A Numerical Study on Atangana-Baleanu and Caputo-Fabrizio Fractional Derivatives for MHD Flow Past a Moving Vertical Plate with Heat Source and Variable Viscosity and Thermal Conductivity

Abstract

A numerical investigation on MHD free convective flow past a moving vertical plate with heat and mass transfer has been done by using Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives. As the viscosity and thermal conductivity of a fluid are dependent on temperature, these properties are considered as a variable. We have also considered heat source, radiation and chemical reaction. The governing partial differential equations along with the boundary conditions are made dimensionless using suitable similarity transformations so that physical parameters appear in the equations and interpretations on these parameters can be done suitably. The equations so obtained are discritized using ordinary finite difference scheme and we solved the discritized equations numerically adopting a method based on the Gauss-Seidel iteration scheme. Numerical techniques are used to find the values from AB and CF formulae for fractional derivatives on time. The effects of various parameters involved in the problem viz., viscosity parameter, thermal conductivity parameter, magnetic field parameter, radiation parameter, heat source parameter, Schmidt number, chemical reaction parameter etc. on velocity, temperature, concentration distribution, skin-friction, heat transfer rate, and Sherwood number at the plate have been shown graphically. The effects of each parameter are prominent. A comparison has been given on AB and CF methods in tabular form. It is observed that both the methods agreed well.