Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Textbook Question
Chapter 5, Problem 5.109P
A thin rod of diameter D is initially in equilibrium with its surroundings, a large vacuum enclosure at temperature
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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?
(a) Consider nodal configuration shown below. (a) Derive the finite-difference
equations under steady-state conditions if the boundary is insulated. (b) Find the value of
Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k =
W
3
m. k
Ay
m-1, n
11-
m2, 11
m, n+1
m, n-1
The side insulated
(a) Consider nodal configuration shown below. (a) Derive the finite-difference
equations under steady-state conditions if the boundary is insulated. (b) Find the value of
Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k
=
=
W
3
m. k
.
Ay
m-1, n
m, n
| Δx="
m, n+1
m, n-1
The side insulated
Chapter 5 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 5 - Consider a thin electrical heater attached to a...Ch. 5 - The inner surface of a plane wall is insulated...Ch. 5 - A microwave oven operates on the principle that...Ch. 5 - A plate of thickness 2L, surface area As, mass M,...Ch. 5 - For each of the following cases, determine an...Ch. 5 - Steel balls 12 mm in diameter are annealed by...Ch. 5 - Consider the steel balls of Problem 5.6, except...Ch. 5 - The heat transfer coefficient for air flowing over...Ch. 5 - A solid steel sphere (AISI 1010), 300 mm in...Ch. 5 - A flaked cereal is of thickness 2L=1.2mm. The...
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