Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 4, Problem 4.4P
A two-dimensional rectangular plate is subjected to the boundary conditions shown. Derive an expression for the steady-state temperature distribution
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2. The slab shown is embedded in insulating materials on five
sides, while the front face experiences convection off its face.
Heat is generated inside the material by an exothermic
reaction equal to 1.0 kW/m'. The thermal conductivity of the
slab is 0.2 W/mk.
a. Simplify the heat conduction equation and integrate
the resulting ID steady form of to find the
temperature distribution of the slab, T(x).
b. Present the temperature of the front and back faces of
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n-20-
10 cm
IT- 25°C)
100 cm
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Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2)
under steady state condition. The density, conductivity and specific heat of the material are p=(1200*32)kg/mº, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux 9" =1000 W/m² is applied to the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated.
9" (W/m)
T=0°C
T=0°C
W=(10*32)cm
B=(30*32)cm
A solid cylinder of radius R and length L is made from material with thermal conductivity 2.
Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time).
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(b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and
length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat
generation in the animal is 10-³ W/cm³, find the skin temperature (Ts) for the mouse. The
external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along
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Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
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