Research Papers: Conduction

Boundary Control of Temperature Distribution in a Spherical Shell With Spatially Varying Parameters

[+] Author and Article Information
Hossein Rastgoftar

Mechanical, Materials and Aerospace Engineering,  University of Central Florida, Orlando, Florida

Mohammad Eghtesad

Department of Mechanical Engineering,  School of Engineering, Shiraz University, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iraneghtesad@shirazu.ac.ir

Alireza Khayatian

Department of Electrical Engineering,  School of Engineering, Shiraz University, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran

J. Heat Transfer 134(1), 011302 (Nov 18, 2011) (5 pages) doi:10.1115/1.4004451 History: Received October 29, 2010; Revised June 19, 2011; Published November 18, 2011; Online November 18, 2011

This paper presents a solution to the control (stabilization) problem of temperature distribution in spherical shells with spatially varying properties. The desired temperature distribution satisfies the steady-state heat conduction equation. For the spherical shell under consideration, it is assumed that material properties such as thermal conductivity, density, and specific heat capacity may vary in radial, polar, and azimuthal directions of the spherical shell; the governing heat conduction equation of the shell is a second-order partial differential equation. Using Lyapunov’s theorem, it is shown how to obtain boundary heat flux required for producing a desired steady-state distribution of the temperature. Finally, numerical simulation is provided to verify the effectiveness of the proposed method such that by applying the boundary transient heat flux, in-domain distributed temperature converges to its desired steady-state temperature.

Copyright © 2012 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The level curves of the desired temperature distribution contour Td(θ,ϕ) on the polar plane




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