A Numerical Study on Atangana–Baleanu and Caputo–Fabrizio Analysis of Fractional Derivatives for the Effects of Variable Viscosity and Thermal Conductivity on an MHD Flow Over a Vertical Hot Stretching Sheet with Radiation and Viscous Dissipation

Abstract

A numerical analysis has been made to study the effects of variable viscosity and thermal conductivity over a vertical hot stretching sheet by using Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) fractional derivatives under the application of magnetic field in two-dimensional steady flow. As the viscosity and thermal conductivity of a fluid are dependent on temperature, these properties are taken as a variable. The effects of radiation and viscous dissipation are also taken into account. The governing partial differential equations along with the boundary conditions are transformed into ordinary form by 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 the discritized equations are solved numerically using 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., parameter of viscosity, parameter of thermal conductivity, parameter of magnetic field, radiation parameter, heat source parameter, Schmidt number, chemical reaction parameter, etc., on velocity, temperature, and concentration distribution are represented 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.