Consider a one-dimensional plane wall at a uniform initial temperature T_i. The wall is 10 mm thick, and has a thermal diffusivity of α = 6 x 10^–7 m²/s. The left face is insulated, and suddenly the right face is lowered to a temperature T_s,r.
(a) Using the implicit finite-difference technique with Δx = 2 mm and Δt = 2 s, determine how long it will take for the temperature at the left face T_s,l to achieve 50% of its maximum possible temperature reduction.
(b) At the time determined in part (a), the right face is suddenly returned to the initial temperature. Determine how long it will take for the temperature at the left face to recover to a 20% temperature reduction, that is, T_i – T_s,l  0.2(T_i – T_s,r).