Atangana-Baleanu and Caputo-Fabrizio Analysis of Fractional Derivatives on MHD Flow past a Moving Vertical Plate with Variable Viscosity and Thermal Conductivity in a Porous Medium

Dipen Saikia,Utpal Kumar Saha,Gopal Chandra Hazarika

doi:10.33889/ijmems.2021.6.2.030

Abstract

In this paper, a numerical investigation is presented for non-integer order derivatives with Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives for the variable viscosity and thermal conductivity over a moving vertical plate in a porous medium two dimensional free convection unsteady MHD flow. The effects of radiation have also been considered. The governing partial differential equations along with the boundary conditions are changed to ordinary form by similarity transformations. Hence physical parameters show up in the equations and interpretations on these parameters can be achieved suitably.By using ordinary finite difference scheme the equations are discritized and developed in fractional form. These discritized equations are numerically solved by the approach based on Gauss-seidel iteration scheme. Some numerical strategies are used to find the values of AB and CF approaches on time by developing programming code in MATLAB. The effects of all the physical parameters involved in the problem on velocity, temperature and concentration distribution are compared graphically as well as in tabular form. The effects of each parameter are found to be prominent. We have observed a significant variation of values under different parameters using AB and CF approaches on velocity, temperature and concentration distribution with respect to time.

Highlights

The boundary layer and heat transfer flow of a viscous fluid over a moving vertical plate in a porous medium have been investigated in a number of technological approaches such as warm rolling, metallic extrusion, petroleum industries, polymer extrusion, wires drawing and metallic spinning
A comparative study of Atangana-Baleanu and Caputo-Fabrizio evaluation of fractional derivatives for heat and mass transfer of fluid over a vertical plate has been done by Khan et al (2017)
The main objective of this paper is to investigate the effects of variable viscosity and thermal conductivity over a moving vertical plate in porous medium and comparing the results with the approaches AB and CF fractional derivatives

Summary

Introduction

The boundary layer and heat transfer flow of a viscous fluid over a moving vertical plate in a porous medium have been investigated in a number of technological approaches such as warm rolling, metallic extrusion, petroleum industries, polymer extrusion, wires drawing and metallic spinning. Javaherdeh et al (2015) studied the natural convection heat and mass transfer in MHD fluid flow past a moving vertical plate with variable surface temperature and concentration in a porous medium. A comparative study of Atangana-Baleanu and Caputo-Fabrizio evaluation of fractional derivatives for heat and mass transfer of fluid over a vertical plate has been done by Khan et al (2017). The main objective of this paper is to investigate the effects of variable viscosity and thermal conductivity over a moving vertical plate in porous medium and comparing the results with the approaches AB and CF fractional derivatives. 2. Mathematical Formulation Consider a two-dimensional free convection steady heat and mass transfer flow of viscous incompressible electrically conducting fluid past a moving vertical plate in a porous medium (Figure 1).

Atangana-Baleanu (AB) Fractional Derivatives

Caputo-Fabrizio (CF) Fractional Derivatives

Important Physical Parameters

Graphical Representation In

Comparision of AB and CF Fractional Derivatives for Various Values of the

Conclusion