Heuristics as an alternative to variational calculus for optimization of a class of thermal insulation systems

This article reports an alternative treatment in lieu of the principle of variational calculus for a certain class of optimization problems. In particular, the optimum distribution of insulating material on one side of a flat plate for minimum heat transfer is sought when the other side is exposed to a laminar forced convection. Both conjugate and non-conjugate formulations of the problem are conceived and closed form solutions are presented. Interestingly, optimized insulation profile exhibits a category of equipartition principle in some macroscopic domain. Expression for minimum heat transfer is a function of Biot number in non-conjugate analysis of the model. Contrastingly, the non-dimensional group image is the characteristic parameter for conjugate formulation. Finally, Bejan’s method of intersecting asymptotes is employed to find an order of magnitude for a ceiling value of the wall material. With some scale factor, a range image for the representative material volume can be ascertained, beyond which the optimization exercise reduces to a trivial one and traditional constant thickness profile becomes a recognized design.