubes is,in fact,of varying temperatures.As a result,thermal interference,or thermal‘‘short-circuiting’’,among U-tube legs is inevitable, which degrades the eﬀective heat transfer in the GHEs.With the assumption of identical temperature of all the pipes,it is impossible for all the models mentioned above to reveal impact of this thermal interference on GHE performances.On the other hand,Mei and Baxter[10]considered the two-dimensional model of the radial and longitudinal heat transfer,which was solved with aﬁnite diﬀerence scheme.Recently,Yavuzturk et al.[7]employed the two-dimensional ﬁnite element method to analyze the heat conduction in the plane perpendicular to the borehole for short time step responses.Requiring numerical solutions,these models are of limited practical value for use by designers of GCHP systems although they may result in more exact solutions for research and parametric analysis of GHEs.Taking into account theﬂuid temperature variation along the borehole depth and its axial convection,the authors have developed a quasi-three-dimensional model to determine analytically the thermal resistance inside boreholes with a single U-tube under arbitrary disposal[11].The new model reveals the thermal interference between the U-tube pipes, and formulates the borehole heat transfer process on a solid analytical basis.This paper focuses further on discussing heat transfer inside a borehole with double U-tubes.Analytical expressions of the thermal resistance of the double U-tube boreholes are to be derived,and then,performance can be compared between single and double U-tube boreholes.3.Formulation of heatﬂow balanceAs an extension of the work of Eskilson[12]and Hellstrom[9],following analysis focuses on heat transfer inside the borehole,which serves as a part of the entire thermal process in the GHEs.To keep the problem analytically man-ageable some simpliﬁcations are assumed.They are(1)The heat capacity of the materials inside the borehole is neglected.(2)The heat conduction in the axial direction is negligible,and only the conductive heatﬂow among the borehole walland the pipes in the transverse cross-section is counted.(3)The borehole wall temperature,T b,is constant along its depth,but may vary with time.(4)The ground outside the borehole and grout in it are homogeneous,and all the thermal properties involved are in-dependent of temperature.Number the pipes in the borehole clockwise as shown in Fig.2.If the temperature on the borehole wall,T b,is taken as the reference of the temperature excess,the temperature excess distribution inside the borehole and theﬂuid tem-perature in the pipes may be expressed as the sum of four separate temperature excesses caused by the heatﬂuxes per unit length,q1,q2,q3and q4from the four legs of the U-tubes.Thus,the following expressions may be obtained T f1ÀT b¼R11q1þR12q2þR13q3þR14q4T f2ÀT b¼R21q1þR22q2þR23q3þR24q4 T f3ÀT b¼R31q1þR32q2þR33q3þR34q4 T f4ÀT b¼R41q1þR42q2þR43q3þR44q4ð4Þ4470H.Zeng et al./International Journal of Heat and Mass Transfer46(2003)4467–4481where R ii (i ¼1;2;3;4)is the thermal resistance between the circulating ﬂuid in a certain U-tube leg and the borehole wall,and R ij (i ;j ¼1;2;3;4)the resistance between two individual pipes.It is most likely that in engineering practice the U-tube legs are disposed in the borehole symmetrically as shown in Fig.2.In this case one gets R ij ¼R ji ,R ii ¼R jj (i ;j ¼1;2;3;4)and R 14¼R 12and so on.Hellstrom [9]analyzed the steady-state conduction problem in the borehole cross-section in detail with the line-source and multipole approximations.The line-source assumption has resulted in the following solution R 11¼12p k b ln r b r p Àk b Àk k b þk ln r 2b ÀD 2r 2b þR p R 12¼12p k b ln r b ﬃﬃﬃ2p D Àk b Àk 2ðk b þk Þln r 4bþD 4r 4b R 13¼12p k b ln r b 2D Àk b Àk k b þk ln r 2bþD 2r 2bð5Þwhere k denotes the thermal conductivity of soil/rock around the borehole,while k b the conductivity of grouting material,and R p the heat transfer resistance from the ﬂuid inside the U-tubes to the pipe outer surface.A linear transformation of Eq.(4)leads toq 1¼T f1ÀT b R 1þT f1ÀT f2R 12þT f1ÀT f3R 13þT f1ÀT f4R 12q 2¼T f2ÀT f1R D 12þT f2ÀT b R D 1þT f2ÀT f3R D 12þT f2ÀT f4R D 13q 3¼T f3ÀT f1R D 13þT f3ÀT f2R D 12þT f3ÀT b R D 1þT f3ÀT f4R D 12q 4¼T f4ÀT f1R D 12þT f4ÀT f2R D 13þT f4ÀT f3R D 12þT f4ÀT b R D 1ð6ÞwhereR D 1¼R 11þR 13þ2R 12R D12¼R 211þR 213þ2R 11R 13À4R 212R 12R D 13¼ðR 11ÀR 13ÞðR 211þR 213þ2R 11R 13À4R 212ÞR 213þR 11R 13À2R 212Ignoring the convective transfer of the ﬂuid in the axial direction,the two-dimensional approach of the problem has to assume that the temperatures and heat ﬂuxes of the circulating ﬂuid in the individual pipes are identical.This simpliﬁcation leads to Eq.(3)for the symmetric double U-tube boreholes.It is impossible for this model to reveal the impact of thermal short-circuiting among the U-tube legs on the performance of the GHE.Our study on the single U-tube borehole has shown that this simpliﬁcation may result in considerable distortion of the borehole resistance [13].So,the ﬂuid temperature variation along the channels ought be taken into consideration.In order to keep the model concise and analytically manageable,the conductive heat ﬂow in the grout and ground in the axial direction,however,isstill neglected.We refer to this model as quasi-three-dimensional.In this model the convective heatﬂow along theﬂuid channels is balanced by the conductive heatﬂows among theﬂuid channels and borehole wall.According to Eq.(6)the heat equilibrium of theﬂuid in individual pipes can be formulated asÆMc d T f1ðzÞd z¼T f1ðzÞÀT bR1þT f1ðzÞÀT f2ðzÞR12þT f1ðzÞÀT f3ðzÞR13þT f1ðzÞÀT f4ðzÞR12ÆMc d T f2ðzÞd z¼T f2ðzÞÀT f1ðzÞR D12þT f2ðzÞÀT bR D1þT f2ðzÞÀT f3ðzÞR D12þT f2ðzÞÀT f4ðzÞR D13ÆMc d T f3ðzÞd z¼T f3ðzÞÀT f1ðzÞR D13þT f3ðzÞÀT f2ðzÞR D12þT f3ðzÞÀT bR D1þT f3ðzÞÀT f4ðzÞR D12ÆMc d T f4ðzÞd z¼T f4ðzÞÀT f1ðzÞR D12þT f4ðzÞÀT f2ðzÞR D13þT f4ðzÞÀT f3ðzÞR D12þT f4ðzÞÀT bR D1ð7ÞHere the sign±on the left side of the equations depends on the condition whether theﬂuidﬂows in the same direction as the z-coordinate,which is designated to be downward.When theﬂuid moves downwards along the channel the sign is positive,and vice versa.Diﬀerentﬂow circuit arrangements will lead to diﬀerentﬂow directions in the channels.This formulation indicates that theﬂuid temperature proﬁles along the channels satisfy a set of coupled linear diﬀerential bined with certain connecting conditions from theﬂow circuit arrangement,the energy equilibrium equation can be solved by means of Laplace transforms.Then,the temperature distributions of circulatingﬂuid along the channels can be analytically worked