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Flow of viscoelastic fluids through a porous channel—I
Author(s) -
Ariel P. D.
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650170705
Subject(s) - newtonian fluid , viscoelasticity , mechanics , boundary value problem , porous medium , exact solutions in general relativity , fluid dynamics , reynolds number , mathematics , herschel–bulkley fluid , open channel flow , non newtonian fluid , generalized newtonian fluid , flow (mathematics) , physics , porosity , mathematical analysis , materials science , viscosity , thermodynamics , shear rate , turbulence , composite material
The flow of viscoelastic fluids through a porous channel with one impermeable wall is computed. The flow is characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. Three solutions are developed: (i) an exact numerical solution, (ii) a perturbation solution for small R , the cross‐flow Reynold's number and (iii) an asymptotic solution for large R . The results from exact numerical integration reveal that the solutions for a non‐Newtonian fluid are possible only up to a critical value of the viscoelastic fluid parameter, which decreases with an increase in R . It is further demonstrated that the perturbation solution gives acceptable results only if the viscoelastic fluid parameter is also small. Two more related problems are considered: fluid dynamics of a long porous slider, and injection of fluid through one side of a long vertical porous channel. For both the problems, exact numerical and other solutions are derived and appropriate conclusions drawn.