Prediction of Maximum Temperature in Cylinders with Internal Heat Generation

Thehot-spot temperature occurring within a heat source is determined for each of eleven sets of boundary conditions. The shape of the heat source is that of a hollow, right-circular cylinder. The internal heat generation is considered to be uniformly distributed. The mathematical model of each boundary-value problem consists of a central difference approximation to the Poisson equation and the temperature and heat flow boundary conditions. Each model is expressed in terms of normalized (dimensionless) variables so that its solution is applicable to hollow, cylindrical heat sources regardless of dimension or thermal conductivity. Some of the solutions are presented in analytical form and all are presented graphically. An example illustrates the ease with which the six-step procedure given may be used to determine the hot-spot temperature in a heat source that is characterized by one of the eleven sets of boundary conditions.