A plate of thickness 2L, surface area A, mass m, and specific heat op, initially at a uniform temperature T, is suddenly heated on both surfaces by a convection pro- cess (To, h) for a period of time t, following which the plate is insulated. Assume that the midplane tempera ture does not reach To 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 → oo), T(x, t), and at two intermediate times between t, and t → oo,
(b) Sketch and label, on T- t coordinates, the midplane 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 tempera ture Tx, oo) = T, leaving your result in terms of plate parameters (m, cp), thermal conditions (T, T, h), the surface temperature TL, ), and the heating time t