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.