Application of modern approach of Caputo-Fabrizio fractional derivative to MHD second grade fluid through oscillating porous plate with heat and mass transfer

In this research paper, we analyze the flow characteristics of magnetohydrodynamic second grade fluid with heat and mass transfer embedded in porous medium. The modeling of partial differential equations governs the flow have been established with modern approach of Caputo-Fabrizio fractional operator (CF)(partial derivative(delta)/partial derivative t(delta)). The partial differential equations of non-integer order derivatives have been solved by invoking Laplace and Fourier sine transforms. The new analytic solutions for temperature, concentration and velocity are investigated and expressed in terms of simple elementary functions. The corresponding general solutions have been particularized with and without magnetic field and porous medium for the classical Newtonian and second grade fluids as the limiting cases of our general results. The effects of the embedded physical and geometric parameters have been depicted through graphs for velocity, temperature and concentration respectively. The graphical results show several physical discrepancies and analogies on the fluid flow. Finally, our results suggest that increasing the Grashof number, heat transfer due to convection facilitates the flow velocity profile and an opposite trend is observed in thermal Grashof number as well. (C) 2018 The Authors. Published by IASE.