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Analytical Solutions to Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fuid
Version 1
: Received: 2 June 2022 / Approved: 3 June 2022 / Online: 3 June 2022 (09:58:29 CEST)
How to cite: Wang, F.; Wang, Y. Analytical Solutions to Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fuid. Preprints 2022, 2022060041. https://doi.org/10.20944/preprints202206.0041.v1 Wang, F.; Wang, Y. Analytical Solutions to Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fuid. Preprints 2022, 2022060041. https://doi.org/10.20944/preprints202206.0041.v1
Abstract
For solving the fractional differential equations in computational fluid dynamics (CFD), it’s complicated and difficult by the Laplace and Fourier transforms. Based on the Caputo fractional derivative, the analytical solutions for unsteady unidirectional flows of a generalized Oldroyd-B fluid are deduced by the separation of variables method. Results show that the analytical solutions are given easily, and have good university. For some specific parameter values, the well-known analytical solutions for the generalized second grade fluid, the generalized Upper-Convected Maxwell (UCM) fluid as well as the ordinary Oldroyd-B fluid can be obtained.
Keywords
Fractional calculus; Generalized Oldroyd-B fluid; separation of variables method; Unidirectional flow; Caputo fractional derivative
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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