Bounds of stability in heat conduction with internal heat generation

The criterion for the existence of a steady-state temperature distribution in a plane slab or system with internal heat generation is critically examined. The rate of heat generation from the non-uniformly populated heat sources in the slab is assumed to be linearly dependent on the temperature differential between the slab and the environment. The critical combination of the parameters under which the system can function satisfactorily is found to depend not only on the manner in which the heat sources are populated but also on the boundary conditions imposed on the system. The results of this study thus indicate that an inadvertent change from the designed boundary conditions can significantly alter the life span of the system.