Research Papers: Conduction

Transient Two-Dimensional Heat Conduction Problem With Partial Heating Near Corners

[+] Author and Article Information
Robert L. McMasters

Department of Mechanical Engineering,
Virginia Military Institute,
Lexington, VA 24450
e-mail: mcmastersrl@vmi.edu

Filippo de Monte

Department of Industrial and Information
Engineering and Economics,
University of L'Aquila,
Via G. Gronchi n. 18,
L'Aquila 67100, Italy
e-mail: filippo.demonte@ing.univaq.it

James V. Beck

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: beck@egr.msu.edu

Donald E. Amos

Sandia National Laboratories,
Albuquerque, NM 87110
e-mail: deamos@swcp.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 6, 2017; final manuscript received June 28, 2017; published online September 13, 2017. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(2), 021301 (Sep 13, 2017) (10 pages) Paper No: HT-17-1191; doi: 10.1115/1.4037542 History: Received April 06, 2017; Revised June 28, 2017

This paper provides a solution for two-dimensional (2D) 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 (GFs). 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.

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Grahic Jump Location
Fig. 1

Geometry for nonhomogeneous problem

Grahic Jump Location
Fig. 2

Plot of dimensionless temperature as a function of dimensionless vertical position with ã=1, x̃=0, and b̃=10

Grahic Jump Location
Fig. 3

Plot of dimensionless temperature as a function of dimensionless vertical position with ã=1, x̃=0, and b̃=10



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