Solve the following problem:
Q: 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 generation
Length (L) = 0.3 m
Diameter (D) = 2.5 cm = 0.025 m
Internal heat generation rate ( qG V) = 12 W
End temperature of the rod: T1 = 90°C T2 = 70°C
ASSUMPTIONS
The system has reached steady state
The heat loss through the insulation is negligible
The steel is 1% carbon steel
Constant thermal conductivity
The plate temperatures are constant
Heat is generated uniformly throughout therod