out,and the thermal resistance inside the borehole can be determined more adequately.In following discussions some dimensionless variables are deﬁned to make expressions more concise and generalized. They areH1¼T f1ðzÞÀT bT0fÀT b;H2¼T f2ðzÞÀT bT0fÀT b;H3¼T f3ðzÞÀT bT0fÀT b;H4¼T f4ðzÞÀT bT0fÀT bRÃ1¼McR D1H;RÃ12¼McR D12H;RÃ13¼McR D13Hand Z¼zH4.Fluid temperature proﬁles along the borehole depthTheﬂuid temperature proﬁles in theﬂow channels,and,then,the borehole resistance are aﬀected by borehole conﬁguration.As mentioned above,there are single U-tube and double U-tube boreholes.The latter can be arranged in series or parallelﬂow circuits,and each of them includes a few connecting patterns.All these options have to be an-alyzed separately.4.1.Single U-tube ground heat exchangerTheﬂuid temperature proﬁles in the single U-tube borehole with arbitrary leg disposal were presented in our pre-vious paper[11].The solution is introduced here brieﬂy for comparison with those of the double U-tube boreholes.In this case there are only two pipes in the borehole,i.e.those numbered1and3,or2and4,in Fig.2.Designate theﬂuid temperature of downward and upwardﬂows as T d and T u,and the dimensionless energy equilibrium equation can be expressed aÀd H dd Z¼H dS1þH dÀH uS12d H u d Z ¼H uÀH dS12þH uS19>=>;06Z61ð8ÞwhereH d¼T dðzÞÀT bT0fÀT b;H u¼T uðzÞÀT bT0fÀT band the two-dimensionless thermal resistances,i.e.S1and S12can be worked out as4472H.Zeng et al./International Journal of Heat and Mass Transfer46(2003)4467–4481S1¼McHðR11þR13ÞS12¼McÁR211ÀR21313ð9ÞWith the coupling conditions,H dð1Þ¼H uð1Þand H dð0Þ¼1,the solution of Eq.(8)can be written asH dðZÞ¼chðb ZÞÀ1b S12S12S1þ1Àb S1ÁchðbÞÀ1b S1ÁchðbÞþ1shðb ZÞH uðZÞ¼b S1ÁchðbÞÀ11chðb ZÞÀ1121ÀS121þ1b S1ÁchðbÞÀ11shðb ZÞð10Þwhereb¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1S21þ2S1S12 sIn consequence,the outletﬂuid temperature for single U-tube GHE isH00¼b S1ÁchðbÞÀ1b S1ÁchðbÞþ1ð11Þ4.2.Double U-tubes in parallel circuitFor the two U-tubes in the borehole connected in parallel circuit,diﬀerent combinations of circuit arrangement come down to two options that make diﬀerence to its heat transfer.They may be represented by notations of(1-3,2-4) and(1-2,3-4).Here1-3denotes that theﬂuidﬂows through pipes1and3as indicated in Fig.2,and also through pipes 2and4in parallel.Ignoring diﬀerence in massﬂow rates in the two U-tubes,and assuming symmetric disposal of the pipes,the temperature proﬁles of theﬂuidﬂowing in the same direction may be regarded as identical.Applying these conditions to Eq.(7),studies show that the energy equilibrium equations for both(1-3,2-4)and(1-2,3-4)parallel conﬁgurations take the same form as Eq.(8)with the only diﬀerence in the expression of the dimensionless thermal resistance S1and S2.Thus,the solutions for the double U-tubes in parallel circuit must have the same form as Eq.(10).4.2.1.(1-3,2-4)conﬁguration in parallelIn this case we have T f1ðzÞ¼T f2ðzÞ¼T dðzÞand T f3ðzÞ¼T f4ðzÞ¼T uðzÞfor the symmetric conﬁguration.Then,(7) reduces to the following dimensionless expressionÀd H dd Z¼H dR1þH dÀH uRÃ12RÃ13RÃ12þRÃ13d H u d Z ¼H uÀH dRÃ12RÃ13RÃ12þRÃ13þH uR19>>>>>>>>=>>>>>>>>;06Z61ð12Þwith coupling conditions H dð1Þ¼H uð1Þand H dð0Þ¼1.Comparing Eq.(12)with Eq.(8),one comes to the conclusion that Eq.(10)represents also the temperature proﬁles of the(1-3,2-4)parallel conﬁguration as long as the dimensionless variables S1and S12in Eq.(10)are deﬁned otherwise as follows:S1¼RÃ1S12¼RÃ12RÃ13RÃ12þRÃ13ð13ÞThe borehole with double U-tubes in(1-2,4-3)parallel conﬁguration is of the same nature as the one in this(1-3,2-4) conﬁguration.H.Zeng et al./International Journal of Heat and Mass Transfer46(2003)4467–448144734.2.2.(1-2,3-4)conﬁguration in parallelSimilarly,we have T f1ðz Þ¼T f3ðz Þ¼T d ðz Þand T f2ðz Þ¼T f4ðz Þ¼T u ðz Þin this case.Then,Eq.(7)is reduced to the following expression Àd H d d Z ¼H d R Ã1þ2H d ÀH u R Ã12d H u ¼2H u ÀH d 12þH u 19>>=>>;06Z 61ð14Þwith the same coupling conditions H d ð1Þ¼H u ð1Þand H d ð0Þ¼1.The temperature proﬁles of the (1-2,3-4)parallel conﬁguration take the same expression as Eq.(10)while the di-mensionless variables S 1and S 12are deﬁned otherwise as follows:S 1¼R Ã1S 12¼R Ã122ð15Þ4.3.Double U-tubes in series circuitWhen the ﬂuid circulates through the four legs of the double U-tubes in a series circuit,there are quite a few possible layouts.Only three of them,however,bear diﬀerent impact on the performance of GHE on the assumption of sym-metrical disposal of the pipes.The three representative layouts in series are marked as 1-3-2-4,1-2-3-4and 1-2-4-3,where the sequence indicates ﬂow succession of the pipes as shown in Fig.2.4.3.1.1-3-2-4conﬁguration in seriesIn this case the energy equilibrium equation can be normalized as Àd H 1ðZ Þd Z ¼H 1ðZ ÞR 1þH 1ðZ ÞÀH 2ðZ ÞR 12þH 1ðZ ÞÀH 3ðZ ÞR 13þH 1ðZ ÞÀH 4ðZ ÞR 12Àd H 2ðZ Þd Z ¼H 2ðZ ÞÀH 1ðZ ÞR Ã12þH 2ðZ ÞR Ã1þH 2ðZ ÞÀH 3ðZ ÞR Ã12þH 2ðZ ÞÀH 4ðZ ÞR Ã13d H 3ðZ Þd Z ¼H 3ðZ ÞÀH 1ðZ ÞR 13þH 3ðZ ÞÀH 2ðZ ÞR 12þH 3ðZ ÞR 1þH 3ðZ ÞÀH 4ðZ ÞR 12d H 4ðZ Þd Z ¼H 4ðZ ÞÀH 1ðZ ÞR Ã12þH 4ðZ ÞÀH 2ðZ ÞR Ã13þH 4ðZ ÞÀH 3ðZ ÞR Ã12þH 4ðZ ÞR Ã19>>>>>>>>>>>>=>>>>>>>>>>>>;06Z 61ð16Þwith its dimensionless coupling conditions H 1ð0Þ¼1,H 1ð1Þ¼H 3ð1Þ,H 3ð0Þ¼H 2ð0Þand H 2ð1Þ¼H 4ð1Þ.Eq.(16)represents a set of four linear diﬀerential equations,which can be solved with Laplace transformation in a straightforward way despite intricacy and tediousness of its derivation,which can be found elsewhere [14].The tem-perature proﬁles in individual pipes along the borehole depth can be expressed in the following formH 1ðZ Þ¼E 11ðZ ÞH 1ð0ÞþE 12ðZ ÞH 2ð0ÞþE 13ðZ ÞH 3ð0ÞþE 14ðZ ÞH 4ð0ÞH 2ðZ Þ¼E 12ðZ ÞH 1ð0ÞþE 11ðZ ÞH 2ð0ÞþE 14ðZ ÞH 3ð0ÞþE 13ðZ ÞH 4ð0ÞH 3ðZ Þ¼ÀE 13ðZ ÞH 1ð0ÞÀE 14ðZ ÞH 2ð0ÞþE 33ðZ ÞH 3ð0ÞþE 34ðZ ÞH 4ð0ÞH 4ðZ Þ¼ÀE 14ðZ ÞH 1ð0ÞÀE 13ðZ ÞH 2ð0ÞþE 34ðZ ÞH 3ð0ÞþE 33ðZ ÞH 4ð0Þð17Þwhere E 11ðZ Þ,E 12ðZ Þ,E 13ðZ Þ,E 14ðZ Þ,E 33ðZ Þand E 34ðZ Þmay be referred to as distribution functions.The detailed ex-pressions of these functions are listed in Appendix A.Based on Eq.(17),the outlet ﬂuid temperature in the case of 1-3-2-4series conﬁguration can be ﬁgured out asH 001-3-2-4¼E 12ð1ÞþE 14ð1ÞE 13ð1ÞþE 11ð1ÞÀE 34ð1ÞþE 14ð1ÞÀE 11ð1ÞþE 13ð1ÞE 14ð1ÞþE 12ð1ÞÀE 33ð1ÞþE 13ð1Þ1434E 14ð1ÞþE 12ð1ÞÀE 33ð1ÞþE 13ð1Þþ3313E 13ð1ÞþE 11ð1ÞÀE 34ð1ÞþE 14ð1Þð18Þ4474H.Zeng et al./International Journal of Heat and Mass Transfer 46(2003)4467–44814.3.2.1-2-3-4conﬁguration in seriesThe energy equilibrium equation in the case of1-2-3-4series conﬁguration can be obtained from Eq.