Natural convection flow of a fluid using Atangana and Baleanu fractional model

Thabet Abdeljawad,Sidra Aman,Qasem Al-Mdallal

doi:10.1186/s13662-020-02768-w

Abstract

A modified fractional model for the magnetohydrodynamic (MHD) flow of a fluid is developed utilizing Atangana–Baleanu fractional derivative (ABFD). Natural convection and wall oscillation instigate the flow over a vertical plate positioned in a porous medium. The partial differential equations (PDEs) are transmuted to ordinary differential equations (ODEs). The Laplace transform method with its inversion is employed to accomplish the exact solutions of momentum and heat equations. The final solution is expressed in terms of gamma function, modified Bessel function, and Mittag-Leffler function. The previous definitions Caputo fractional and Riemann–Liouville are rarely used by the researchers now due to their limitations. The newly introduced ABFD has got significance nowadays due to its nonlocal and nonsingular kernel. This work focuses on the oscillating boundary conditions for the viscous model in terms of ABFD. The influence of involved parameters is interpreted through plots. The velocity profile is an increasing function of fractional parameter and jumps for a higher Grashof number due to buoyancy push. Furthermore, the Atangana–Baleanu (AB) model is compared with the ordinary derivative model for limiting case and analyzed in detail. It is noted that the ordinary fluid flows faster compared to the fractional fluid.

Highlights

The literature of natural convection is sufficiently rich for magnetohydrodynamic oscillatory flow with classical fluid models
The analytical solution for the present problem in terms of the Atangana–Baleanu fractional model has been established via the Laplace transform method
The flow and heat are analyzed for the influence of the parameters such as fractional parameter, radiation parameter, magnetic parameter, porosity parameter, and Grashof number

Summary

Introduction

The literature of natural convection is sufficiently rich for magnetohydrodynamic oscillatory flow with classical fluid models. Azhar et al [16] used the Caputo–Fabrizio time fractional derivative to the problem of nanofluid flow over a moving vertical plate. Fetecau et al [17] conducted an analysis on the flow of a nanofluid over an isothermal plate Caputo-time fractional derivative.

Results

Conclusion