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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


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

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
Department of Basic and Applied Science, National Institute of Technology Arunachal Pradesh, Yupia, Arunachal Pradesh, India.

Utpal Kumar Saha
Department of Basic and Applied Science, National Institute of Technology Arunachal Pradesh, Yupia, Arunachal Pradesh, India.

Gopal Chandra Hazarika
Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, India.

DOI https://doi.org/10.33889/IJMEMS.2021.6.2.030

Received on April 06, 2020
  ;
Accepted on September 08, 2020

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.

Keywords- AB and CF derivatives, Viscosity, Thermal conductivity, Porous medium, Radiation.

Citation

Saikia, D., Saha, U. K., & Hazarika, G. C. (2021). 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. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 493-509. https://doi.org/10.33889/IJMEMS.2021.6.2.030.