(7)asÀd H1d Z¼H1RÃ1þH1ÀH2RÃ12þH1ÀH3RÃ13þH1ÀH4RÃ12d H2 d Z ¼H2ÀH1RÃ12þH2RÃ1þH2ÀH3RÃ12þH2ÀH4RÃ13Àd H3d Z¼H3ÀH1RÃ13þH3ÀH2RÃ12þH3RÃ1þH3ÀH4RÃ12d H4 d Z ¼H4ÀH1RÃ12þH4ÀH2RÃ13þH4ÀH3RÃ12þH4RÃ19>>>>>>>>>>=>>>>>>>>>>;06Z61ð19Þwith coupling conditions H1ð0Þ¼1,H1ð1Þ¼H2ð1Þ,H2ð0Þ¼H3ð0Þand H3ð1Þ¼H4ð1Þ.In the same way the temperature proﬁles of this circuit conﬁguration have been worked out,and their dimensionless expressions can be written asH1ðZÞ¼F11ðZÞH1ð0ÞþF12ðZÞH2ð0ÞþF13ðZÞH3ð0ÞþF12ðZÞH4ð0ÞH2ðZÞ¼ÀF12ðZÞH1ð0ÞþF22ðZÞH2ð0ÞÀF12ðZÞH3ð0ÞþF24ðZÞH4ð0ÞH3ðZÞ¼F13ðZÞH1ð0ÞþF12ðZÞH2ð0ÞþF11ðZÞH3ð0ÞþF12ðZÞH4ð0ÞH4ðZÞ¼ÀF12ðZÞH1ð0ÞþF24ðZÞH2ð0ÞÀF12ðZÞH3ð0ÞþF22ðZÞH4ð0Þð20ÞThe distribution functions F11ðZÞ,F12ðZÞ,F13ðZÞ,F22ðZÞand F24ðZÞcan be found in Appendix B.According to Eq.(20) the outletﬂuid temperature in the case of1-2-3-4series conﬁguration can be obtained asH001-2-3-4¼F13ð1ÞþF12ð1Þ241211ÀF11ð1ÞþF12ð1Þ221213F22ð1ÞÀF12ð1ÞF24ð1ÞÀ2F12ð1ÞÀF11ð1ÞÀF24ð1ÞÀF12ð1ÞF22ð1ÞÀ2F12ð1ÞÀF13ð1Þð21Þ4.3.3.1-2-4-3conﬁguration in seriesThe dimensionless energy equilibrium equation for this conﬁguration can be obtained asÀd H1¼H11þH1ÀH212þH1ÀH313þH1ÀH412d H2¼H2ÀH112þH21þH2ÀH312þH2ÀH413d H3¼H3ÀH113þH3ÀH212þH31þH3ÀH412Àd H4d Z¼H4ÀH1RÃ12þH4ÀH2RÃ13þH4ÀH3RÃ12þH4RÃ19>>>>>>>>>>=>>>>>>>>>>;06Z61ð22Þwith coupling condition as H1ð0Þ¼1,H1ð1Þ¼H2ð1Þ,H2ð0Þ¼H4ð0Þand H4ð1Þ¼H3ð1Þ.The temperature proﬁles of the1-2-4-3conﬁguration have also been obtained.They areH1ðZÞ¼G11ðZÞH1ð0ÞþG12ðZÞH2ð0ÞþG13ðZÞH3ð0ÞþG14ðZÞH4ð0ÞH2ðZÞ¼ÀG12ðZÞH1ð0ÞþG22ðZÞH2ð0ÞþG23ðZÞH3ð0ÞÀG13ðZÞH4ð0ÞH3ðZÞ¼ÀG13ðZÞH1ð0ÞþG23ðZÞH2ð0ÞþG22ðZÞH3ð0ÞÀG12ðZÞH4ð0ÞH4ðZÞ¼G14ðZÞH1ð0ÞþG13ðZÞH2ð0ÞþG12ðZÞH3ð0ÞþG11ðZÞH4ð0Þð23ÞThe distribution functions G11ðZÞ,G12ðZÞ,G13ðZÞ,G14ðZÞ,G22ðZÞand G23ðZÞin this case are presented in Appendix C. Based on Eq.(23),the outletﬂuid temperature in the case of1-2-4-3series conﬁguration is obtained asH001À2À4À3¼G14ð1ÞþG13ð1ÞG23ð1ÞÀG12ð1ÞÀG13ð1ÞÀG11ð1ÞþG12ð1ÞþG11ð1ÞG12ð1ÞþG14ð1ÞÀG22ð1ÞþG13ð1Þ221223121311À132312142213ð24ÞH.Zeng et al./International Journal of Heat and Mass Transfer46(2003)4467–44814475。

好奇探索星之源的英语作文

Curiosity is a rover designed by NASA to explore the Gale Crater on Mars,which is believed to be the source of a vast lake that once existed on the planet.This mission aims to investigate the planets climate and geology,as well as search for signs of ancient life.Launched in November2011,Curiosity landed on Mars in August2012.It is equipped with a variety of scientific instruments to study the Martian surface and atmosphere.One of its key instruments is the Mars Hand Lens Imager MAHLI,which captures highresolution images of the rovers surroundings.The rover has discovered evidence of an ancient riverbed and lakebed,suggesting that Mars once had liquid water.This is significant because water is considered a key ingredient for life.Curiosity has also found organic molecules,which are the building blocks of life,in Martian rocks.Curiosity has also measured the Martian atmosphere and found it to be composed mainly of carbon dioxide,with traces of other gases.The rover has also detected methane,a gas that can be produced by geological or biological processes.In addition to its scientific mission,Curiosity has also captured stunning images of the Martian landscape.The rover has sent back panoramic views of the Gale Crater,showing its rugged terrain and the towering Mount Sharp in the distance.Despite facing technical challenges and harsh conditions on Mars,Curiosity has exceeded its expected lifespan and continues to explore the Red Planet.It has provided valuable insights into Mars past and present,and has inspired further exploration of our neighboring planet.In conclusion,the Curiosity rovers mission to explore the source of Mars ancient lake has been a remarkable success.It has expanded our understanding of the planets history and potential for life,and has paved the way for future Mars missions.。

New flow boilling heat transfer model and flow pattern map for carbon dioxide evaporating

New ﬂow boiling heat transfer model and ﬂow pattern map for carbon dioxide evaporating inside horizontal tubesLixin Chenga,b,Gherhardt Ribatski a ,Leszek Wojtan a ,John R.Thomea,*aLaboratory of Heat and Mass Transfer (LTCM),Faculty of Engineering Science (STI),E´cole Polytechnique Fe ´de ´rale de Lausanne (EPFL),CH-1015Lausanne,SwitzerlandbInstitute of Process Engineering,University of Hannover,Callinstraße 36,30167Hannover,GermanyReceived 8June 2005;received in revised form 24March 2006Available online 5June 2006AbstractA new ﬂow boiling heat transfer model and a new ﬂow pattern map based on the ﬂow boiling heat transfer mechanisms for horizontal tubes have been developed speciﬁcally for CO 2.Firstly,a nucleate boiling heat transfer correlation incorporating the eﬀects of reduced pressure and heat ﬂux at low vapor qualities has been proposed for CO 2.Secondly,a nucleate boiling heat transfer suppression factor correlation incorporating liquid ﬁlm thickness and tube diameters has been proposed based on the ﬂow boiling heat transfer mechanisms so as to capture the trends in the ﬂow boiling heat transfer data.In addition,a dryout inception correlation has been developed.Accord-ingly,the heat transfer correlation in the dryout region has been modiﬁed.In the new ﬂow pattern map,an intermittent ﬂow to annular ﬂow transition criterion and an annular ﬂow to dryout region transition criterion have been proposed based on the changes in the ﬂow boiling heat transfer trends.The ﬂow boiling heat transfer model predicts 75.5%of all the CO 2database within ±30%.The ﬂow boiling heat transfer model and the ﬂow pattern map are applicable to a wide range of conditions:tube diameters (equivalent diameters for non-circular channels)from 0.8to 10mm,mass velocities from 170to 570kg/m 2s,heat ﬂuxes from 5to 32kW/m 2and saturation temper-atures from À28to 25°C (reduced pressures from 0.21to 0.87).