Consider the process of heat conduction through the bottom section of a 14-cm th

Question

Consider the process of heat conduction through the bottom section of a 14-cm thick circular aluminum pan that is used to cook stew on top of an electric range. The 900W electric range is at 90% efficiency, and the diameter of the pan is 18cm. Assume that the pan cooks at a steady temperature of 108C with a constant thermal conductivity, k = 23.5 W/mK.

a) Develop an appropriate set of equations with respects to temperature, T(x), that can be used to model this heat transfer problem,
b) Solve this system of equations to obtain a solution for T(x) and plot it, and
c) Evaluate heat flux through the metal pan.

Explanation / Answer

the heat that enters is 900x0.9= 810 W

so conduction equation isgiven by:

Q=kA(T-T0)/x

810=23.5 * (1/4)*pi*((0.14)^2) *( T(x) - 108) / x

so we solve T (x)

a) T(x) = 2239.09 x + 108 [°C]

b)

c) Q= 23.5 * (1/4)*pi*((0.18)^2) *( T(x) - 108) / x

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