Consider a steel pan used to boil water on top of an electric range. The bottom section of the pan is L = 0.5 cm thick and has a diameter of D = 20 cm. The electric heating unit on the range top consumes 1250 W of power during cooking, and 85 percent of the heat generated in the heating element is transferred uniformly to the pan. Heat transfer from the top surface of the bottom section to the water is by convection with a heat transfer coefficient of h. Assuming constant 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

Answer 1

Heat conduction through the bottom section of a steel pan that is used to boil water on top of an electric range is considered. Assuming constant 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 constant. 3 There is no heat generation in the medium. 4 The top surface at x = L is subjected to convection 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