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