General solution of the Maxwell equations for the stagnation point problem with cylindrical symmetry for all values of the parameter in the Johnson-Segalman derivative

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-18 DOI:10.1016/j.cnsns.2024.108527

C. Chittam, S.V. Meleshko

引用次数: 0

Abstract

This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive the general solution for the Maxwell model with the Johnson-Segalman convected derivative in cylindrical coordinates for an arbitrary model parameter

α

. The analysis reveals the necessity of separately considering the upper-convected, lower-convected, and Jaumann derivatives when solving the stagnation point flow problem.

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Johnson-Segalman导数中所有参数值的圆柱对称驻点问题Maxwell方程的通解

本文研究了不可压缩粘弹性麦克斯韦介质中自由临界点附近的二维流动，该流动受流变本构律支配。虽然驻点流动问题已被广泛研究，但圆柱坐标下应力的一般精确解析解——更实用和适合某些实验——仍未被发现。本文推导了具有Johnson-Segalman卷积导数的麦克斯韦模型在柱坐标下的通解，该通解具有任意模型参数α。分析表明，在求解驻点流动问题时，必须分别考虑上、下、Jaumann导数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.