The optimization method in design problems of spherical layered thermal shells

Abstract

The inverse problem of designing multilayered spherical shells, intended for thermal cloaking a spherical body or concentrating heat in it, has been analyzed. The stationary heat conduction equation for an anisotropic medium is applied as an original mathematical model. The optimization method is used to reduce this inverse problem to an extreme problem, where the role of controls is played by the thermal conductivities of shell layers. A numerical algorithm for solving the problem is proposed, and the results of computational experiments are discussed.