Heat transfer is not an intuitive process muses the Curious Cook. Does doubling the thickness of a hamburger approximately double the cooking time? What effect does the initial temperature have on cooking time? To answer these questions, develop a model to do virtual cooking of meat of thickness 2L in a double-sided grill. The meat is initially at 20°C when it is placed in the grill and both sides experience convection heat transfer characterized by an ambient temperature of 100°C and a convection coefficient of 5000 W/m2 ∙ K. Assume the meat to have the properties of liquid water at 300 K and to be properly cooked when the center temperature is 60°C.

(a) For hamburgers of thickness 2L = 10, 20, and 30 mm, calculate the time for the center to reach the required cooking temperature of 60°C. Determine a relationship between the cooking time and the thickness. For your solution use the finite-element method of FEHT, the ready-to-solve model in the Models/Transient Conduction/Plane Wall section of IHT, or a numerical procedure of your choice. For one of the thicknesses, use an appropriate analytical solution to validate your numerical results.

(b) Without performing a detailed numerical solution, but drawing on the results of part (a), what can you say about the effect on the cooking time of changing the initial temperature of the me.