International Journal of Theoretical and Applied Mathematics 2022; 8(2): 30-39 http://www.sciencepublishinggroup.com/j/ijtam doi: 10.11648/j.ijtam.20220802.11 ISSN: 2575-5072 (Print); ISSN: 2575-5080 (Online) MHD Flow of Second Grade Fluid with Heat Absorption and Chemical Reaction Muhammad Ramzan 1, * , Ahmad Shafique 1 , Mudassar Nazar 1, 2 1 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan 2 School of Mathematical Sciences, University of Science and Technology of China, Hefei, China Email address: * Corresponding author To cite this article: Muhammad Ramzan, Ahmad Shafique, Mudassar Nazar. MHD Flow of Second Grade Fluid with Heat Absorption and Chemical Reaction. International Journal of Theoretical and Applied Mathematics. Vol. 8, No. 2, 2022, pp. 30-39. doi: 10.11648/j.ijtam.20220802.11 Received: January 26, 2022; Accepted: March 2, 2022; Published: March 18, 2022 Abstract: The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynamics (MHD) flow of fractional second grade fluid immersed in a porous media over an exponentially accelerated vertical plate. In addition, other factors such as heat absorption and chemical reaction are used in the problem. More exactly, the fractional model has been developed using the generalized Fick’s and Fourier’s laws. The Caputo-Fabrizio (CF) fractional derivative has been used to solved the model. Initially, the flow modeled system of partial differential equations are transformed into dimensional form through suitable dimensionless variable and then Laplace transform technique has been used to solved the set of dimensionless governing equations for velocity profile, temperature profile, and concentration profile. The influence of different parameters like diffusion-thermo, fractional parameter, magnetic field, chemical reaction, heat obsorption, Schmidt number, time, Prandtl number and second grade parameter are discussed through numerous graphs. From figures, it is observed that fluid motion decreases with increasing values of Schmidt number, Prandtl number, magnetic parameter, and chemical reaction, whereas velocity field decreases with decreasing values of diffusion-thermo and mass grashof number. In order to check the athenticity of present work, we compare the present work with already published model graphically. Keywords: Free Convection, Chemical Reaction, Diffusion-thermo, Magnetic Field 1. Introduction Now a days, magnetohydrodynamic (MHD) has been extended into wide areas of basic and applied research in sciences and engineering. The study of non-Newtonian fluid becomes very interested due to variety of technological applications like making of plastic sheets, lubricant’s performance and motion of biological fluid. Numerous fluid models have been presented to demonstrate the distinction between Newtonian and non-Newtonian fluids. Kai-Long Hsiao [1] worked on magnetohydrodynamics Maxwell fluid. Shah et al. [2] discussed the influence of magnetic field of fractional order. The model on Jeffrey fluid be the simplest and most popular, and it has attracted the interest of researchers in the field. Some of the work on Jeffrey fluid are of Das [3] and Qasim [4]. Ahmad et al. [5] compared the generalized form of Jeffrey fluid flow acquired by contemplating fractional derivative of singular kernel (Caputo) and non-singular kernel (Caputo-Fabrizio). During the last decade, different generalized fractional derivatives have appeared in the literature that are derivatives of Caputo, Caputo-Fabrizio, constant proportional Caputo [6, 7]. Some studies of free convection on an inclined plane invarious thermal and mechanical situations have recently been presented by mathematicians [8-14]. Some mathematical models of second grade fluids are industrial oils, slurry streams, and dilute polymer solutions with different geometry and boundary conditions. The Sheikh et al. [15] discussed the casson fluid. Ahmed et al. [16] has analyzed MHD heat transfer into convective boundary layer with a minimal pressure gradient. Convective mixed MHD flow studied by Narayana [17], while Authors in [18] worked on MHD fluid over a plate. Khan et al. [19] presented a fractional flow of fluid on a vertical surface