A plane wall of thickness 2L and thermal conductivity k experiences a uniform volumetric generation rate q.

Question:

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 T_o. 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 R_t = 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 T_o = 50°C.

Case 1 Case 2 Thin dielectric strip, R; 4. k --L- +L +L

(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.

(d) What is the location of the maximum temperature in the composite wall of Case 2? Calculate this temperature.

Distribution
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