Consider an aluminum pan used to cook stew on top of an electric range. The bottom section of the pan is L = 0.25 cm thick and has a diameter of D = 18 cm. The electric heating unit on the range top consumes 900 W of power during cooking, and 90 percent of the heat generated in the heating element is transferred to the pan. During steady operation, the temperature of the inner surface of the pan is measured to be 108°?C. Assuming temperature-dependent thermal conductivity and one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of this heat conduction problem during steady operation. Do not solve.

Question

What will be an ideal response?

Answer 1

Heat conduction through the bottom section of an aluminum pan that is used to cook stew on top of an electric range is considered. Assuming variable thermal conductivity and one-dimensional heat transfer, the mathematical formulation (the differential equation and the boundary conditions) of this heat conduction problem is to be obtained for steady operation.

Assumptions 1 Heat transfer is given to be steady and one-dimensional. 2 Thermal conductivity is given to be variable. 3 There is no heat generation in the medium. 4 The top surface at x = L is subjected to specified temperature and the bottom surface at x = 0 is subjected to uniform heat flux.

Analysis The heat flux at the bottom of the pan is



Then the differential equation and the boundary conditions for this heat conduction problem can be expressed as