Method of synthetic constraint, Fermat’s principle and the constructal law in the fundamental principle of conductive heat transport

This article documents the method of synthetic constraint, a physical principle, to be applicable in the fundamental methodology of conductive heat flow, in replacement of calculus of variations and other optimal control theories. In particular, the optimum distribution of limited volume of insulating material on one side of a plane wall as well as cylindrically curved surface is obtained when the amount of insulating material is noninfluential to the imposed exponential temperature profile. The same physical theory is exercised for a generalized case of a stream suspended in an environment of different temperature and where the exponential wall temperature distribution is affected by the amount of insulation added. The result obtained conforms to those existing in open literature. Further from the physics of the problem it has been argued that a minimum exists for such class of problems of heat transfer from an insulated wall. Finally, it has been synthesized that Schmidt’s criterion for the fin design, the tangent law of conductive heat transport and Fermat’s principle in geometrical optics are but special stipulations of the method of synthetic constraint, which in turn is a corollary of constructal law. Thus the basis for analogies among physical theories is sought. The fundamental solution exhibits a category of equipartition principle.