The Nield-Kuznetsov Functions and How they Arise in Modelling Flow in the Transition Layer

IF 2.6 3区工程技术 Q3 ENGINEERING, CHEMICAL

Transport in Porous Media Pub Date : 2025-08-26 DOI:10.1007/s11242-025-02219-8

M. H. Hamdan, M. S. Abu Zaytoon

引用次数: 0

Abstract

Flow through the configuration of a three-layer channel containing a transition porous layer of variable permeability is revisited in this work to illustrate how Brinkman’s equation, which governs the flow in the transition layer, is reduced to the classic inhomogeneous differential equations of Airy and Weber, with constant forcing terms. Solutions to the homogeneous parts of these equations are given in terms of Airy’s and Weber’s special functions. Particular solutions to the resulting inhomogeneous equations give rise to three Nield-Kuznetsov functions of the first kind, which are analyzed in this work and extended to obtain general solutions to equations with variable forcing terms whose general solutions are expressed in terms of three Nield-Kuznetsov functions of the second kind. Methods of evaluation of all resulting special functions are presented.

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涅尔德-库兹涅佐夫函数及其在过渡层流建模中的出现

通过包含可变渗透率过渡多孔层的三层通道配置的流动在本工作中被重新审视，以说明如何将控制过渡层流动的Brinkman方程简化为具有恒定强迫项的Airy和Weber的经典非齐次微分方程。这些方程的齐次部分的解用艾里和韦伯的特殊函数给出。所得非齐次方程的特解得到了第一类的三个nielsen - kuznetsov函数，本文对其进行了分析，并将其推广到具有变量强迫项的方程的一般解，这些方程的一般解用三个第二类的nielsen - kuznetsov函数表示。给出了所有得到的特殊函数的求值方法。

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

Transport in Porous Media 工程技术-工程：化工

CiteScore

5.30

自引率

7.40%

发文量

155

审稿时长

4.2 months

期刊介绍： -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).