Temperature Field Due to a Time Dependent Heat Source of Spherical Geometry in an Infinite Medium

Abstract

A solution is given for the heat conduction problem in which a sphere generating heat, at a rate which is proportional to time raised to the minus one-half power, is embedded in an infinite medium. The solution is of use in the thermistor probe technique for the determination of both the thermal conductivity and diffusivity of media which wet the surface of the thermistor. The thermistor bead is treated as a spherical distributed thermal mass and the coupled thermal response of the bead and the medium are presented. Typical temperature profiles both in the sphere and in the surrounding medium are presented.