Flow of heat from a wedge into a surrounding medium

Abstract

In this report the transient temperature field due to the cooling of a thin, liquid wedge by a surrounding infinite solid is calculated. It is shown that there exists a self-similar solution which is a function of two indepedent variables, namely, the angular co-ordinate and a combination of radial distance, time and diffusivity. On the assumption that the change in phase of the medium may be ignored, a solution in infinite series for the temperature field is derived, using a step-by-step procedure. When the theory is applied to a practical case, the step-by-step calculations converge rapidly everywhere, except near the tip of the wedge. The predicted motion of the isothermal surfaces is displayed graphically for an arbitrary time sequence. From these results it may be inferred that solidificatlon proceeds from the vertex primarily in the radial direction. An attempt is made in the appendix to extend the theory by allowing for a change in the state of the medium. Certain applications of the theory to other heat conduction problems are suggested.