Exact solutions of the mhd three-dimensional casson flow of a ternary hybrid nanofluid over a porous stretching/shrinking surface with mass transpiration

In this paper, the three-dimensional Casson (cid:29)ow of a ternary hybrid nano(cid:29)uid over a porous linearly stretching/shrinking surface in the presence of an external magnetic (cid:28)eld is considered. The surface deformation process is described by introducing two parameters of stretching/shrinking in the lateral directions. Using similarity transformations, the basic set of nonlinear partial di(cid:27)erential equations is converted into ordinary di(cid:27)erential equations. An exact analytical solution to this boundary value problem is obtained. The in(cid:29)uence of the Casson parameter, magnetic (cid:28)eld, porosity medium, and stretching/shrinking parameter, taking into account mass transpiration, on the velocity pro(cid:28)les and the skin friction coe(cid:30)cients is considered in detail. It has been established that the results obtained in some limited cases are in excellent agreement with the available data. Tables show the new results for the skin friction coe(cid:30)cients in the lateral directions ( x and y ) for di(cid:27)erent variants of surface deformation