Optimal insulation of structures with varying thermal conductivity

The optimal distribution of a limited amount of insulation material on a composite structure is obtained. Three cases for the variation of the composite wall thermal conductivity were considered. These are 1) power, 2) linear, and 3) exponential types of variation of wall thermal conductivity with an in-plane direction along the surface of the wall. The surfaces of the wall are assumed to either have constant temperatures or be exposed to ambient at given temperatures. The variation of the optimum insulation thickness is shown to be relatively smooth and easily applicable for all three profiles of thermal conductivity. For a certain optimum length of composite structure, optimal distribution of the insulation material provides maximum percent energy savings. Optimal distribution of the insulation material may require partially covering the surface.