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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Chapter 3, Problem 3.112P
A thin flat plate of length L thickness t. and width
- Derive the differential equation that determines the steady-state temperature distribution
- Solve the foregoing equation for the temperature distribution, and obtain an expression for the rate of heat transfer from the plate to the heat sinks.
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A plane wall of thickness 8cm and thermal conductivity k=5W/mK experiences uniform volumetric heat generation, while convection heat transfer occurs at both of its surfaces (x= -L, x= + L), each of which is exposed to a fluid of temperature T∞ = 20˚C. The origin of the x-coordinate is at the midplane of the wall. Under steady-state conditions, the temperature distribution in the wall is of the form T(˚C) = a + bx - cx^2, where x is in meters, a =86˚C, b = -500˚C/m, and c=4459.
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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).
(a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature
distribution in the cylinder, given that the surface temperature is Ts.
(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
the axis of the mouse, as in part a.)
Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
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