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