Ó2006Elsevier Ltd.All rights reserved.Keywords:Model;Flow boiling;Heat transfer;Flow map;Flow patterns;Flow regimes;CO 21.IntroductionCarbon dioxide (CO 2or R744)has been receiving renewed interest as an eﬃcient and environmentally safe refrigerant in a number of applications,including mobile air conditioning,heat pump systems and hot water heat pumps in recent years [1–4].Due to its low critical temper-ature (T crit =31.1°C)and high critical pressure (p crit =73.8bar),CO 2is utilized at much higher operating pres-sures compared to other conventional refrigerants.The higher operating pressures result in high vapor densities,very low surface tensions,high vapor viscosities and lowliquid viscosities and thus yield ﬂow boiling heat transfer and two-phase ﬂow characteristics that are quite diﬀerent from those of conventional refrigerants.High pressures and low surface tensions have major eﬀects on nucleate boiling heat transfer characteristics and previous experi-mental studies have suggested a clear dominance of nucle-ate boiling heat transfer even at very high mass velocity.Therefore,CO 2has higher heat transfer coeﬃcients than those of conventional refrigerants at the same saturation temperature and the available heat transfer correlations generally underpredict the experimental data of CO 2.In addition,previous experimental studies have demonstrated that dryout may occur at moderate vapor quality in CO 2ﬂow boiling,particularly at high mass velocity and high temperature conditions.Signiﬁcant deviations for the ﬂow patterns of CO 2compared with the ﬂow pattern maps that0017-9310/$-see front matter Ó2006Elsevier Ltd.All rights reserved.doi:10.1016/j.ijheatmasstransfer.2006.04.003*Corresponding author.Tel.:+41216935981;fax:+41216935960.E-mail addresses:lixincheng@ (L.Cheng),john.thome @epﬂ.ch (J.R.Thome)./locate/ijhmtInternational Journal of Heat and Mass Transfer 49(2006)4082–4094were developed for otherﬂuids at lower pressures have been observed as well.In order to design evaporators for these thermal systems eﬀectively,it is very important to understand and predict theﬂow boiling heat transfer and two-phaseﬂow charac-teristics of CO2inside horizontal tubes.A lot of studies onﬂow boiling and two-phaseﬂow of CO2have been car-ried out in recent years to explore the fundamental aspects with respect to the characteristics of heat transfer and two-phaseﬂow of CO2.Thome and Ribatski[5]have recently given a review ofﬂow boiling heat transfer and two-phase ﬂow of CO2in the literature.The review addresses the extensive experimental studies on heat transfer and two-phaseﬂow in macro-channels[6–15]and micro-channels [12,16–25],macro-and micro-scale heat transfer prediction methods for CO2[12–14,26]and comparisons of these methods to the experimental database.In addition,the study of CO2two-phaseﬂow patterns[13,14,22,23,25]are summarized and compared to some of the leadingﬂow pat-tern maps in their review.Taking into account the lack of a well-established criterion to identify macro-and micro-scale channels,Thome and Ribatski[5]arbitrary adopted a hydraulic diameter of3mm to segregate the databases and heat transfer models.They found that the prediction methods by[12–14]failed to predict most of macro-scale experimental data while the method proposed by Thome and El Hajal[26]for CO2predicted reasonably well the macro-scale database of CO2at low vapor qualities.They also found that small diameter data were poorly predicted by either micro-scale or macro-scale predictive methods. Based on the results for macro-scale diameters,Thome and Ribatski suggested that the method of Thome and El Hajal should be further updated to include CO2eﬀects on the annular to mistﬂow in order to more accurately pre-dict heat transfer coeﬃcients at moderate/high vapor qual-ities.Based on this recent and comprehensive review that is recommended as a reference study,a section describing the previous studies was judged as unnecessary in this paper and the literature concerning CO2studies is presented in this text just when required to the development of the heat transfer model.In the present study,the objectives are to develop a new general heat transfer prediction method and a newﬂow pattern map especially for CO2,which covers channelNomenclatureCo Conﬁnement number[r/g(q LÀq V)D2]1/2c p speciﬁc heat at constant pressure,J/kg KD internal tube diameter,mD eq equivalent diameter,mD h hydraulic diameter,mD th threshold diameter,mFr Froude number[G2/(q2gD)]G total vapor and liquid two-phase mass velocity,kg/m2sg gravitational acceleration,9.81m/s2h heat transfer coeﬃcient,W/m2Kk thermal conductivity,W/m KM molecular weight,kg/kmolPr Prandtl number[c p l/k]p pressure,Pap r reduced pressure[p/p crit]q heatﬂux,W/m2Re H homogeneous Reynolds number[(GD/l V) [x+(1Àx)(q V/q L)]]Re V vapor phase Reynolds number[GxD/(l V e)]S nucleate boiling suppression factorT temperature,°CWe Weber number[G2D/(qr)]x vapor qualityY correction factorGreek symbolsd liquidﬁlm thickness,me cross-sectional vapor void fraction e average deviation,%j e j mean deviation,%l dynamic viscosity,N s/m2h angle of tube perimeter,radq density,kg/m3r surface tension,N/m;standard deviation,% Subscriptscb convection boilingcrit criticalde dryout completiondi dryout inceptiondry drydryout dryout regionexp experimentalIA intermittentﬂow to annularﬂowL liquidmist mistﬂownb nucleate boilingpred predictedsat saturationstrat stratiﬁedﬂowtp two-phaseﬂowV vaporwavy wavyﬂowwet on the wet perimeterL.Cheng et al./International Journal of Heat and Mass Transfer49(2006)4082–40944083diameters found in most of CO2ﬂow boiling applications. Experimental conditions of studies onﬂow boiling of car-bon dioxide covered by this study are summarized in Table 1.It includes experimental results obtained for mass veloc-ities from80to570kg/m2s,heatﬂuxes from5to32.06kW/ m2,saturation temperatures fromÀ28to25°C(the corre-sponding reduced pressures are from0.21to0.87)and tube diameters from0.8to10.06mm.All those experiments were conducted in horizontal tubes.Therefore,at this point,one very important issue must be clariﬁed about the distinction between macro-and micro-channelsﬁrst.Although a uni-versal agreement to distinguish between macro-and micro-channels is not as yet clearly established,the present study covers both macro-and micro-(mini)-channels according to various criteria[27,28].Based on engineering practice and application areas,Kandlikar[27]proposed using the following threshold diameters:conventional chan-nels,D h>3mm;minichannels,D h between200l m and 3mm;and micro-channels,D h between10l m and 200l m.Based on the conﬁnement of bubble departure sizes in channels,Kew and Cornwell[28]proposed an approxi-mate physical criterion for macro-to micro-channel thresh-old diameter as follows:D th¼4rgðqLÀq VÞ1=2ð1ÞWhen hydraulic diameters are larger than the threshold diameter,the channels are deﬁned as macro-scale channels. When hydraulic diameters are smaller than the threshold diameter,the channels are deﬁned as micro-scale channels. The test conditions of the present selected database(see Table1)are compared to these two criteria in Fig.1. Unlike theﬁxed values for the threshold diameters deﬁned by Kandlikar,the threshold diameters based on Conﬁne-ment number decrease with increasing reduced pressure and they vary from2.3mm at low reduced pressures toTable1The database ofﬂow boiling heat transfer of CO2Data source Channel conﬁgurationand material D h(mm)T sat(°C)p r G(kg/m2s)q(kW/m2)Data points HeatingmethodKnudsen and Jensen[7]Single circular tube,stainless steel 10.06À280.21808,1316Heated bycondensingR22vaporYun et al.