### Convective heat transfer coefficient of the boiling water

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An aluminum pan whose thermal conductivity is 237 W/(m K) has a flat bottom whose diameter is 20 cm and thickness 0.4 cm. Heat is transferred steadily to the boiling water through the bottom of the pan. The temperature on the underside of the pan is 105°C; the bulk of the boiling water is at 100°C. The convective heat transfer coefficient of the boiling water is 5,000 W/(m^2 K).

a) Draw a picture showing the dimensions of the pan, heat flowing through the bottom of the pan and the heat transferred from the bottom of the pan to the bulk of the liquid. Show the temperature on the underside of the pan and in the bulk liquid. Label the temperature at the inside bottom of the pan T*. Explain why it is reasonable to assume that the heat flow through the bottom of the pan equals the heat transferred from the bottom of the pan to the bulk liquid.

b) Find equations relating the heat flow through the bottom of pan and the heat transferred from the bottom of the pan to the bulk of the liquid. Both of these equations should contain T* as an unknown. Solve these equations, and find the heat flow and T*. Report T* to 4 significant figures. Show all steps and work.

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