Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
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 3.141P
An electrical cable, experiencing uniform volumetric generation
(a) Derive the explicit, finite-difference equations for an interior node (m, n ), the center node
(b) Obtain the stability criterion for each of the finite-difference equations. Identify the most restrictive criterion.
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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
the slab.
n-20-
10 cm
IT- 25°C)
100 cm
100 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).
(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.)
2. Consider the temperature distributions associated with a dx differential control
volume within the one-dimensional plane walls shown below.
T(x,00)
T\x,00)
* dx
* dx
(a)
(Б)
Tx,1)
T(x,1)
* dx
dx
(c)
(d)
(a) Steady-state conditions exist. Is thermal energy being generated within
the differential control volume? If so, is the generation rate positive or
negative?
(b) Steady-state conditions exist as in part (a). Is the volumetric generation
rate positive or negative within the differential control volume?
(c) Steady-state conditions do not exist, and there is no volumetric thermal
energy generation. Is the temperature of the material in the differential
control volume increasing or decreasing with time?
(d) Transient conditions exist as in part (c). Is the temperature increasing
or decreasing with time?
Chapter 3 Solutions
Introduction to Heat Transfer
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