The quenching of a sphere with a uniform time dependent heat transfer coefficient, and the response of a sphere with a constant uniform heat source to a changing heat transfer coefficient, are formulated as integral equations for the surface temperature histories. Exact semi-analytical solutions are obtained for a rising or falling exponential approach of the heat transfer coefficient to a new value, and the results computed numerically, to show the good efficiency of an approximate method of solution based on the use of a synthetic kernel. Graphs are presented showing transient surface temperatures, and surface thermal stress histories for a range of Biot number variations. © 1969.
