Optimization of surface reflectivity in a model of complex heat transfer Gleb V. Grenkin

• Гренкин Глеб Владимирович

  Gleb V. Grenkin. Vladivostok State University. Vladivostok. Russ

he paper deals with a mathematical model that is a boundary-value problem for the heat conduction equation coupled with an approximation of the radiative transfer equation within the third order simplified spherical harmonics method. These equations provide a description of the steady state of the process of complex heat transfer in a bounded domain. The problem of optimal control of surface reflectivity to obtain the desired heat distribution is considered. Problems of this class may arise when calculations are needed for heat transfer at high temperatures and the coating of the inner surface is to be chosen to achieve optimal heat outflow by providing an optimal relationship between absorbed and reflected radiation. For the solution of this problem, optimality conditions are obtained, the existence of optimal solutions
is proved, and the bang-bang property of optimal controls is established.
Keywords: radiative heat transfer, optimal control, spherical harmonics method, diffusion approximation.