Transient Heat Transfer in a Partially Cooled Cylindrical Rod

Finite element and finite difference solutions are obtained for transient temperature distribution in a partially cooled cylindrical rod that generates heat at a uniform rate. A portion of the rod is immersed in a coolant reservoir that is maintained at constant temperature, and the exposed portion of the rod is cooled by convective heat transfer. Because thermal conductivity of the rod is temperature dependent, the governing partial differential equation is nonlinear. The analytical techniques utilized in solving the problem could be applied to analyzing the cooling of spent nuclear fuel rods. The finite difference method used to solve the problem utilizes an implicit formulation of the governing equation, and a numerical technique for handling the nonlinear terms. Validation of the numerical solution is obtained by comparing the results at a specified time against those generated by a commercial finite element software package. The computer model for the problem was used to estimate heat generation rates that could initiate meltdown of a fuel rod.