AEE 331 Heat Transfer Homework II not to be collected ! 1. A house has a composite wall of wood, fiberglass insulation, and plaster board, as indicated in the sketch. On a cold winter day the convection heat transfer coefficients are h0 = 60W/m2 · K and hi = 30W/m2 · K. The total wall surface area is 350m2 . a) Determine a symbolic expression for the total thermal resistance of the wall, including inside and outside convection effects for the prescribed conditions. b) Determine the total heat loss through the wall. c) If the wind were blowing violently, raising h0 to 300W/m2 , determine the percentage increase in the heat loss. d) What is the controlling resistance that determines the amount of heat flow through the wall? 2. The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax1/2 , where a = 0.5m1/2 . The small end is located at x1 = 25mm and the large end is at x2 = 125mm. The end temperatures are T1 = 600K and T2 = 400K, while the lateral surface is well insulated. a) Derive an expression for the temperature distribution T (x) in symbolic form, asssuming one dimensional conditions. Sketch the temperature distribution. b) Calculate the heat rate qx . 3. A thin electrical heater inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40mm. The rod (A) has a thermal conductivity of kA = 0.15W/m, while the tube (B) has a thermal conductivity of kB = 1.5W/m and its outer surface is subject to convection with a fluid of temperature T∞ = −15o C and heat transfer coefficient 50W/m. The thermal contact resistance between the cylinder surfaces and the heater is negligible. a) Determine the electrical power per unit length of the cylinders (W/m) that is required to maintain the outer surface of cylinder B at 5o C. b) What is the temperature at the center of cylinder A? 2

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