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There is homogeneous constant heat generation for a cylindrical metal rod of length L and diameter D (heat conductivity coefficient, k). One side of the

There is homogeneous constant heat generation for a cylindrical metal rod of length L and diameter D (heat conductivity coefficient, k). One side of the rod is kept stable at T1 temperature while the other end is insulated. The lateral surface of the bar is in contact with the air at temperature T0. If the heat transfer coefficient between the air and the cylindrical surface is h, derive the model equation describing the two-dimensional and time-dependent temperature distribution in the cylindrical metal rod. Write the boundary conditions and initial condition. Draw a figure and list your assumptions with justifications. Do not solve the differential equation you have obtained.

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