[9]Single circular tube,stainless steel 650.54170,240,34010,15,2053Electricalheating 100.61Yoon et al.[14]Single circular tube,stainless steel 7.3500.4731812.5,16.4,18.6127Electricalheating50.54100.61150.69200.78Koyama et al.[16]Single circular tube,stainless steel 1.80.30.47250,26032.0636Electricalheating 100.6110.90.62Pettersen[20]Multi-channel with25circular channels,aluminium 0.800.47190,280,380,5705,10,15,2046Heated bywater 100.61200.78250.87Yun et al.[21]a Multi-channels withrectangle channels 1.14(2.7)50.54200,300,40010,15,2056Electricalheating 1.53(3.08)1.54(3.21)a Material is not mentioned in the paper and the values in the parentheses are equivalent diameters.4084L.Cheng et al./International Journal of Heat and Mass Transfer49(2006)4082–40940.7mm at high reduced pressures.According to Kandli-kar’s criteria,the test conditions include both conventional and mini-channels but not micro-channels.According to the criteria based on Conﬁnement number,Co,the test conditions mostly include macro-channels with a few micro-channels.Here,it is important to highlight the fact that the macro-to-micro transition should be identiﬁed by distinction in the heat transfer,pressure drop andﬂow pat-terns behaviors instead ofﬁxed tube diameter ranges deﬁned according to the applications.Therefore,the fact that,according to the available transition criteria,the proposed model covers both macro-and micro-(mini)-channels is perfectly reasonable since a threshold diameter based on the analysis of the heat transfer behavior of the present database was not identiﬁed.In the present study,a new general heat transfer model and a newﬂow pattern map physically related to the heat transfer mechanisms based on a selected database from the literature were developed specially for CO2.As the starting point,the model developed by Wojtan et al. [29,30]which is an updated version of the Kattan–Thome–Favratﬂow pattern map andﬂow boiling heat transfer model[31–33]was used.The new proposed predic-tion method includes new correlations for the nucleate boil-ing heat transfer and the suppression factor based on CO2 experimental data.In addition,a dryout inception vapor quality correlation was proposed for CO2and accordingly the heat transfer correlation in the dryout region was obtained.Based on the heat transfer mechanisms,a new ﬂow patterns map was proposed and thus can physically explain the heat transfer phenomena according to theﬂow regimes deﬁned by the newﬂow map.2.CO2ﬂow boiling heat transfer database and comparisons 2.1.Selection of CO2ﬂow boiling heat transfer dataSix independent experimental studies from diﬀerent lab-oratories have been carefully selected to form the present database forﬂow boiling heat transfer of CO2.They are the experimental data of Knudsen and Jensen[7],Yun et al.[9],Yoon et al.[14],Koyama et al.[16],Pettersen [20]and Yun et al.[21].The detailed test conditions of the database are summarized in Table1.The test channels include single circular channels and multi-channels with circular and rectangle channels at a wide range of test con-ditions,by electrical heating orﬂuid heating.The data were taken from tables where available or by digitizing the heat transfer graphs in these publications to extract the plotted heat transfer coeﬃcients.All together,334heat transfer data points including heat transfer data in the dryout region were obtained.In order to develop a generalﬂow boiling heat transfer prediction model,extensive comparisons of the data avail-able in the literature have been made.However,some of the data available have not been selected due to various reasons.For example,the data of Bredesen et al.[6]for a 7mm inside diameter tube have been excluded because they diﬀer signiﬁcantly from comparable data for6mm and10.06mm inside diameter tubes in two other studies and also because there is a large scatter among their data. Hwang et al.[34]also noted an anomaly in the[6]data at a mass velocity of300kg/m2s when correlating them.Yet, since their tests were run with the same rigor as the other tests,it is not clear where these problems come from. Also,the data of Huai et al.[17]have been excluded because the available correlations overpredict their data as indicated in their study,which contradicts the general conclusion that the available correlations underpredict experimental CO2data.It is unclear why they obtained the opposite trend.In the present study,the physical properties of CO2have been obtained from REFPROP of NIST[35].For non-cir-cular channels,equivalent diameters rather than hydraulic diameters were ing equivalent diameter gives the same mass velocity as in the non-circular channel and thus correctly reﬂects the mean liquid and vapor velocities, something using hydraulic diameter does not.2.2.Analysis of theﬂow boiling heat transfer data in the databaseAlthough some anomalous data have already been excluded as pointed out earlier,the heat transfer data in the database show still some diﬀerent behaviors at similar test conditions.Fig.2(a)shows two opposite heat transfer characteristics with saturation temperature in the studies of Pettersen[20]and Yoon et al.[14].The heat transfer coef-ﬁcients increase with the increasing saturation tempera-tures in the study of Pettersen while they decrease in the study of Yoon et al.The only big diﬀerence between the two studies is the diameters of the test channels as indicated in Fig.2(a).Fig.2(b)shows the comparison of the heat transfer coeﬃcients of Pettersen[20]to those of Koyama et al.[16].The biggest diﬀerence between them is that in Koyama et al.the heatﬂux is32.06kW/m2while in Petter-sen is10kW/m2.The heat transfer coeﬃcients fall oﬀat the vapor quality of about0.7in the study of Pettersen while the heat transfer coeﬃcients increase even at qualities lar-ger than0.7in the study of Koyama et al.It is diﬃcult to explain why the heat transfer coeﬃcients fall oﬀat the lower heatﬂux in one study while they still increase at the higher heatﬂux in the other study.This could be an eﬀect of the heating methods or multi-channel vs.single-channel data.However,these heat transfer data of Koyama et al.at higher vapor qualities seem to be unrea-sonable since they should correspond to the dryout region and their trend contradicts in general with the other results. Another example of anomaly was found in the experimen-tal data of Yun et al.