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.
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Boundary Control of Temperature Distribution in a Spherical Shell With Spatially Varying Parameters
Hossein Rastgoftar,
Hossein Rastgoftar
Mechanical, Materials and Aerospace Engineering,
University of Central Florida
, Orlando, Florida
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Mohammad Eghtesad,
Mohammad Eghtesad
Professor
Department of Mechanical Engineering,
e-mail: eghtesad@shirazu.ac.ir
School of Engineering, Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
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Alireza Khayatian
Alireza Khayatian
Associate Professor
Department of Electrical Engineering,
School of Engineering, Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
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Hossein Rastgoftar
Mechanical, Materials and Aerospace Engineering,
University of Central Florida
, Orlando, Florida
Mohammad Eghtesad
Professor
Department of Mechanical Engineering,
School of Engineering, Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
e-mail: eghtesad@shirazu.ac.ir
Alireza Khayatian
Associate Professor
Department of Electrical Engineering,
School of Engineering, Shiraz University
, Mollasadra Avenue, Shiraz, Fars 71348-51154, Iran
J. Heat Transfer. Jan 2012, 134(1): 011302 (5 pages)
Published Online: November 18, 2011
Article history
Received:
October 29, 2010
Revised:
June 19, 2011
Online:
November 18, 2011
Published:
November 18, 2011
Citation
Rastgoftar, H., Eghtesad, M., and Khayatian, A. (November 18, 2011). "Boundary Control of Temperature Distribution in a Spherical Shell With Spatially Varying Parameters." ASME. J. Heat Transfer. January 2012; 134(1): 011302. https://doi.org/10.1115/1.4004451
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