Heat and Mass Transfer: Fundamentals and Applications
5th Edition
ISBN: 9780073398181
Author: Yunus A. Cengel Dr., Afshin J. Ghajar
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 2, Problem 157P
Consider a medium in which the heat conduction equation is given in its simplest forms as
Is heat transfer steady or transient?
Is heat transfer one-. two-, or thee-dimensional?
Is there heat generation in the medium?
Is the thermal conductivity of the medium constant or variable?
Is the medium a plane wall, a cylinder, or a sphere?
Is this differential equation for heat conduction linear or nonlinear?
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Students have asked these similar questions
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?
Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m-K and a
thickness L = 0.3 m, with no internal heat generation.
T2
L
Determine the heat flux, in kW/m?, and the unknown quantity for each case.
T1 (°C)
T2(°C)
dT/dx(K/m)
9 (kW/m?)
Case
1
50
-20
i
i
2
-30
-10
i
70
i
160
i
40
-80
i
5
i
30
200
i
Chapter 2 Solutions
Heat and Mass Transfer: Fundamentals and Applications
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