AEE 331 Heat Transfer Homework III

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.
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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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