Thermal stability of squire cylinders with non-uniform internal heat generation

Abstract

Squire's problem of thermal stability of a solid cylinder is examined with the augmentation of a non-uniform rate of internal heat generation. The non-uniformity is exemplified by a single term of the cylinder radius with a power of m. Three commonly encountered constant temperature, insulated and convective boundary conditions are used in the study. It is found that although analyses yield results covering the whole range of m, logical and useful formulations are found only in the realm of m ⩾- 0. When m ⩽- -2, the results are difficult to interpret without further study.