Answer to Problem 49
Substituting in (5.4) the values
Equation 64
gives the rate of heat flow,
,
as a function of the parameter
:
Equation 65
Again, substituting for
and
in (5.6) yields the
temperature distribution
in terms of
.
Equation 66
where the dependence of
on
is expressed by (5.7).
For the 3 specified values of
,
(5.7) gives corresponding values of
as follows:
Equation 67
Equation 68
Equation 69
For each of these pairs
the function
given by (5.8) is graphed below.

Figure 7:
NOTE: The case
is handled by using the Taylor approximation
(see ).
Equation 70
Then from (5.8) we get
Equation 71