(Solution) - A wall 0 12 m thick having a thermal diffusivity of 1 5 x 10 6 m -(2025 Original AI-Free Solution)

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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 tss 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.