A numerical study of atangana baleanu and caputofabrizio analysis of fractional derivatives for certain heat and mass transfer problems of fluid mechanics

Abstract

In this thesis the problems comprise of incompressible fluid flow under different flow situations. The first chapter is the introductory chapter. In this chapter, Newtonian fluid, magnetohydrodynamics and its applications, heat and mass transfer, temperature dependent viscosity and thermal conductivity, porous media, fundamental equations of magnetohydrodynamics and non-dimensional parameters, fractional derivatives, AB and CF fractional derivatives are discussed. The second chapter is the review of literature. The third chapter comprises the numerical investigation to study an MHD free convective flow past a moving vertical plate with heat and mass transfer has been done using fractional derivative using AB and CF methods. In the fourth chapter, a numerical study on Atangana-Baleanu and CaputoFabrizio fractional derivatives for MHD flow past an impulsively started vertical plate with ramped temperature and concentration with viscous dissipation has been made. But here we consider viscosity and thermal conductivity as a variable. In the fifth chapter, a numerical investigation is presented for non-integer order derivatives with AB and CF fractional derivatives for the variable viscosity and thermal conductivity over a moving vertical plate in a porous medium two dimensional free convection MHD flow. In the sixth chapter, a numerical study on the effects of variable viscosity and thermal conductivity on unsteady MHD free convective heat transfer flow between two horizontal parallel plates by using AB and CF fractional derivatives is presented. The flow governing equations are transformed into non-dimensional form by using non-dimensional quantities and parameters. The effects of velocity and temperature profiles for different parameters are studied graphically and compared these values by AB and CF fractional derivatives. In this chapter we have compared the present numerical results of skin-friction and Nusselt number with the earlier work.