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Open AccessArticle

Numerical Solutions of Unsteady Boundary Layer Flow with a Time-Space Fractional Constitutive Relationship

1
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2
School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China
3
Research Institute of Petroleum Exploration and Development, Xueyuan Road No.20, Haidian District, Beijing 100083, China
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(9), 1446; https://doi.org/10.3390/sym12091446
Received: 17 August 2020 / Revised: 30 August 2020 / Accepted: 31 August 2020 / Published: 2 September 2020
(This article belongs to the Special Issue Theory and Applications of Special Functions in Mathematical Physics)
In this paper, we develop a new time-space fractional constitution relation to study the unsteady boundary layer flow over a stretching sheet. For the convenience of calculation, the boundary layer flow is simulated as a symmetrical rectangular area. The implicit difference method combined with an L1-algorithm and shift Grünwald scheme is used to obtain the numerical solutions of the fractional governing equation. The validity and solvability of the present numerical method are analyzed systematically. The numerical results show that the thickness of the velocity boundary layer increases with an increase in the space fractional parameter γ. For a different stress fractional parameter α, the viscoelastic fluid will exhibit viscous or elastic behavior, respectively. Furthermore, the numerical method in this study is validated and can be extended to other time-space fractional boundary layer models. View Full-Text
Keywords: time-space fractional order; finite difference method; Grünwald scheme; stretching sheet; boundary layer flow time-space fractional order; finite difference method; Grünwald scheme; stretching sheet; boundary layer flow
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Yang, W.; Chen, X.; Meng, Y.; Zhang, X.; Mi, S. Numerical Solutions of Unsteady Boundary Layer Flow with a Time-Space Fractional Constitutive Relationship. Symmetry 2020, 12, 1446.

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