An aluminum pan whose thermal conductivity is 237 W/m•K has a flat bottom with diameter 15 cm and thickness 0.4 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 800 W. If the inner surface of the bottom of the pan is at 105°C, determine the temperature of the outer surface of the bottom of the pan.
Heat is transferred steadily to boiling water in the pan through its bottom. The inner surface temperature of the bottom of the pan is given. The temperature of the outer surface is to be determined.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the pan remain constant at the specified values. 2 Thermal properties of the aluminum pan are constant.
Properties The thermal conductivity of the aluminum is given to be k = 237 W/m*C.
Analysis The heat transfer area is
A = ? r2 = ? (0.075 m)2 = 0.0177 m2
Under steady conditions, the rate of heat transfer through the bottom of the pan by conduction is
Substituting,
T2 = 105.76°C
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