Chapter 3, Problem 3.125P

From Problem 1.71, consider the wire leads connecting the transistor to the circuit board. The leads are of thermal conductivity k, thickness t, width w, and length L. One end of a lead is maintained at a temperature $T_c$ corresponding to the transistor case, while the other end assumes the temperature $T_b$ of the circuit board. During steady-state operation, current flow through the leads provides for uniform volumetric heating in the amount $\stackrel{.}{q},$ while there is convection cooling to air that is at $T_{\infty }$ and maintains a convection coefficient h.

1. Derive an equation from which the temperature distribution in a wire lead may be determined. List all pertinent assumptions.
2. Determine the temperature distribution in a wire lead, expressing your results in terms of the prescribed variables.