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 2, Problem 2.37P
The steady-state temperature distribution in a semi-transparent material of thermal conductivity k and thickness L exposed to laser irradiation is of the form
where A, a, B, and C are known constants. For this situation, radiation absorption in the material is manifested by a distributed heat generation term,
- Obtain expressions for the conduction heat fluxes at the front and rear surfaces.
- Derive an expression for
- Derive an expression for the rate at which radiation is absorbed in the entire material. per unit surface area. Express your result in terms of the known constants for the temperature distribution, the thermal conductivity of the material, and its thickness.
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(3) Determine the permissible value of electrical current flowing copper wire of d=2 mm
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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?
Consider a solid sphere of radius R with a fixed surface temperature, TR. Heat is generated within
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(a) Assuming constant thermal conductivity, use the conduction equation to derive an expression
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(b) Calculate the temperature at the center of the sphere for the following parameter values:
R=3 m 1₁-20 W/m³ TR-20 °C k-0.5 W/(m K) ₂-10 W/m³
Chapter 2 Solutions
Fundamentals of Heat and Mass Transfer
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