文章基本信息

标题：Natural convection flow of a fluid using Atangana and Baleanu fractional model
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作者：Sidra Aman ; Thabet Abdeljawad ; Qasem Al-Mdallal 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-15
DOI：10.1186/s13662-020-02768-w
出版社：Hindawi Publishing Corporation
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.
关键词：Fluid flow;Natural convection;Atangana–Baleanu fractional derivative;Laplace transform method;