General solution for the temperature distribution

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Reference no: EM13947764

Consider a long solid tube, insulated at the outer radius r2 and cooled at the inner radius r1, with uniform heat generation q (W/m3) within the solid.

1. Obtain the general solution for the temperature distribution in the tube.

2. In a practical application a limit would be placed on the maximum temperature that is permissible at the insulated surface (r = r2). Specifying this limit as Ts,2, identify appropriate boundary conditions that could be used to determine the arbitrary con- stants appearing in the general solution. Determine these constants and the correspond- ing form of the temperature distribution.

3. Determine the heat removal rate per unit length of tube.

4. If the coolant is available at a temperature T00, obtain an expression for the convection coefficient that would have to be maintained at the inner surface to allow for operation at prescribed values of Ts,2 and q.

Reference no: EM13947764

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