Chapter 4, Problem 4.53P

A long conducting rod of rectangular cross section $\left(20\text{mm}\text{×}\text{30}\text{mm}\right)$ and thermal conductivity $k=20\text{W/m}\cdot \text{K}$ experiences uniform heat generation at a rate $\stackrel{.}{q}=5\times {10}^7{\text{W/m}}^{\text{3}},$ while its surfaces are maintained at 300 K.

1. Using a finite-difference method with a grid spacing of 5 mm, determine the temperature distribution in the rod.
2. With the boundary conditions unchanged, what heat generation rate will cause the midpoint temperature to reach 600 K?