Answer 5.3
Substituting in (5.4) the values
gives the rate of heat flow, , as a function of the parameter a:
Again, substituting for k0 and T0 in (5.6) yields the temperature distribution in terms of a
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
Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.