A plane wall has constant properties, no internal heat generation, and is initially at a uniform temperature Ti. Suddenly, the surface at x = L is heated by a fluid at T∞ having a convection coefficient h. At the same instant, the electrical heater is energized, providing a constant heat flux qx at x = O.

(a) On T – x coordinates, sketch the temperature distributions for the following conditions: initial condition (t ≤ 0), steady-state condition (t → ∞), and for two intermediate times.

(b) On q; - x coordinates, sketch the heat flux corresponding to the four temperature distributions of part (a).

(c) On q; - t coordinates, sketch the heat flux at the locations x = 0 and x = L. That is, show qualitatively how q_x (0. t) and q_x (L, t) vary with time.

(d) Derive an expression for the steady-state temperature at the heater surface, T (0, ∞), in terms of q₀, T∞, k, h. and L.

T h Heater !! Insulation- L..