Optimization of Multiple Thin Thermal Insulation Layers

Abstract:- Given prescribed quantities of two or more thermal insulation materials, how should they be distributed around a body so as to minimize the rate of loss of heat from that body? The application of the calculus of variations enables us to answer this question. The governing optimal coupled boundary-value problem posed over the domains occupied by the two materials has been formulated previously by the author and solved for the special case of a spherical body. In this paper the optimal boundary-value problem is posed for the general two-dimensional case where several thin layers of material are to be distributed around an arbitrary infinite prismatic body, whose surface has smoothly varying curvature. A regular perturbation procedure is applied to obtain the solution. The interesting finding emerges, that there is no unique optimal solution, but a family of solutions satisfying the optimality conditions