The plane wall of Problem 2.48 (k = 50 W/m ∙ K, a = 1.5 X 10-6 m2/s) has a thickness of L = 40 mm and an initial uniform temperature of To = 25°C. Suddenly, the boundary at x = L experiences heating by a fluid for which T'X) = 50°C and h = 1000 W/m2 ∙ K, while heat is uniformly generated within the wall at q = 1 x 107 W/m3. The boundary at x = 0 remains at To.

(a) With ∆x = 4 mm and ∆t = 1 s, plot temperature distributions in the wall for (i) the initial condition, (ii) the steady-state condition, and (iii) two intermediate times.

(b) On q; -t coordinates, plot the heat flux at x = 0 and x = L. At what elapsed time is there zero heat flux at x = L?