Consider the system of Problem 5.1 where the temperature of the plate is space wise isothermal during the transient process.

(a) Obtain an expression for the temperature of the plate as a function of time T(t) in terms of q"₀, T_∞, h. L, and the plate properties p and c.

(b) Determine the thermal time constant and the steady-state temperature for a 12-mm-thick plate of pure copper when T_∝ = 27°C, h = 50 W/m² ∙ K, and q"₀ = 5000 W/m². Estimate the time required to reach steady-state conditions.

(c) For the conditions of part (b), as well as for h = 100 and 200 W/m² ∙ K, compute and plot the corresponding temperature histories of the plate for o < t < 2500 s.