Transient Two-Dimensional Heat Conduction Problem with Partial Heating near Corners

[+] Author and Article Information
Robert McMasters

Department of Mechanical Engineering, Virginia Military Institute, Lexington, Virginia 24450

Filippo de Monte

Department of Industrial and Information Engineering and Economics, University of L'Aquila, Via G. Gronchi n. 18, 67100 L'Aquila, Italy

James Beck

Department of Mechanical Engineering, Michigan State University, East Lansing, Mich. 48824

Donald Amos

Sandia National Laboratories, Albuquerque, NM 87110

1Corresponding author.

ASME doi:10.1115/1.4037542 History: Received April 06, 2017; Revised June 28, 2017


This paper provides a solution for two-dimensional heating over a rectangular region on a homogeneous plate. It has application to verification of numerical conduction codes as well as direct application for heating and cooling of electronic equipment. Additionally, it can be applied as a direct solution for the inverse heat conduction problem, most notably used in thermal protection systems for re-entry vehicles. The solutions used in this work are generated using Green's functions. Two approaches are used which provide solutions for either semi-infinite plates or finite plates with isothermal conditions which are located a long distance from the heating. The methods are both efficient numerically and have extreme accuracy, which can be used to provide additional solution verification. The solutions have components that are shown to have physical significance. The procedure involves the derivation of previously-unknown simpler forms for the summations, in some cases by virtue of the use of algebraic components. Also, a mathematical identity given in this paper can be used for a variety of related problems.

Copyright (c) 2017 by ASME
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