Consider Problem 4.5 for the case where the plate is of square cross section, W = L.

(a) Derive an expression for the shape factor, Smax associated with the maximum top surface temperature, such that q = Smax k (T2,max – T1) where T2.max is the maximum temperature along y = W.

(b) Derive an expression for the shape factor, Savg' associated with the average top surface temperature, q = Savg k(T2 – T1) where T2 is the average temperature along y = W.

(c) Evaluate the shape factors that can be used to determine the maximum and average temperatures along y = W. Evaluate the maximum and average temperatures for T1 = 0°C, L = W = 10 mm, k = 20 W/m ∙ K. and q"s; = 1000 W/m2.