Equivalences and correspondences between the deforming body induced flow and heat in two-three dimensions

This paper is concerned with the analysis of magnetohydrodynamic fluid flow and heat transfer due to two-three dimensional porous and deforming (stretching/ shrinking) bodies. It is aimed to prove from a theoretical approach that several boundary value problems regardless of two or three dimensions associated with the stretching/shrinking surfaces having different physical origin result in either the equivalent structure of governing equations or the interchangeable role of mechanisms of stretching or shrinking. Therefore, a link is created between the deforming surface phenomena considered in different geometries in the open literature. On the grounds of the provided theorems, a special care must be paid before working on the variations of this physical phenomenon, since the skin friction and the rate of heat transfer of engineering interest may have already been extracted from an already studied twin problem, namely the two-dimensional nonlinear (power-law) deformation analysis. It is further shown that the radial nonlinear stretching/shrinking sheet problem also evolves into the two-dimensional nonlinear wall deformation problem.