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