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The Impulsive Motion of Flat Plate in Generalized Second Grade Fluid with Anomalous Diffusion
American Journal of Applied Mathematics
Volume 8, Issue 6, December 2020, Pages: 327-333
Received: Sep. 26, 2020; Accepted: Nov. 3, 2020; Published: Dec. 11, 2020
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Authors
Mohammad Tanzil Hasan, Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Maritime University, Dhaka, Bangladesh
Md. Shafiqul Islam, Department of Applied Mathematics, Dhaka University, Dhaka, Bangladesh
Mir Shariful Islam, Department of Oceanography, Dhaka University, Dhaka, Bangladesh
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Abstract
The flow adjacent to a wall rapidly set in motion for a generalized second-grade fluid with anomalous diffusion is examined. For the elucidation of such a fluid, the fractional-order derivative approach in the constitutive relationship model is presented because models based on ordinary differential equations have a relatively limited class of solutions, which does not provide compatible description of the complex systems in general. The current model of second-order fluid involving fractional calculus is based on the formal replacement of the first-order derivative in ordinary rheological constitutive equation by fractional derivative of a non-integer order. In addition, the time-fractional equation considered in this article describes the anomalous sub-diffusion. In this article, the velocity and stress field of generalized second-grade fluid with fractional anomalous diffusion are studied by fractional partial differential equations. Analytic solutions are given in closed form, from these differential equations in terms of the generalized G-functions or Fox's H-function with the discrete Laplace transform technique. Thus, many previous and classical results, namely, the solution of fractional diffusion equation obtained by Wyss, the classical Rayleigh’s time-space regularity solution, the relationship between velocity field and stress field obtained by Bagley and Torvik, are represented by particular cases of our proposed derivation.
Keywords
Time Fractional Navier-Stokes Equation, Generalized Second Grade Fluid, Anomalous Diffusion, Fox's H-function
To cite this article
Mohammad Tanzil Hasan, Md. Shafiqul Islam, Mir Shariful Islam, The Impulsive Motion of Flat Plate in Generalized Second Grade Fluid with Anomalous Diffusion, American Journal of Applied Mathematics. Vol. 8, No. 6, 2020, pp. 327-333. doi: 10.11648/j.ajam.20200806.15
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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