Analytical Formulation for the Temperature Profile by Duhamel’s Theorem in Bodies Subjected to an Oscillatory Heat Source

[+] Author and Article Information
Jun Wen

Department of Mechanical Engineering, Louisiana State University, 2508 CEBA, Baton Rouge, LA 70803

M. M. Khonsari1

Department of Mechanical Engineering, Louisiana State University, 2508 CEBA, Baton Rouge, LA 70803Khonsari@me.lsu.edu


Corresponding author.

J. Heat Transfer 129(2), 236-240 (Jul 05, 2005) (5 pages) doi:10.1115/1.2424236 History: Revised July 05, 2005; Received December 31, 2005

An analytical technique is presented for treating heat conduction problems involving a body experiencing oscillating heat flux on its boundary. The boundary heat flux is treated as a combination of many point heat sources, each of which emits heat intermittently based on the motion of the flux. The working function of the intermittent heat source with respect to time is evaluated by using the Fourier series and temperature profile of each point heat source is derived by using the Duhamel’s theorem. Finally, by superposition of the temperature fields over all the point heat sources, the temperature profile due to the original moving heat flux is determined. Prediction results and verification using finite element method are presented for an oscillatory heat flux in a rectangular domain.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A rectangular domain subject to oscillatory heat flux on its top boundary

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Figure 2

Periodic square wave of working function of the point heat source

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Figure 3

Model of finite element method

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Figure 4

Temperature contour at steady state

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Figure 5

Comparison of temperature rise obtained analytically and by the finite element method at locations (L∕2,h), (L∕6,h), (5L∕6,h), and (L∕2,h∕2)



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