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

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.

A new approach for the generalized fractional Casson fluid model with Newtonian heating described by the modified Riemann–Liouville fractional operator

“…Boundary layer flow and heat transfer of non‐Newtonian fluids are analyzed in a previous study 8 . There are so many techniques available in the literature such as differential transform method, homotopy perturbation method, and variational iteration method for identifying the solutions of extensive applications in various areas of biochemical, rheology, physics, and petroleum industries 9–14 . Because of these applications, the perception and the study of non‐Newtonian fluids become a fascinating topic of current research in this field.…”

“…8 There are so many techniques available in the literature such as differential transform method, homotopy perturbation method, and variational iteration method for identifying the solutions of extensive applications in various areas of biochemical, rheology, physics, and petroleum industries. [9][10][11][12][13][14] Because of these applications, the perception and the study of non-Newtonian fluids become a fascinating topic of current research in this field. In all the above cases, the solutions of generalized fractional Casson fluid are determined by using either approximate or any numerical methods.…”

On the iterative methods for solving fractional initial value problems: new perspective

“…In recent years, huge interests from scientists in modelling problems in the fields of fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences using fractional differential equations (FDEs); see, by way of example not exhaustive enumeration, [1,2,3,4,5,6,7,8,9]. However, unlike the integer differential equations (DEs), the determination of the exact solutions of FDEs is so complicated.…”

Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system

“…In this continuity, the studies can be continued on the theory of fractional calculus but we end here categorically as role of fractional calculus in induction machines and electrical engineering [23–28], role of fractional calculus in epidemiological diseases [29, 30], role of fractional calculus in fluids and nanofluids [31–35], role of fractional calculus in heat transfer through nanoparticles [36–38], and role of fractional calculus in magnetohydrodynamics and porosity [39, 40]. Additionally, the different dynamical studies with and without fractional differential operators can be studied [41–49]. Meanwhile, integral fractional operators have been employed in [50–58].…”