Answer to Problem 32
Equation 25
Equation 26
Subtraction gives:
Equation 27
Therefore
Equation 28
Then
Equation 29
Equation 30
Substitution for
and
in (4.4) yields
Equation 31
Equation 32
Note that when
,
is positive, the heat flow is directed radially
outward. Note further that in this case of radial
conduction through a cylindrical wall, the
temperature distribution is logarithmic.
A little manipulation yields the result in the symmetric form
Equation 33