[21].According to their results,a heat transfer coeﬃcients up to80%higher was obtained with a very little change of hydraulic diameters from1.53mm to 1.54mm at equal test conditions.Those authors have not explained why there is such a big diﬀerence even at nearlyL.Cheng et al./International Journal of Heat and Mass Transfer49(2006)4082–40944085the same test conditions.In all,the experimental data from diﬀerent studies show somehow diﬀerent heat transfer behaviors and thus will aﬀect the accuracy of the new heat transfer model and the newﬂow pattern map to be devel-oped for CO2in the present study since no conclusive rea-sons for the contradicting trends could be found and it is not possible to say which study is right either.3.New CO2ﬂow pattern mapThe newﬂow pattern map for CO2is developed accord-ing to the corresponding heat transfer mechanisms in var-iousﬂow regimes.Based on the heat transfer data in the database,the intermittentﬂow to annularﬂow(I–A)and the annularﬂow to dryout region(A–D)transition criteria in theﬂow pattern map of Wojtan et al.[29]have been modiﬁed toﬁt the experimental data of CO2.The newﬂow pattern map is intrinsically related to the corresponding heat transfer mechanisms of CO2.To reﬂect the real mass ﬂow velocities,equivalent diameters are used for non-circu-lar channels.Other transition criteria are the same as that of Wotjan et al.Thus,based on the fact that the original publications can be easily found,the otherﬂow patterns transition criteria by[29]will not be described here.3.1.Modiﬁcations to theﬂow pattern map for CO2Flow patterns at diabatic conditions are intrinsically related to the correspondingﬂow boiling heat transfer characteristics.Theﬂow patterns can be used to explain physically the heat transfer mechanisms and characteris-tics.Vice versa,the heat transfer mechanisms and charac-teristics can be used to backout the correspondingﬂow patterns.CO2reveals strong nucleate boiling heat transfer characteristics in intermittentﬂow at low vapor quality due to its physical properties.The distinction between intermit-tentﬂow and annularﬂow was indicated by the sharp fall-oﬀof heat transfer coeﬃcients between the twoﬂow regimes.The onset of dryout inception was also observed by a sharp drop in heat transfer.Therefore,the distinction between annularﬂow and dryout region can be bining with the heat transfer model for CO2 (in Section4),the I–A and A–D transition boundaries pro-posed by Wotjan et al.[29]were further modiﬁed so as to ﬁt the heat transfer characteristics.Based on the experi-mental data,the following I–A and A–D transition criteria are proposed for CO2as1.The I–A transition boundary is calculated with the newcriterion as follows:x IA¼½1:81=0:875ðq V=q LÞÀ1=1:75ðl L=l VÞÀ1=7þ1 À1ð2Þ2.The A–D transition boundary is calculated with the newcriterion as follows:G dryout¼10:67ln0:58xþ0:52!Dq V rÀ0:17(Â1gD q Vðq LÀq VÞ!À0:348qVq LÀ0:25qqcritÀ0:7)0:965ð3Þ4086L.Cheng et al./International Journal of Heat and Mass Transfer49(2006)4082–4094which is extracted from Eq.(15)(in Section4)for the dry-out inception of CO2.In this equation,q crit is calculated according to Kutateladze[36].For non-circular channels, equivalent diameters are used.parison of the newﬂow pattern map for CO2to experimental dataFig.3(a)shows the comparison of the newﬂow pattern map for CO2and theﬂow pattern map of Wojtan et al.to the experimental data of Yun et al.[21]at the indicated test conditions(in theﬂow pattern map,A stands for annular ﬂow,D stands for dryout region,I stands for intermittent ﬂow,M stands for mistﬂow,S stands for stratiﬁedﬂow and SW stands for stratiﬁed-wavyﬂow.The stratiﬁed to stratiﬁed-wavyﬂow transition is designated as S–SW,the stratiﬁed-wavy to intermittent/annularﬂow transition is designated as SW–I/A,the intermittent to annularﬂow transition is designated as I–A and so on.).Arrow1shows the change of I–A transition boundaries and arrow2shows the change of A–D transition boundaries from theﬂow pattern map of Wojtan et al.to the newﬂow pattern map for CO2.Arrow3shows the changes of the S–SW/ Slug+SW transition boundaries that are automatically changed due to the change of I–A and A–D transition boundaries.Other transition boundaries are the same. Fig.3(b)shows the corresponding comparison of the pre-dicted heat transfer coeﬃcients with the heat transfer model of Wojtan et al.and the new heat transfer model for CO2(in Section4)to the experimental data at the same conditions as that in Fig.3(a).Obviously,theﬂow pattern map of Wojtan et al.cannot reﬂect the corresponding CO2heat transfer characteristics correctly and the heat transfer model of Wojtan et al.predicts poorly the experimental heat transfer coeﬃcients of CO2.The new CO2ﬂow pattern map reﬂects the heat transfer mechanisms well in the corre-spondingﬂow regimes and the CO2heat transfer model predicts the corresponding CO2experimental heat transfer coeﬃcients well.The heat transfer coeﬃcients start to fall in the A–D transition due to the inception of dryout at the top of the tube and then fall oﬀsharply in the dryout region.The predicted and the experimental heat transfer coeﬃcients are in good agreement in theseﬂow regimes. It should be mentioned here that there are only two studies ofﬂow visualization of CO2ﬂow boiling[23,24]in the lit-erature.Unfortunately,neither contains the corresponding study of heat transfer characteristics which should be related to the observedﬂow patterns.In addition,in the study of Yun et al.[23],the maximum mass velocity reaches1500kg/m2s,which is much higher than the max-imum value570kg/m2s in the present database and their heatﬂux is100kW/m2,which is also much higher than the maximum heatﬂux32kW/m2in the present database. In the study of Pettersen[24],it is diﬃcult to interpret some of his observations by his deﬁnitions of theﬂow regimes in ourﬂow pattern map.It is also diﬃcult to judge some of hisﬂow regimes so as to compare to the newﬂow pattern map.4.Newﬂow boiling heat transfer model for CO2It is a formidable task to develop a generalﬂow boiling heat transfer model for CO2because of the diversities of the heat transfer trends in the database.To develop a gen-eral prediction method,it is important that the method isL.Cheng et al./International Journal of Heat and Mass Transfer49(2006)4082–40944087not only numerically accurate but that it captures correctly the trends in the data.Most importantly,the heat transfer mechanisms should be related to the corresponding ﬂow patterns and be physically explained according to ﬂow pat-tern transitions.Accordingly,a new general heat transfer model is proposed here using the Wojtan et al.[30]model as our starting point.Equivalent diameters are used for non-circular channels.4.1.Brief description of the ﬂow boiling heat transfer model of Wojtan et al.Wojtan et al.