A long copper bar of rectangular cross-section, whose width w is much greater than its thickness L, is maintained in contact with a heat sink at its lower surface, and the temperature throughout the bar is approximately equal to that of the sink, To. Suddenly, an electric current is passed through the bar and an airstream of temperature T is passed over the top surface, while the bottom surface continues to be maintained at To. Obtain the differential equation and the top surface boundary condition that could be solved to determine the temperature as a function of position and time in the bar.

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01-02-2021
Physics

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A long copper bar of rectangular cross-section, whose width w is much greater than its thickness L, is maintained in contact with a heat sink at its lower surface, and the temperature throughout the bar is approximately equal to that of the sink, To. Suddenly, an electric current is passed through the bar and an airstream of temperature T is passed over the top surface, while the bottom surface continues to be maintained at To. Obtain the differential equation and the top surface boundary condition that could be solved to determine the temperature as a function of position and time in the bar.

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