On the Optimal Insulation of Conductors

S. J. Cox, B. Kawohl and P. X. Uhlig
Additional contact information
S. J. Cox: Rice University
B. Kawohl: Universität Köln
P. X. Uhlig: St. Mary's University

Journal of Optimization Theory and Applications, 1999, vol. 100, issue 2, No 1, 253-263

Abstract: Abstract We coat a conductor with an insulator and equate the effectiveness of this procedure with the rate at which the body dissipates heat when immersed in an ice bath. In the limit, as the thickness and conductivity of the insulator approach zero, the dissipation rate approaches the first eigenvalue of a Robin problem with a coefficient determined by the shape of the insulator. Fixing the mean of the shape function, we search for the shape with the least associated Robin eigenvalue. We offer exact solutions for balls; for general domains, we establish existence and necessary conditions and report on the results of a numerical method.

Keywords: Two-phase conductors; eigenvalues; reinforcements; boundary conditions of the third type (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021773901158

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