Technical Briefs

Green’s Function Approach to Nonlinear Conduction and Surface Radiation Problems

[+] Author and Article Information
Matthew R. Jones, Vladimir P. Solovjov

Department of Mechanical Engineering, Ira A. Fulton College of Engineering and Technology, Brigham Young University, Provo, UT 84602-4201

J. Heat Transfer 132(2), 024502 (Dec 04, 2009) (5 pages) doi:10.1115/1.4000234 History: Received November 15, 2008; Revised May 14, 2009; Published December 04, 2009; Online December 04, 2009

An exact approach for solving both transient and steady state conduction and surface radiation problems is presented. The method is based on the use of Green’s function, and the temperature field is obtained by solving an integral equation. This is in contrast to the approach presented in radiative heat transfer texts in which temperature profiles are obtained from the simultaneous solution of coupled integral and differential equations. The analysis presented in this paper provides insight into the solution of this important class of problems. The method is illustrated by solving two representative problems. The first problem considered is the steady state analysis of a radiating fin. The second problem considered is the transient analysis of a radiating target, which is used to determine the temporal response of radiation thermometers.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Illustration of the radiating fin problem

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Figure 2

Nondimensional radial temperature profile for the base case

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Figure 3

Fin performance parameters as a function of (a) the profile number, (b) the solar heating parameter, and (c) the aspect ratio

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Figure 4

Target used to assess the temporal response of a radiation thermometer

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Figure 5

Comparison between the exact and linearized temperature profiles (a) time-dependent temperature profile at the center of the target and (b) radial temperature profile at steady state




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