Question

A hot plate consists of a flat electrical resistor, which is adiabatically insulated on one side and on the other side is in contact with a ceramic layer of 1 cm thickness and 30 W/mK thermal conductivity. The hot plate is operated inside a fume hood, where air at 20 C flows over producing convective cooling on the top surface of the heater with a heat transfer coefficient of 15 W/mK The plate generate a total heat transfer rate of 100 W and has an area of 30 cm x 30 cm. What is the temperature at the interface between the plate and the ceramic layer? Find the answer WITHOUT using the resistance model. Instead, you may only use conservation of energy and Fourier law. You may have to consider multiple control volumes to arrive at a solution, for instance the resistor, the ceramic, and some of the interfaces. You cannot assume that q=q=kA ∆T/L, unless you prove mathematically that dT/dx=∆T/L Plot the temperature variation in the ceramic layer as function of the ceramic layer thickness. What is the heat transfer rate at the midplane of the ceramic layer thickness? How is that compared with the heat transfer rate at the surface of the layer? Express this heat transfer rate in terms of temperature across the ceramic layer and a thermal resistance. Plot the temperature variation in the resistor as function of the resistor layer thickness. Assume the resistor has a thermal conductivity of 80 W/mK and a thickness of 5 mm. What is the heat transfer rate in the resistor at the bottom (interface between the resistor and adiabatic insulation), at the midplane of the resistor and at the top (interface between the ceramic layer and the resistor). Can you express the heat transfer rate as the ratio between the temperature difference between the top and bottom of the resistor and a thermal resistance? Why not?

To the commenter asking for more data, I was not given any more data by my professor.

Answer 1