A plate of thickness 2L, surface area A_s, mass M, and specific heat c p ' initially at a uniform temperature T_∞, is suddenly heated on both surfaces by a convection process (T_∞, h) for a period of time t_o following which the plate is insulated. Assume that the mid plane temperature does not reach T_∞ within this period of time.

(a) Assuming Bi >> 1 for the heating process, sketch and label, on T -x coordinates, the following temperature distributions: initial, steady-state (t → ∞), T(x, t_o)' and at two intermediate times between

t = to and t → ∞.

(b) Sketch and label, on T – t coordinates, the mid plane and exposed surface temperature distributions.

(c) Repeat parts (a) and (b) assuming Bi << 1 for the plate

(d) Derive an expression for the steady-state temperature T(x, ∞) = T_f' leaving your result in terms of plate parameters (M, c p), thermal conditions (T_i, T_∞, h), the surface temperature T (L, t) and the heating time t_o'