Chap 传热传质1.3

• For an ideal gas with constant specific heat: iin iout c p Tin Tout
2
• gz W 0 2 out
• For an incompressible liquid: uin uout c Tin Tout
华中科技大学 力学系 传热传质学 2014 Spring
Problem: Silicon Wafer
Problem 1.43: Thermal processing of silicon wafers in a two-zone furnace. Determine (a) the initial rate of change of the wafer temperature and (b) the steady-state temperature.
KNOWN: Silicon wafer positioned in furnace with top and bottom surfaces exposed to hot and cool zones, respectively.
FIND: (a) Initial rate of change of the wafer temperature from a value of Tw,i 300 K, and (b) steady-state temperature. Is convection significant? Sketch the variation of wafer temperature with vertical distance.
dUt dT Mc dt dt
• Heat transfer is from the conductor (negative q ) • Generation may be viewed as electrical work done on the system (negative W )
华中科技大学 力学系 传热传质学 2014 Spring
At an instant or Over a time interval
Type of System:
Control volume Control surface
华中科技大学 力学系 传热传质学 2014 Spring
CV at an Instant and over a Time Interval
E st :
rate of change of energy storage in the system.
dEst E st dt
Conservation of Energy
E in E out E g
• Over a Time Interval
(1.11c)
Each term has units of J/s or W.
Ein E out :
,
rate of thermal and/or mechanical energy transfer across the control surface due to heat transfer, fluid flow and/or work interactions.
Volumetric Phenomena
pv in pv out 0
• For systems with significant heat transfer:

V
2
2
in
gz in
0 2 out gz out 0
V
2
华中科技大学 力学系 传热传质学 2014 Spring
Surface Energy Balance
• Applies for steady-state and transient conditions.
• With no mass and volume, energy storage and generation are not pertinent to the energy balance, even if they occur in the medium bounded by the surface. Consider surface of wall with heat transfer by conduction, convection and radiation.
• An important tool in heat transfer analysis, often providing the basis for determining the temperature of a system.
• Alternative Formulations
Time Basis:
• Write the governing form of the Conservation of Energy requirement.
• Substitute appropriate expressions for terms of the energy equation.
• Solve for the unknown quantity.
• On a schematic of the system, represent the control surface by dashed line(s).
• Choose the appropriate time basis.
• Identify relevant energy transport, generation and/or storage terms by labeled arrows on the schematic.
qconv qrad 0 qcond
k
T1 T2 4 h T2 T 2 T24 Tsur 0 L


华中科技大学 力学系 传热传质学 2014 Spring
Methodology
METHODOLOGY OF FIRST LAW ANALYSIS
华中科技大学 力学系 传热传质学 2014 Spring
Example 1.3
Example 1.3: Application to thermal response of a conductor with Ohmic heating (generation):
• Involves change in thermal energy and for an incompressible substance.
Example 1.5
Example 1.5: Application to isothermal solid-liquid phase change in a container:
Latent Heat of Fusion
U t U1at M hsf
华中科技大学 力学系 传热传质学 2014 Spring
Introduction: Conservation of Energy
Chapter One Section 1.3
华中科技大学 力学系 传热传质学 2014 Spring
Alternative Formulations
CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS)
Open System
Steady State for Flow through an Open System without Phase Change or Generation:
At an Instant of Time: 2 • • m ut pv V 2 gz q m ut pv V in • pv flow work (v : specific volume) • ut pv i enthalpy
Ein Eout Eg Est
(1.11b) 华中科技大学 力学系 传热传质学 2014 Spring
Each term has units of J.
Closed System
• Special Cases (Linkages to Thermodynamics)
Transient Process for a Closed System of Mass (M) Assuming Heat Transfer to the System (Inflow) and Work Done by the System (Outflow).
•
APPLICATION TO A CONTROL VOLUME
At an Instant of Time:
Note: representation of system by a control surface (dashed line) at the boundaries.
Surface Phenomena
Ein E out E st
or, per unit surface area
, h qrad ,c qcv ,u qcv ,l cd qrad
4 T 4 4 4 Tw sur , h Tw Biblioteka Baidu Tsur ,c hu Tw T hl Tw T cd
SCHEMATIC:
•
华中科技大学 力学系 传热传质学 2014 Spring
Problem: Silicon Wafer (cont.)
ASSUMPTIONS: (1) Wafer temperature is uniform, (2) Hot and cool zones have uniform temperatures, (3) Radiation exchange is between small surface (wafer) and large enclosure (chamber, hot or cold zone), and (4) Negligible heat losses from wafer to pin holder.
THE SURFACE ENERGY BALANCE
A special case for which no volume or mass is encompassed by the control surface.
Conservation Energy (Instant in Time):
Ein Eout 0
ANALYSIS: The energy balance on the wafer includes convection from the upper (u) and lower (l) surfaces with the ambient gas, radiation exchange with the hot- and cool-zone and an energy storage term for the transient condition. Hence, from Eq. (1.11c),
Over a time interval
tot Q W Est
For negligible changes in potential or kinetic energy
Q W U t
Internal thermal energy At an instant
q W
dUt dt
Eg :
rate of thermal energy generation due to conversion from another enegy form (e.g., electrical, nuclear, or chemical); energy conversion process occurs within the system.