[30]extended the Kattan–Thome–Favrat [31–33]heat transfer model to include dryout region and mist ﬂow heat transfer methods and improved the heat transfer prediction in stratiﬁed-wavy ﬂows.The Kattan–Thome–Favrat general equation for the local heat transfer coeﬃcients h tp in a horizontal tube ish tp ¼h dry h V þ2p Àh dry ÀÁh wet ÃÂ2pð4Þwhere h dry is the dry angle as shown in Fig.4.The dry angledeﬁnes the ﬂow structures and the ratio of the tube perim-eters in contact with liquid and vapor.In stratiﬁed ﬂow,h dry equals the stratiﬁed angle,h strat ,which is calculated according to Thome and El Hajal [37].In annular and intermittent ﬂows,h dry =0.For stratiﬁed-wavy ﬂow,h dry varies from zero up to its maximum value h strat .Wojtan et al.subdivided the stratiﬁed-wavy ﬂow into three sub-zones (slug,slug/stratiﬁed-wavy and stratiﬁed-wavy).Based on the fact that the high frequency slugs maintain a continuous thin liquid layer on the upper tube perimeter,h dry is deﬁned equal to 0in the slug zone.The dry angles in the slug/stratiﬁed-wavy and stratiﬁed-wavy regions are cal-culated according to equations developed by Wojtan et al.[30]based in exponential interpolations giving smooth transition in the determination of dry angle between respective zones and also a smooth transition in the heat transfer coeﬃcient from zone to zone.The vapor phase heat transfer coeﬃcient on the dry perimeter h V is calculated with the Dittus–Boelter [38]cor-relation assuming tubular ﬂow in the tube:h V ¼0:023Re 0:8V Pr 0:4V ðk V =D Þð5Þand the heat transfer coeﬃcient on the wet perimeter is cal-culated with an asymptotic model that combines the nucle-ate boiling and convective boiling contributions to the heattransfer by the third power:h wet ¼½ðh nb Þ3þh 3cb1=3ð6ÞIn this equation,the correlation proposed by Cooper [39]multiplied by a ﬁxed boiling suppression factor of 0.8is used to calculate the nucleate boiling contribution.The convective contribution is calculated with the following correlation assuming a liquid ﬁlm ﬂow:h cb ¼0:01334G ð1Àx Þd l L ð1Àe Þ 0:69Pr 0:4Lk Ld ð7Þwhere the term in the bracket is the liquid ﬁlm Reynoldsnumber.In this equation,the void fraction is determined with the Rouhani and Axelsson [40]drift ﬂux model (as in [29–33])and the liquid ﬁlm thickness is calculated as suggested by El Hajal et al.[41].The heat transfer coeﬃcient in mist ﬂow is calculated as follows [30]:h mist ¼0:0117Re 0:79H Pr 1:06V YÀ1:83ðk V =D Þð8Þwhere Re H is the homogeneous Reynolds number and Y is the correction factor originally proposed by Groeneveld [42]and given byY ¼1À0:1½ðq L =q V À1Þð1Àx Þ0:4ð9ÞThe heat transfer coeﬃcient in the dryout region is calculated by proration as [30]h dryout ¼h tp ðx di ÞÀx Àx dix de Àx di½h tp ðx di ÞÀh mist ðx de Þð10Þwhere h tp (x di )is the two-phase ﬂow heat transfer coeﬃcient calculated from Eq.(4)at the dryout inception quality x di and h mist (x de )is the mist ﬂow heat transfer coeﬃcient calcu-lated from Eq.(8)at the dryout completion quality x de .If x de is not deﬁned at the considered mass velocity it is assumed that x de =0.999.For more details about the ﬂow boiling heat transfer model and ﬂow patterns map pro-posed by Wotjan et al.[29,30],we suggest to consult the original papers.4.2.Modiﬁcations in the new ﬂow boiling heat transfer model for CO 2Like any other ﬂow boiling heat transfer model,both the Kattan–Thome–Favrat model and the modiﬁed model of Wojtan et al.drastically underpredicts the heat transfer coeﬃcients for CO 2,particularly at low and intermediate vapor qualities as shown in Fig.3(b).Moreover,CO 2at high saturation pressures gives a trend of a monotonic decrease in heat transfer coeﬃcient versus vapor quality in intermittent and annular ﬂows,which is the exact oppo-site of the trend for other refrigerants such as R-134a at low pressures [8,9].The nucleate boiling contribution is much larger than the convective boiling contribution for CO 2while the opposite is true for R-134a.Hence,Fig.4.Schematic diagram of annular ﬂow with partial dryout.4088L.Cheng et al./International Journal of Heat and Mass Transfer 49(2006)4082–4094。

The Thermodynamics of the Earths Atmosphere

The Thermodynamics of the Earths Atmosphere The Earth's atmosphere is a complex system that interacts with the planet's surface, oceans, and biosphere. The study of the thermodynamics of the atmosphere is essential in understanding the behavior of this system and how it affects our planet. Thermodynamics is the study of the relationships between heat, energy, and work. In the context of the Earth's atmosphere, thermodynamics helps us understand the processes that govern the movement of air, the formation of weather patterns, and the distribution of energy throughout the system.One of the key principles of thermodynamics is the conservation of energy. This principle states that energy cannot be created or destroyed; it can only be transferred or converted from one form to another. In the Earth's atmosphere, energy is transferred through a variety of processes, including radiation, conduction, and convection. Radiation is the transfer of energy through electromagnetic waves, such as those from the sun. Conduction is the transfer of energy through direct contact, such as when the ground heats the air above it. Convection is the transfer of energy through the movement of fluids, such as when warm air rises and cool air sinks.Another important principle of thermodynamics is the second law of thermodynamics, which states that the total entropy of a closed system always increases over time. Entropy is a measure of the disorder or randomness of a system. In the Earth's atmosphere, entropy increases as energy is transferred from one place to another. This means that the atmosphere tends towards a state of maximum disorder, which can lead to the formation of weather patterns and other complex phenomena.The thermodynamics of the Earth's atmosphere also plays a crucial role in the global climate system. The atmosphere acts as a greenhouse, trapping heat from the sun and regulating the temperature of the planet. This is known as the greenhouse effect, and it is essential for life on Earth. However, human activities such as the burning of fossil fuels have increased the concentration of greenhouse gases in the atmosphere, leading to an enhanced greenhouse effect and global warming. Understanding the thermodynamics ofthe atmosphere is therefore crucial in addressing the challenges of climate change and developing strategies to mitigate its impacts.From a human perspective, the thermodynamics of the Earth's atmosphere has a profound impact on our daily lives. Weather patterns such as hurricanes, tornadoes, and thunderstorms are all driven by the movement of air and the transfer of energy through the atmosphere. These phenomena can have devastating