In a variation of the Example 13.5-1, the heat transfer coefficient was specified for a wire that generated a specific amount of heat per unit length, and the surface temperature of the wire was computed. An initial temperature was guessed and the heat rate required to maintain that temperature was calculated. This was iterated until the calculated value of the heat rate equaled the given heat transfer value.

In order to accomplish this iteration, the properties of the fluid (air) had to be extrapolated for the changing Tf. This was done by condensing the values of g, b, r2, Cp, m, and k into a single value, a, corresponding to Gr x Pr. This is given in the below equation

where:

The values of a (the condensed properties of air at atmospheric pressure) and the properties of air at atmospheric pressure are given in Table 1. These values were put into an array where an extrapolated value could be derived and used in the iteration. The same process was repeated for the thermal conductivity value, k.

Matlab was used to do this iterative process through two functions that we wrote:

• Using Matlab to Solve