Analytical solution of a couple stress fluid saturated in a porous medium through a Reiner–Rivlin liquid sphere

Selvi, R. Tamil; Maurya, Deepak Kumar; Shukla, Pankaj

doi:10.1063/5.0149507

Cited by 8 publications

(1 citation statement)

References 23 publications

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“…[38] considered a three‐zone model with an inner core of Reiner–Rivlin non‐Newtonian liquid particle, surrounded with a Newtonian liquid shell and encased in a permeable medium. Selvi and Shukla [39] addressed the two‐zone case of a Reiner–Rivlin liquid sphere surrounded by a micropolar fluid with Mehta–Morse boundary conditions and asymptotic expansions. El‐Sapa and Alsudais [40] considered the hydromagnetic slip flow of Newtonian concentric spheres surrounded with a porous medium.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Selvi,

Bég

2024

Z Angew Math Mech

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The focus of this article is to study theoretically the steady‐axisymmetric creeping flow dynamics of a couple stress fluid external to a semi‐permeable sphere containing a solid core. This problem is motivated by emulsion hydrodynamics in chemical engineering where rheological behaviour often arises in addition to porous media effects. The non‐Newtonian Stokes’ couple stress fluid model features couple stresses and body couples that are absent in the classical Navier–Stokes viscous model. It provides a robust framework for simulating emulsions, complex suspensions and other liquids which possess microstructure. The physical regime is delineated into two zones – the interior of the semi‐permeable zone (region II) which engulfs the solid core and the external couple stress fluid zone (region I). The model is formulated using a spherical polar coordinate system in terms of the stream function ψ. The Brinkman‐extended Darcy model is deployed for the porous medium hydrodynamics and isotropic permeability is considered. Analytical expressions are derived for dimensionless pressure, tangential stress and the couple stress components using the method of separation of variables and Gegenbauer functions of the first kind. The integration constants are evaluated with appropriate boundary conditions on the inner and outer boundary of the semi‐permeable zone with the aid of Mathematica symbolic software. Solutions for the drag force exerted by the couple stress fluid on the semi‐permeable sphere and volumetric flow rate are also derived with corresponding expressions for the drag coefficient and non‐dimensional volumetric flow rate. The influence of permeability (k), separation parameter (l), couple stress viscosity coefficient (η), couple stress inverse length dependent parameter (λ = √(μ/η)) and couple stress viscosity ratio (τ = η/η/) on all key variables is studied graphically. Additionally, streamline contours are computed for a range of parameters including inverse permeability parameter (α = 1/k). The computations show that increasing couple stress inverse length dependent parameter (λ) greatly reduces the dimensionless volumetric flow rate in particular at high values of separation parameter (l). Flow rate is, however, markedly enhanced with permeability (k) and also couple stress viscosity parameter (η). In the presence of the solid core, a much greater drag coefficient is observed at all values of couple stress inverse length dependent parameter (λ) relative to the case without a solid core. A significant distortion in streamlines is computed with increasing separation parameter (l) with a dual vortex structure emanating. With greater couple stress viscosity parameter (τ), no tangible modification is observed in the streamline contours. The present work generalizes the earlier study of Krishnan and Shukla to consider a semi‐permeable (porous medium) outer sphere and furthermore presents detailed streamline visualizations of the creeping flow for a range of emerging parameters of relevance to non‐Newtonian chemical engineering processes including emulsion droplet dynamics in porous materials.

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Section: Introductionmentioning

confidence: 99%

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Selvi,

Bég

2024

Z Angew Math Mech

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Hydromagnetic flow of Casson fluid over a stretching plane through porous medium

Maurya,

Deo,

Maurya

2024

Z Angew Math Mech

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The current investigation concentrates on the magnetohydrodynamic (MHD) effects of a steady Casson fluid flowing over a stretching sheet in the porous medium. A mathematical model for Casson fluid is developed in order to investigate the characteristics of non‐Newtonian fluid. The governing higher order nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformation. The appropriate boundary conditions have been applied to generate analytical expressions of flow characteristics such as velocity and skin friction coefficient. Results are reported on specific cases of fluid velocity (horizontal/transversal) and skin friction coefficient. The skin friction coefficient, and the fluid flow characteristics, i.e., velocity profiles, are sketched for various values of the flow parameters, such as the Casson parameter, suction velocity, conductivity, and permeability parameter and analyzed. The velocity components are a decreasing function of the Casson parameter and electrical conductivity, whereas, the skin friction coefficient is an increasing function of permeability parameter. Deduced results validate the existing results.

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Creeping flow of a couple stress fluid past a semipermeable spherical particle consisting of a solid core: magnetic field effect

Ramasamy,

Chauhan

2024

J Braz. Soc. Mech. Sci. Eng.

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Analytical solution of a couple stress fluid saturated in a porous medium through a Reiner–Rivlin liquid sphere

Cited by 8 publications

References 23 publications

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Mathematical modelling of couple stress fluid flow around a semi‐permeable sphere enclosing a solid core

Hydromagnetic flow of Casson fluid over a stretching plane through porous medium

Creeping flow of a couple stress fluid past a semipermeable spherical particle consisting of a solid core: magnetic field effect

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