Answer 4.2

 
 
Subtraction gives:
Therefore  

(4.5)

Then

 

Substitution for C and Q in (4.4) yields  
 
(4.6)
   
   
   

Note that when Ta > Tb, Q 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
(4.7)

 

 

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