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 2, Problem 2.41P
One-dimensional, steady-state conduction with no energy generation is occurring in a plane wall of constant thermal conductivity.
(a) Is the prescribed temperature distribution possible? Briefly explain your reasoning.
(b) With the temperature at
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1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with
a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature
distribution has the form T = a + bx + cx² °C. The surface at x=0 has a temperature of To =
120 °C and experiences convection with a fluid for which T..
surface at x= 50 mm is well insulated (no heat transfer). Find:
(a) The volumetric energy generation rate q. (15)
(b) Determine the coefficients a, b, and c.
20 °C and h 500 W/m² K. The
To:
= 120°C
T = 20°C
h = 500 W/m².K
111
Fluid
T(x)-
=
q, k = 5 W/m.K
L = 50 mm
A plane wall of thickness 2L = 30 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a
rate q, while convection heat transfer occurs at both of its surfaces (x = − L, + L), each of which is exposed to a fluid of
temperature T = 20°C. Under steady-state conditions, the temperature distribution in the wall is of the form
T(x) = a + bx + cx² where a = 82.0°C, b = -210°C/m, c = -2x 10°C/m², and x is in meters. The origin of the x-coordinate is at
the midplane of the wall.
(a) What is the volumetric rate à of heat generation in the wall?
(b) Determine the surface heat fluxes, q" (L)and q ( + L).
(c) What are the convection coefficients for the surfaces at x = - Land x = + L?
The volumetric rate of heat generation in the wall, in W/m³:
q = i
W/m³
The surface heat flux, in W/m²:
qx ( - L) = i
The surface heat flux, in W/m²:
q (+ L) = i
W/m²
W/m²
The convection coefficients for the surface at x = - L, in W/m²-K:
h(- L) = i
W/m².K
The convection…
A plane wall of thickness 2L = 2*33 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a rate q˙, while convection heat transfer occurs at both of its surfaces (x = −L, + L), each of which is exposed to a fluid of temperature T∞ = 31°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx2 where a = 85°C, b = −-218°C/m, c = −-23,942°C/m2, and x is in meters. The origin of the x-coordinate is at the midplane of the wall.
(a) Sketch the temperature distribution and identify significant physical features.
(b) What is the volumetric rate of heat generation q˙ in the wall?
(c) Obtain an expression for the heat flux distribution qx″(x). Is the heat flux zero at any location? Explain any significant features of the distribution.
(d) Determine the surface heat fluxes, qx″(−L) and qx″(+L). How are these fluxes related to the heat generation rate?
(e) What are the convection coefficients…
Chapter 2 Solutions
Introduction to Heat Transfer
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