Open AccessOn the Sigmoid Function as a Variable Permeability Model for Brinkman Equation
Author(s) -
Valeriy Bunak,
Elena Prokhorova,
Vladimir Zhuravsky,
Sergei Volodin,
Andrei Frolov
Publication year - 2022
Publication title -
wseas transactions on applied and theoretical mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.211
H-Index - 10
eISSN - 2224-3429
pISSN - 1991-8747
DOI - 10.37394/232011.2022.17.5
Subject(s) - sigmoid function , permeability (electromagnetism) , hagen–poiseuille equation , porous medium , mechanics , variable (mathematics) , mathematics , logistic function , work (physics) , mathematical analysis , porosity , flow (mathematics) , materials science , physics , thermodynamics , computer science , chemistry , membrane , statistics , composite material , biochemistry , artificial neural network , machine learning
A collection of popular variable permeability functions is presented and discussed in this work. The functions have been used largely in Brinkman’s equation which governs the flow through a porous domain in the presence of solid, macroscopic boundaries on which the no-slip condition is imposed, and has been used in transition layer modelling. A convenient classification of permeability functions is also provided. The sigmoid logistic function is presented in this work in a modified form that is suitable for variable permeability modelling, and is used in obtaining solution to Poiseuille flow through a Brinkman porous channel.