A plane wall of thickness 2L and thermal conductivity k experiences a uniform volumetric generation rate q. As shown in the sketch for Case I, the surface at x = - L is perfectly insulated, while the other surface is maintained at a uniform, constant temperature To. For Case 2, a very thin dielectric strip is inserted at the midpoint of the wall (x = 0) in order to electrically isolate the two sections, A and B. The thermal resistance of the strip is Rt = 0.0005 m2 · K/W. The parameters associated with the wall are k = 50 W/m · K, L = 20 mm, q = 5 X 106 W/m3 · and To = 50°C
(a) Sketch the temperature distribution for case 1 on T - x coordinates. Describe the key features of this distribution. Identify the location of the maximum temperature in the wall and calculate this temperature.
(b) Sketch the temperature distribution for Case 2 on the same T - x coordinates. Describe the key features of this distribution.
(c) What is the temperature difference between the two walls at x = 0 for Case 2?
(d) What is the location of the maximum temperature in the composite wall of Case 2? Calculate this temperature.