The Numerical Analysis of the Fractional Maxwell Fluid in Porous Rock Formations

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-19 DOI:10.1002/mma.10786

Jinxia Jiang, Mengqi Liu, Haojie Zhao, Yan Zhang

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引用次数: 0

Abstract

Fractional derivatives are global operators in which the time and space fractional derivatives represent temporal memory and spatial nonlocality, respectively. It is confirmed that the fractional Maxwell fluid model is more suitable for describing crude oil constitutive relation by the rheological experiment. In this paper, an investigation of the magnetohydrodynamic (MHD) flow and heat transfer of crude oil nanofluid in porous rock formations is presented. The fractional governing equations with the time and space fractional derivatives have been established. Numerical solutions are obtained by the finite difference method with the L1 algorithm and L2 algorithm to discrete the fractional derivatives. The numerical solution is verified by comparing with the exact solution constructed by introducing a source term. The effects of the involved parameters on the velocity and temperature distributions are analyzed and discussed in detail. It is noteworthy that the velocity profiles decrease significantly with the increasing $β_{1}$ while the temperature profiles increase with the increasing $β_{2}$ .

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多孔岩层中分数阶麦克斯韦流体的数值分析

分数阶导数是一种全局算子，其中时间和空间分数阶导数分别表示时间记忆和空间非局域性。流变实验证实分数阶麦克斯韦流体模型更适合描述原油的本构关系。本文研究了原油纳米流体在多孔岩层中的磁流体动力学（MHD）流动和传热。建立了具有时间和空间分数阶导数的分数阶控制方程。采用有限差分法分别用L1算法和L2算法对分数阶导数进行离散，得到数值解。通过与引入源项构造的精确解的比较，验证了数值解的正确性。详细分析和讨论了相关参数对速度和温度分布的影响。值得注意的是，速度分布随着β 1的增大而显著减小$$ {\beta}_1 $$，而温度分布随着β 2的增大而增大$$ {\beta}_2 $$。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.