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

Advances in Difference Equations

article

Aman, Sidra¹  Abdeljawad, Thabet²  Al-Mdallal, Qasem¹ 

[1] Department of Mathematical Sciences, UAE University, United Arab Emirates;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University

关键词: Fluid flow;    Natural convection;    Atangana–Baleanu fractional derivative;    Laplace transform method;   

DOI  :  10.1186/s13662-020-02768-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY