传热学-讲稿第一章

Φ ∂ T ~ A ∂ x
When the proportionality constant is inserted,(当加入 比例常数时我们得到：)
∂ T Φ= − kA ∂ x
(1-1)
Φ ——the heat transfer rate;(热流通量或热流量）
heat flow ；
∂T / ∂x —— the temperature gradient in the direction of the
∂ T = Φ +dx = − |x+dx kA Energy out right face x ∂ x
∂ T ∂ ∂ T = −A k [ + (k )d ] x ∂ x ∂ x ∂ x
where q= energy generated per unit volume, W/m3 ɺ
c = specific heat of material, J/kg . 0C
工程热力学用于研究平衡系统；它只研究系统从一个平衡状态到另 一个平衡状态所需要的能量数，而不研究这种变化进行的快慢，因 为系统处于变化时是不平衡的。
For example（例如）
Consider the cooling of a hot steel bar which is placed in a pail of water
ρ= density, kg/m3
Combining the relations above gives
∂T ∂T ∂T ∂ ∂T ɺ −kA +qAdx = ρ cA dx− A k [ + (k )dx] ∂x ∂x ∂x ∂x ∂x
Or
∂ ∂ T ∂ T ɺ (k ) +q = ρ c ∂ x ∂ x ∂ τ
传热学将研究金属棒和水的温度随时间的变化函数。 传热学将研究金属棒和水的温度随时间的变化函数。
1-1 CONDUCTION HEAT TRANSFER（传导传热）
When a temperature gradient exists in a body(solid), experience has shown that there is an energy transfer from the high-temperature region to the low-temperature region. We say that the energy is transferred by conduction and that the heattransfer rate per unit area is proportional to the normal temperature gradient: 当物体内部存在温差（温度梯度）时，将 有能量从温度高的地方传到温度低的地方，我们把这样传递能量 的方式称为传导传热，并且所传递的单位热流与法向温度梯度成 比例:
传热学不仅要探求热量是如何传递的，而且要预示在特定的条件下传递 热程热力学：
Thermodynamics deals with systems in equilibrium; it may be used to predict the amount of energy required to change a system from one equilibrium state to an other; it may not be used to predict how fast a change will take place since the system is not in equilibrium during the process.
(1-2)
This is the one-dimensional heat-conduction equation.
To treat more than one-dimensional heat flow, we need consider only the heat conducted in and out of a unit volume in all three coordinate directions, as shown in Fig. l-3a. The energy balance yields
These energy quantities are given as follows:
∂ T Φx = −kA Energy in left face = ∂ x
ɺ Energy generated within element = qAdx
∂T Change in internal energy = ρ cA dx ∂τ
Heat transfer
Edited by J. P. Holman
Introduction
The definition of heat transfer： transfer：
传热学的定义： Heat transfer is that science which seeks to predict the energy transfer which may take place between material bodies as a result of a temperature difference. Thermodynamics teaches that this energy transferred is defined as heat.
ɺ q gen = qAdx
qx+dx
qx
Consider the one-dimensional system shown in Fig. 1-2. If the system is in a steady state, i.e., if the temperature does not change with time, then the problem is a simple one, and we need only integrate( 积 分 ) Eq. (1-1) and substitute the appropriate values to solve for the desired quantity. However, if the temperature of the solid is changing with time, or if there are heat sources or sinks within the solid, the situation is more complex. We consider the general case where the temperature may be changing with time and heat sources may be present within the body. For the element of thickness dx the following energy balance may be made: Energy conducted in left face + heat generated within element = change in conducted out right face internal energy + energy
Thermodynamics may be used to predict the final equilibrium temperature of the steel bar-water combination. Thermodynamics will not tell us how long it takes to reach this equilibrium condition or what the temperature of the bar will be after a certain length of time before the equilibrium condition is attained.
k——is called the thermal conductivity of the material ; the minus sign—— present the heat must flow downhill on the temperature scale . as indicated in the coordinate system of Fig. 1-1
dE Φx +Φy +Φz +qgen =Φx+dx +Φy+dy +Φz+dz + dτ
and the energy quantities are given by
∂ T Φ =− y z kd d x ∂ x ∂ T ∂ ∂T Φx+dx = − k [ + (k )dx]dydz ∂ x ∂x ∂ x
传热学——预示不同物体之间由于温差的作用而发生能量传递的 规律的科学。 工程热力学中把这个传递的能量叫——热量。
The difference between heat transfer and thermodynamics： thermodynamics：
热量传递与工程热力学的差别：
Heat transfer: The science of heat transfer seeks not merely to explain how heat energy may be transferred, but also to predict the rate at which the exchange will take place under certain specified conditions.
∂ T Φy = −K xd d z ∂ y ∂ T ∂ ∂ T Φy+dy = − k [ + (k )dy]dxdz ∂ y ∂ y ∂ y
∂ T Φ = −K xd d y z ∂ z ∂T ∂ ∂T Φz+dz = − k [ + (k )dz]dxdy ∂z ∂z ∂z
热力学只关心最终的平衡温度，并没有告诉我们达到这一平衡需要多长时 间，或者在系统稳定前的某一时间，金属棒能达到什么样的温度。
Heat transfer may be used to predict the temperature of both the bar and the water as a function of time.
qx
Equation (1-1) is called Fourier's law of heat conduction after the French mathematical physicist Joseph Fourier, who made very significant contributions to the analytical treatment of conduction heat transfer. It is important to note that Eq. (11) is the defining equation for the thermal conductivity and that k has the units of watts per meter per Celsius degree in a typical system of units in which the heat flow is expressed in watts. ( w/m.℃, w ) We now set ourselves the problem of determining the basic equation which governs the transfer of heat in a solid, using Eq. (1-1) as a starting point.（现在，我们建立控制固体导热的基本 方程式的着眼点就是公式（1-1）