Solution of a Heat Flow Problem

Abstract

This paper deals with the heat flow through a rectangle subject to the following boundary conditions : One end is completely insulated (without heat flux across it) and at the opposite end a constant temperature gradient is maintained; the remaining sides radiate into a medium which is at zero temperature. Initially the rectangle is at zero temperature. The problem is converted into a homogeneous one by considering a rectangle of twice the length with a uniformly distributed heat source along the centre line. The solution of this problem is effected by using particular solutions given in Carslaw and Jaeger. The problem considered is of interest in connection with the testing of heat-insulating materials.