Constructal distribution of multi-layer insulation

Here, we show how to distribute multiple layers of insulation along a nonisothermal enclosure so that the total heat loss is minimal. The types and total amounts of insulation materials are fixed. Variables are the thicknesses of the insulation layers, their relative amounts, the temperature of the insulated surface, and the cross-sectional area of the enclosure. We show that, first, the structure of the multi-layer insulation must be such that the thicknesses of all the layers vary in the same way in the longitudinal direction x. Second, the x dependence of the enclosure cross-sectional area has a significant effect on the heat loss reduction associated with using the distributed insulation design. Greater reductions in heat loss are obtained when the enclosure is tapered such that it is narrower in the direction of the warm end. Third, the x dependence of the temperature distribution along the insulated wall has a significant effect on the reduction in heat loss through reduction in heat loss through the multi-layer insulation. Greater reductions are obtained when the wall temperature distribution is more convex. Even greater reductions in heat loss are possible when the three design features summarized previously are implemented simultaneously. Copyright © 2011 John Wiley & Sons, Ltd.