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Two large steel plates at temperatures of 90° and 70°C are separated by a steel rod 0.3 m long and 2.5 cm in diameter. The rod is welded to each plate. The space between the plates is filled with insulation, which also insulates the circumference of the rod. Because of a voltage difference between the two plates, current flows through the rod, dissipating electrical energy at a rate of 12 W. Determine the maximum temperature in the rod and the heat flow rate at each end. Check your results by comparing the net heat flow rate at the two ends with the total rate of heat generation.
GIVEN
Insulated steel rod with internal heat generationLength (L) = 0.3 mDiameter (D) = 2.5 cm = 0.025 mInternal heat generation rate ( qG V) = 12 WEnd temperature of the rod: T1 = 90°C T2 = 70°C
ASSUMPTIONS
The system has reached steady stateThe heat loss through the insulation is negligibleThe steel is 1% carbon steelConstant thermal conductivityThe plate temperatures are constantHeat is generated uniformly throughout therod
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