The Initial Stages of Cooling of a Non-homogeneous Sphere

An asymptotic representation is obtained, valid for small valuesof the time variable, of the temperature distribution in a solidsphere cooling from a prescribed (non-symmetrical) initial distributionof temperature by radiative exchange with its surroundings.The thermal properties of the solid are assumed to be known(sufficiently smooth) functions of the radial co-ordinate r.The method of analysis applied to this problem can be used toinvestigate the initial stages of other time-dependent processesin non-homogeneous media.