Simulation and optimization in the problems of design of spherical layered thermal shells

This paper describes the inverse problems of heat transfer, arising in designing multilayered spherical cloaking shells and other functional devices for controlling thermal fields. It is assumed that shells are comprised of a finite number of layers, each filled by a homogeneous isotropic or anisotropic medium. An exact solution for a partial case of a single-layer homogeneous anisotropic shell is presented and analyzed. An optimization approach used to reduce the inverse problems under consideration to control problems. A numerical algorithm for solving them is proposed, which is based on a particle swarm optimization, and the results of numerical experiments are discussed.