In Problem 3.48, the electrical power required to maintain the heater at To = 25°C depends on the thermal conductivity of the wall material k, the thermal contact resistance R’t,c and the convection coefficient h. Compute and plot the separate effect of changes in k and on the total heater power requirement, as well as the rate of heat transfer to the inner surface of the tube and to the fluid.
A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of 5°C. The tube wall has inner and outer radii of 25 and 75 mm, respectively, and a thermal conductivity of 10 W/m K. The thermal contact resistance between the heater and the outer surface of the tube (per unit length of the tube) is R’ t,c = 0.01 m∙ K/W. The outer surface of the heater is exposed to a fluid with T= 10°C and a convection coefficient of h = 100 W/m2 ∙ K. Determine the heater power per unit length of tube required to maintain the heater at To = 25°C.
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