Boris P. Belinskiy, James W. Hiestand, John V. Matthews
Abstract:
We minimize, with respect to the cross sectional area, the mass of a
bar given the rate of heat transfer. The bar enhances the heat transfer
surface of a larger known mass to which the bar is attached.
This article is an extension of a previous publication by two coauthors,
where heat transfer from the sides of the bar was neglected and only
conduction through its length was considered. The rate of cooling is
defined by the first eigenvalue of the corresponding Sturm-Liouville problem.
We compare the mass of the computed variable cross-section bar with the mass
of a bar with constant cross-sectional area and the same rate of heat transfer,
and conclude that a fin design with constant, or near constant, cross-sectional
area is best.
Submitted December 14, 2014. Published August 10,2015.
Math Subject Classifications: 62K05, 80A20, 49R05, 35K05, 34B24, 65H10.
Key Words: Optimal design; heat transfer; heat equation; least eigenvalue;
Sturm-Liouville problem; calculus of variations;
transcendental equation; computer algebra.
Show me the PDF file (275 KB), TEX file, and other files for this article.
 |
Boris P. Belinskiy Department of Mathematics University of Tennessee at Chattanooga 615 Mccallie Avenue Chattanooga, TN 37403-2598, USA email: Boris-Belinskiy@utc.edu |
|---|---|
 |
James W. Hiestand College of Engineering University of Tennessee at Chattanooga 615 Mccallie Avenue Chattanooga, TN 37403-2598, USA email: James-Hiestand@utc.edu |
 |
John V. Matthews Department of Mathematics University of Tennessee at Chattanooga 615 Mccallie Avenue Chattanooga, TN 37403-2598, USA email: Matt-Matthews@utc.edu |
Return to the EJDE web page