Consider a plane composite wall that is composed of three materials (materials A, B, and C are arranged left to right) of thermal conductivities k_A = 0.24 W/m ∙ K, k_B = 0.13 W/m ∙ K, and k_C = 0.50 W/m ∙ K. The thicknesses of the three sections of the wall are L_A = 20 mm, L_B = 13 mm, and L_C = 20 mm. A contact resistance of R_t,c = 10- 2 m² ∙ K/W exists at the interface between materials A and B, as well as at the interface between materials Band C. The left face of the composite wall is insulated, while the right face is exposed to convective conditions characterized by h = 10 W/m² ∙ K, T_∞ = 20°C. For Case I, thermal energy is generated within material A at the rate q A = 5000 W/m³ ∙ For Case 2, thermal energy is generated within material C at the rate qc = 5000 W/m³.

(a) Determine the maximum temperature within the composite wall under steady-state conditions for Case 1.

(b) Sketch the steady-state temperature distribution on T - x coordinates for Case 1.

(c) Sketch the steady-state temperature distribution for Case 2 on the same T - x coordinates used for Case 1.