AEE 331 Heat Transfer Homework III Due 6 November 2014, Thursday, 17.00 (submit to room 005) 1. Electric current flows through a long rod generating thermal energy at a uniform volumetric rate of q˙ = 2 × 106 W/m3 . The rod is concentric with a hollow ceramic cylinder, creating an enclosure that is filled with air. 0 The thermal resistance per unit length due to radiation between the enclosure surfaces is Rrad = 0.30m·K/W , and the coefficient associated with free convection in the enclosure is h = 20W/m2 · K. a) Construct a thermal circuit that can be used to calculate the surface temperature of the rod, Tr . Label all the temperatures, heat rates, and thermal resistances, and evaluate each thermal resistance. b) Calculate the surface temperature of the rod for the prescribed conditions. 2. A nuclear fuel element of thickness 2L is covered with a steel cladding of thickness b. Heat generated within the nuclear fuel at a rate q˙ is removed by a fluid at T∞ , which adjoins one surface and is characterized by a convection coefficient h. The other surface is well insulated, and the fuel and steel have thermal conductivities of kf and ks , respectively. a) Obtain an equation for the temperature distribution T (x) in the nuclear fuel. Express your results in terms of q, ˙ kf , L, b, ks , h, and T∞ . b) Sketch the temperature distribution T (x) for the entire system.
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