Question: Electric current flows through a long rod generating thermal energy at a uniform volumetric rate of q = 2 X 10 6 W/m 3 .

Electric current flows through a long rod generating thermal energy at a uniform volumetric rate of q = 2 X 10⁶ W/m³. The rod is concentric with a hollow ceramic cylinder, creating an enclosure that is filled with air.

T.= 25°C T, Ceramic, k= 1.75 D, = 40 mm Wim-K D, = 120 mm Enclosure, air space Rod, q. D, = 20 mm

The thermal resistance per unit length due to radiation between the enclosure surfaces is R_rad =0.30 m ∙ K/W, and the coefficient associated with free convection in the enclosure is h = 20 W/m² ∙ K.

(a) Construct a thermal circuit that can be used to calculate the surface temperature of the rod, Tr. Label all temperatures, heat rates, and thermal resistances, and evaluate each thermal resistance.

(b) Calculate the surface temperature of the rod for the prescribed conditions.

T.= 25C T, Ceramic, k= 1.75 D, = 40 mm Wim-K D, = 120 mm Enclosure, air space Rod, q. D, = 20 mm

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