A wall 0.12 m thick having a thermal diffusivity of 1.5 x 10^-6 m²/s is initially at a uniform temperature of 85°C. Suddenly one face is lowered to a temperature of 20°C, while the other face is perfectly insulated.

(a) Using the explicit finite-difference technique with space and time increments of 30 mm and 300 s, respectively, determine the temperature distribution at t = 45 min.

(b) With ∆x: = 30 mm and ∆t = 300 s, compute T(x, t) for 0 < t < t 55, where t_ss is the time required for the temperature at each nodal point to reach a value that is within 1°C of the steady-state temperature.

Repeat the foregoing calculations for ∆t = 75 s. For each value of ∆t, plot temperature histories for each face and the mid plane.