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An aluminum pan whose thermal conductivity is 237 W/m^2$^\circ{}$C has a flat bottom whose diameter is 20 cm and thickness 0.6 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 700 W. If the inner surface of the bottom of the pan is 105$^\circ{}$C, determine the temperature of the outer surface of the bottom of the pan.
Solution
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$\text{\textcolor{#4257b2}{\textbf{Given}}}$

Aluminum pan thickness $L = 0.6 \ \mathrm{Cm}$

Aluminum pan diameter $D = 20 \ \mathrm{Cm}$

Thermal conductivity $K = 237 \ \mathrm{\dfrac{W}{m\cdot ^\circ C}}$

Rate of heat transfer $\dot{Q} = 700 \ \mathrm{W}$

Inner surface of the bottom of the pan is $T_{in} = 105 \ \mathrm{^\circ C}$
$\text{\textcolor{#4257b2}{\textbf{Required}}}$
 Determine the temperature of the outer surface of the bottom of the pan.
$\text{\textcolor{#4257b2}{\textbf{Assumptions}}}$

Steady state operation.

heat transfer in neglected by all modes except by conduction.
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