effects on communities, causing loss of life and property damage. Understanding the thermodynamics of the atmosphere can help us predict and prepare for these events, improving our ability to respond and recover from natural disasters.In conclusion, the study of the thermodynamics of the Earth's atmosphere is essential in understanding the behavior of this complex system and its impact on our planet. Through the principles of conservation of energy and the second law of thermodynamics, we can gain insights into the processes that govern the movement of air, the formation of weather patterns, and the distribution of energy throughout the system. From a human perspective, this knowledge is critical in predicting and preparing for natural disasters and addressing the challenges of climate change. As we continue to explore the mysteries of our planet's atmosphere, the principles of thermodynamics will undoubtedly play a central role in our understanding of this fascinating and complex system.。

2021年托福阅读PASSAGE 87 试题及答案

2021年托福阅读PASSAGE 87试题及答案PASSAGE 87Because the low latitudes of the Earth, the areas near the equator, receive more heat than the latitudes near the poles, and because the nature of heat is to expand and move, heat is transported from the tropics to the middle and high latitudes. Some of this heat is moved by winds and some by ocean currents,and some gets stored in the atmosphere in the form of latent heat. The term "latent heat" refers to the energy that has to be used to convert liquid water to water vapor. We know that if we warm a pan of water on a stove, it will evaporate, or turn into vapor, faster than if it is allowed to sit at room temperature. We also know that if we hang wet clothes outside in the summertime they will dry faster than in winter, when temperatures are colder. The energy used in both cases to change liquid water to water vapor is supplied by heat — supplied by the stove in the first case and by the Sun in the latter case. This energy is not lost. It is stored in water vapor in the atmosphere as latent heat. Eventually, the water stored as vapor in the atmosphere will condense to liquid again, and the energy will be released to the atmosphere.In the atmosphere, a large portion of the Sun's incoming energy is used to evaporate water, primarily in the tropical oceans. Scientists have tried to quantify this proportion of the Sun's energy.By analyzing temperature, water vapor, and wind data around the globe, they have estimated the quantity to be about 90 watts per square meter, or nearly 30 percent of the Sun's energy. Once this latent heat is stored within the atmosphere, it can be transported, primarily to higher latitudes, by prevailing, large-scale winds. Or it can be transported vertically to higher levels in the atmosphere,where it forms clouds and subsequent storms, which then release the energy back to the atmosphere.1. The passage mainly discusses how heat(A) is transformed and transported in the Earth's atmosphere(B) is transported by ocean currents(C) can be measured and analyzed by scientists(D) moves about the Earth's equator2. The passage mentions that the tropics differ from the Earth's polar following ways?(A) The height of cloud formation in the atmosphere.(B) The amount of heat they receive from the Sun.(C) The strength of their large scale winds.(D) The strength of their oceanic currents.3. The word "convert" in line 6 is closest in meaning to(A) mix(B) change(C) adapt(D) reduce4. Why does the author mention "the stove" in line 10?(A) To describe the heat of the Sun.(B) To illustrate how water vapor is stored.(C) To show how energy is stored.(D) To give an example of a heat source.5. According to the passage , most ocean water evaporation occurs especially(A) around the higher latitudes(B) in the tropics(C) because of large-scale winds(D) because of strong ocean currents6. According to the passage , 30 percent of the Sun's incoming energy(A) is stored in clouds in the lower latitudes(B) is transported by ocean currents(C) never leaves the upper atmosphere(D) gets stored as latent heat7. The word "it" in line 18 refers to(A) square meter(B) the Sun's energy(C) latent heat(D) the atmosphere8. The word "primarily" in the line 19 is closest in meaning to(A) chiefly(B) originally(C) basically(D) clearly9. The word "prevailing" in line 19 is closest in meaning to(A) essential(B) dominant(C) circular(D) closest10. All of the following words are defined in the passage EXCEPT(A) low latitudes(line 1)(B) latent heat (line 5)(C) evaporate (line 7)(D) atmosphere (line 14)ANSWER KEYSPASSAGE 87 ABBDB DCABD。

关于海水变热的英语四级

关于海水变热的英语四级The warming of seawater is a significant topic in the field of oceanography and environmental science. There are several factors that contribute to the increase in sea surface temperature, including climate change, solar radiation, and human activities.Firstly, climate change has been identified as a major driver of rising sea surface temperatures. The increase in greenhouse gas emissions, such as carbon dioxide and methane, has led to the trapping of heat in the Earth's atmosphere, resulting in a phenomenon known as global warming. As a result, the oceans absorb much of this excess heat, causing their temperatures to rise.Secondly, solar radiation plays a crucial role in heating the surface of the oceans. The sun's energy is absorbed by the seawater, causing it to warm up. This process is essential for the regulation of global climate and the sustenance of marine life.Furthermore, human activities also contribute to the warming of seawater. The discharge of industrial and domestic waste into the oceans, as well as the release of pollutants and chemicals, can lead to an increase in water temperature. Additionally, activities such as deforestation and urbanization can indirectly impact sea surface temperatures through their effects on climate patterns.The warming of seawater has far-reaching implications for marine ecosystems, weather patterns, and coastal communities. It can disrupt the balance of marine ecosystems, leading to coral bleaching, the loss of biodiversity, and changes in the distribution of marine species. Furthermore, warmer sea surface temperatures can fuel the intensification of tropical storms and hurricanes, posing risks to coastal areas and human settlements.In conclusion, the warming of seawater is a complex phenomenon influenced by climate change, solar radiation, and human activities. Understanding the causes and consequences of rising sea surface temperatures is crucialfor the development of effective strategies to mitigate its impacts on marine environments and coastal regions.。