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International Heat Transfer Conference 7

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

TEMPERATURES IN SEMI-INFINITE BODY HEATED BY CONSTANT HEAT FLUX OVER HALF SPACE

B. Litkouhi
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824 USA

James V. Beck
Dept. of Mechanical Engineering, Michigan State University, USA

Abstract

This paper presents the analytical solution for the transient temperature distribution in a semi-infinite body that is heated by a constant flux over half the surface and is insulated over the other half. The solution is a basic one in heat conduction and has a number of direct applications. It is also important because it is a "building block" that can be utilized in several indirect ways. One way is to generate (using the concepts of sources and sinks) solutions for infinite and finite plate geometries with insulated or isothermal surfaces opposite or normal to the heated surface. Some of these applications are discussed. Another use for the basic solution -and others that can be built from it - is as a kernel in the transient surface element method.
The general solution is given in terms of an integral which is shown to be conveniently and efficiently evaluated by two series expressions. Results displayed as tables and figures and examples of the use of the solution are also provided.

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