Answer 5.3

Substituting in (5.4) the values

 

gives the rate of heat flow, , as a function of the parameter a:

(5.7)

Again, substituting for k0 and T0 in (5.6) yields the temperature distribution in terms of a

(5.8)

where the dependence of q on a is expressed by (5.7).

For the 3 specified values of a, (5.7) gives corresponding values of q as follows:
 
 
 

For each of these pairs a, q the function T=T(x) given by (5.8) is graphed below.


NOTE:   The case a = 0 is handled by using the Taylor approximation (see Math Link II).

 
Then from (5.8) we get

 

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