Nonuniform Cooling of a Heat-Generating Cylinder or Sphere

Abstract

A heat-generating solid cylinder or sphere is cooled in steady state with a heat transfer coefficient which varies arbitrarily on the surface. A solution is obtained which permits exact calculation of the temperature distribution. Simple approximate solutions are also obtained for the two cases where (a) the heat transfer coefficient does not differ greatly from its average value, and (b) the coefficient differs greatly from its average value. Numerical studies are made, and the errors resulting from the approximate solutions are calculated.