A long conducting rod of rectangular cross section (20 mm × 30 mm) and thermal conductivity k = 20 W/m · K experiences uniform heat generation at a rate ˙ q = 5 × 10 7 W / m 3 q˙=5×107 W/m3 , while its surfaces are maintained at 300 K.

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