Heat Chap04-026 - Chapter 4 Transient Heat Conduction...

Chapter 4 Transient Heat Conduction
Transient Heat Conduction in Large Plane Walls, Long Cylinders, and Spheres
4-26C A cylinder whose diameter is small relative to its length can be treated as an infinitely long
cylinder. When the diameter and length of the cylinder are comparable, it is not proper to treat the
cylinder as being infinitely long. It is also not proper to use this model when finding the temperatures
near the bottom or top surfaces of a cylinder since heat transfer at those locations can be two-
dimensional.
4-27C Yes. A plane wall whose one side is insulated is equivalent to a plane wall that is twice as thick
and is exposed to convection from both sides. The midplane in the latter case will behave like an
insulated surface because of thermal symmetry.
4-28C The solution for determination of the one-dimensional transient temperature distribution involves
many variables that make the graphical representation of the results impractical. In order to reduce the
number of parameters, some variables are grouped into dimensionless quantities.
4-29C The Fourier number is a measure of heat conducted through a body relative to the heat stored.
Thus a large value of Fourier number indicates faster propagation of heat through body. Since Fourier
number is proportional to time, doubling the time will also double the Fourier number.
4-30C This case can be handled by setting the heat transfer coefficient h to infinity
∞
since the
temperature of the surrounding medium in this case becomes equivalent to the surface temperature.
4-31C The maximum possible amount of heat transfer will occur when the temperature of the body
reaches the temperature of the medium, and can be determined from
Q mC T T
p i max
( ) = -
∞
.
4-32C When the Biot number is less than 0.1, the temperature of the sphere will be nearly uniform at all
times. Therefore, it is more convenient to use the lumped system analysis in this case.
4-33 A student calculates the total heat transfer from a spherical copper ball. It is to be determined
whether his/her result is reasonable.
Assumptions The thermal properties of the copper ball are constant at room temperature.
Properties The density and specific heat of the copper ball are ρ = 8933 kg/m 3 , and C
p
= 0.385 kJ/kg. ° C
(Table A-3).
Analysis The mass of the copper ball and the maximum amount of heat transfer from the copper ball are
kJ 1064 C ) 25 200 )( C kJ/kg. 385 . 0 )( kg 79 . 15 ( ] [
kg 79 . 15
6
m) 15 . 0 (
) kg/m 8933 (
6
max
3
3
3
= ° - ° = - =
=








=








= =
∞
T T mC Q
D
V m
i p
π
π
ρ ρ
Discussion The student's result of 4520 kJ is not reasonable since it is
greater than the maximum possible amount of heat transfer.
4-17
Copper
ball, 200 ° C
Q

Chapter 4 Transient Heat Conduction
4-34 An egg is dropped into boiling water. The cooking time of the egg is to be determined. √
Assumptions 1 The egg is spherical in shape with a radius of r
0
= 2.75 cm. 2 Heat conduction in the egg
is one-dimensional because of symmetry about the midpoint. 3 The thermal properties of the egg are
constant. 4 The heat transfer coefficient is constant and uniform over the entire surface.