Consider a pan placed on top of electric range to cook spaghetti. The bottom section of the pan is 0.4 cm thick and has a diameter of 18 cm. The electric heating unit on the range top consumes 800 W of power during cooking, and 80 percent of the heat generated in the heating element is transferred uniformly to the pan. Assuming constant thermal conductivity and steady state operation. The heat transfer can be approximated as being one- dimensional through the bottom surface to the top. Take the direction normal to the bottom surface to be the x-axis. Required:
a. Perform an energy balance on a thin element of the pan during a small-time interval △t , and indicate which terms may be neglected or ignored and why?
b. Assuming constant thermal conductivity, obtain the differential equation that describes the variation of the temperature in the bottom section of the pan during steady state operation.