Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 4, Problem 4.45P
Upper and lower surfaces of a bus bar are convectively cooled by air at
Consider steady-state conditions for which heat is uniformly generated at a volumetric rate due to passage of an electric current. Using the energy balance method, derive finite-difference equations for nodes 1 and 13.
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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=40 mm and thermal conductivity k=5 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 = -2x10 °C/m², and x is in meters. The origin of the x-
coordinate is at the midplane of the wall.
-L x
-L
(a) Determine the surface heat fluxes, qx(-L) and qx(+L).
(b) What is the volumetric rate of heat generation & in the wall?
(c) What is the convection heat transfer coefficient for the surfaces at x = +L?
(d) Obtain an expression for the heat flux distribution q (as a function of x). Is the heat flux
zero at any location?
(e) If the source of the heat generation is suddenly deactivated (i. e. q = 0), what temperature
will the wall eventually reach with q = 0?
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…
Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
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