A long conducting rod of rectangular cross section (20mm X 30mm) and thermal conductivity k = 20 W/m ∙ K experiences uniform heat generation at a rate q = 5 X 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?