Two-phase modeling of three-dimensional MHD porous flow of Upper-Convected Maxwell (UCM) nanofluids due to a bidirectional stretching surface: Homotopy perturbation method and highly nonlinear system of coupled equations

The present communication concerns with three-dimensional MHD/Porous flow of Maxwell nanofluids generated due to a bidirectional stretching surface in the presence of the Brownian motions of nanoparticles. The ability of Maxwell fluid model to capture the stress relaxation of some polymeric liquids together with the applications of stretching sheet flows in polymer industries shortly exhibit the importance of the subject matter. To this end, the associated conservative equations are initially converted to similarity forms. Here, by means of contemporary mathematics, it is presented an excellent and perhaps the simplest solution to the problem of interest in a generalized form for the first time. The distinctive attributes of the present paper can be summarized as: 1- Presenting the three-dimensional stretching flow of UCM fluid subject to a general consideration including nanoparticles Brownian motions, Darcy porosity and magnetic effects. 2- Analyzing the response of homotopy perturbation method to such nonlinearity. 3- A comprehensive report on the effects of the various engaged parameters. It is hopeful that the main features of such a fluid flow can be documented by means of the presented explicit analytic formulae and with the sufficiently provided figures which were hardly reachable until now. (C) 2018 Karabuk University. Publishing services by Elsevier B.V.