Analytical Solution of Diffusion Thermo Effect on MHD Second Grade Fluid Flow with Heat Generation and Chemical Reaction through an Accelerated Vertical Plate

Abstract: The objective of this model is to examine the Dufour effect on unsteady free convection second-grade fluid flow past an accelerated moving plate subjected to the magnetic field through a porous medium. The thermal radiation and chemical reactions are also taken into account. The constitutive governing equations of the model with all levied initial and boundary conditions are written in non-dimensional form. The non-dimensional equations that govern the flow model are transformed into a time-fractional model using the Caputo, Caputo–Fabrizio, and Atangana–Baleanu time-fractional derivatives. The Laplace transform technique is applied to the differential equations of the flow model to obtain the exact solution for concentration, temperature, and velocity fields. The expression for the Sherwood number, the Nusselt number, and skin friction are also derived analytically. The effects of diffusion-thermo, chemical reactions, second-grade parameterfractional parameter (γ), porosity, magnetic parameter, heat absorption/generation, and thermal radiation on velocity profiles are studied through various figures. It is observed that the velocity profiles for Caputo–Fabrizio fractional derivatives are higher as compared to Caputo and Atangana–Baleanu fractional derivatives. It is also seen that for the value of fractional parameter γ→1, the velocity profiles obtained via Caputo, Caputo–Fabrizo, and Atangana–Baleanu derivatives are identical. Keywords: Second-grade fluid, Free convection, Chemical reaction, Diffusion thermo, Heat generation, Caputo, Caputo–Fabrizio, Atangana–Baleanu fractional derivative.