Maximum Internal Temperatures in One-Dimensional Geometries with Nonuniform Heat Generation and Equal Surface Temperatures

Abstract

The maximum temperature in an infinite slab, an infinite cylindrical shell, or a spherical shell, whose two bounding surfaces are kept at the same constant temperature, depends upon the distribution of heat sources in the region. We find precise upper and lower bounds for the error involved in replacing this maximum temperature by the maximum temperature for a uniform distribution of heat sources with the same average power density.