Determine the temperature distribution at t = 30 min for the conditions of Problem 5.116.
(a) Use an explicit finite-difference technique with a time increment of 600 s and a space increment of 30 mm.

(b) Use the implicit method of the IHT Finite-Difference Equation Tool Pad for One-Dimensional Transient Conduction. 5.125

Data From Problem 5.116.

A wall 0.12 m thick having a thermal diffusivity of 1.5 X 10⁶ 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 Δx = 30 mm and Δt = 300 s, compute T(x, t) for 0 ≤ t ≤  t_ss, 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 Δt = 75 s. For each value of Δt, plot temperature histories for each face and the midplane.