Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Manzoor, Naeema; Bég, O. Anwar; Maqbool, Khadija; Shaheen, Sidra

doi:10.1080/10255842.2019.1582033

Cited by 11 publications

(9 citation statements)

References 47 publications

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“…Non-Newtonian ciliated metachronal propulsion has also been examined by a variety of investigators. Manzoor et al [20] used the Blake elliptic cilia model to study magnetohydrodynamic metachronal slip flow of Johnson-Segalman fluids in a channel. They derived perturbation solutions and showed that with greater viscous force relative to elastic force (i.e.…”

Section: Introductionmentioning

confidence: 99%

Retracted: “Electro-Osmotic Propulsion of Jeffrey Fluid in a Ciliated Channel Under the Effect of Nonlinear Radiation and Heat Source/Sink,” [ASME Journal of Biomechanical Engineering, 2021, 143(5), p. 051008; DOI: 10.1115/1.4049810]

Shaheen

Bég

Gul

et al. 2021

Journal of Biomechanical Engineering

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Mathematical modelling of mechanical system in microfluidics is an emerging area of interest in micro scale engineering. Since microfluidic devices use the hair like structure of artificial cilia for pumping, mixing and sensing in different fields, therefore; electro osmotic cilia driven flow help to generate the fluid velocity for the Newtonian and viscoelastic fluid. Due to the deployment of artificial ciliated walls, the present research reports the combined effect of an electro osmotic flow and convective heat transfer on Jeffrey viscoelastic electrolytic fluid flow in a two-dimensional ciliated vertical channel. Heat generation/absorption and nonlinear radiation effects are included in the present mathematical model. After applying Debye-Huckel approximation and small Reynolds number approximation to momentum and energy equation, the system of nonlinear partial differential equation is reduced into non-homogenous boundary value problem. The problem determines the velocity, pressure and temperature profiles by the application of semi-analytical technique known as Homotopy Perturbation Method (HPM) with the help of software Mathematica. The graphical results of the study suggest that HPM is a reliable methodology for thermo physical electro-osmotic rheological transport in micro channels.

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Section: Introductionmentioning

confidence: 99%

Retracted: “Electro-Osmotic Propulsion of Jeffrey Fluid in a Ciliated Channel Under the Effect of Nonlinear Radiation and Heat Source/Sink,” [ASME Journal of Biomechanical Engineering, 2021, 143(5), p. 051008; DOI: 10.1115/1.4049810]

Shaheen

Bég

Gul

et al. 2021

Journal of Biomechanical Engineering

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“…whereμ B the plastic viscosity, Υ the volume fraction density, ξ ij the deformation rate of component, and y s the yield stress, π denotes the second invariant tensor of ξ ij , π Υ represents the critical value comprises on the non-Newtonian fluid model. The Mathematical expression for the envelope of the cilia tips reads as [31,32]:…”

Section: Problem Formulationmentioning

confidence: 99%

“…where k = 2π/λ, z 0 describes the reference location of the cilia, the non-dimensional parameter φ, which combines with b 0 (mean radius of the outer tube) in the form of b 0 φ and represents the amplitude of metachronal wave, λ is the metachronal wavelength, c the velocity, and α describes the measure of the eccentricity of the elliptical motion. The vertical and axial velocities are evaluated as [31,32]:…”

Section: Problem Formulationmentioning

confidence: 99%

Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy

et al. 2020

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This study deals with the mass transport phenomena on the particle-fluid motion through an annulus. The non-Newtonian fluid propagates through a ciliated annulus in the presence of two phenomenon, namely (i) endoscopy, and (ii) blood clot. The outer tube is ciliated. To examine the flow behavior we consider the bi-viscosity fluid model. The mathematical modeling has been formulated for small Reynolds number to examine the inertia free flow. The purpose of this assumption is that wavelength-to-diameter is maximal, and the pressure could be considerably uniform throughout the entire cross-section. The resulting equations are analytically solved, and exact solutions are given for particle- and fluid-phase profiles. Computational software Mathematica has been used to evaluate both the closed-form and numerical results. The graphical behavior across each parameter has been discussed in detail and presented with graphs. The trapping mechanism is also shown across each parameter. It is noticed clearly that particle volume fraction and the blood clot reveal converse behavior on fluid velocity; however, the velocity of the fluid reduced significantly when the fluid behaves as a Newtonian fluid. Schmidt and Soret numbers enhance the concentration mechanism. Furthermore, more pressure is required to pass the fluid when the blood clot appears.

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“…Singh et al [15] applied the short memory Walters-B viscoelastic fluid model to study combined free and forced convective in reactive electrically conducting vertical channel transport. Further studies have implemented the Saffman dusty fluid-particle model [16], Bingham viscoplastic model [17], a third grade viscoelastic Reiner-Rivlin fluid [18] and more recently the Johnson-Segalman elastic-viscous model [19]. All these studies identified a significant modification in heat and momentum transfer characteristics with non-Newtonian effects and substantial deviation from Newtonian results.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

et al. 2022

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Inspired by simulating duct thermal processing of novel functional polymers, a novel mathematical model is developed for buoyancy‐driven heat transfer in non‐Newtonian Williamson fluid flow in a vertical parallel plate duct containing a permeable medium, under mutually orthogonal electrical and magnetic fields. The momentum equation features electrical and magnetic body force terms, and the Darcy–Brinkman–Forchheimer mode is used for non‐Darcy effects. The energy balance equation includes thermal buoyancy (natural convection body force) and a modified viscous dissipation term. The conservation equations with associated boundary conditions are reframed into a system of coupled non‐linear ordinary differential equations via appropriate similarity transformations. The emerging dimensionless boundary value problem is then solved with a differential transform method (DTM). Validation of DTM solutions with the bvp4c MATLAB collocation solver is included. The influence of key parameters on velocity, temperature and average Nusselt number, are computed and illustrated graphically. With elevation in Weissenberg (non‐Newtonian) number, velocity and temperature are reduced. Velocity is suppressed with increasing non‐Darcian parameter (Forchheimer effect) whereas it is enhanced with increment in buoyancy convection parameter. With increasing Forchheimer, Darcy number and Hartmann number, the average Nusselt number is boosted whereas it is decreased with higher values of buoyancy convection parameter, Brinkman number and Weissenberg number. A strong reduction in temperature is computed with increment in ratio of Joule electrical heating to heat conduction parameter. DTM is shown to be an exceptionally accurate and versatile approach for simulating non‐Newtonian electromagnetohydrodynamic transport in ducts.

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Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Abstract: Ti t l e M a t h e m a tic al m o d elli n g of cilia ry p r o p ul sio n of a n el e c t ric ally c o n d u c ti n g Joh n s o n-S e g al m a n p hy siolo gic al flui d in a c h a n n el wi t h slip

Cited by 11 publications

References 47 publications

Retracted: “Electro-Osmotic Propulsion of Jeffrey Fluid in a Ciliated Channel Under the Effect of Nonlinear Radiation and Heat Source/Sink,” [ASME Journal of Biomechanical Engineering, 2021, 143(5), p. 051008; DOI: 10.1115/1.4049810]

Retracted: “Electro-Osmotic Propulsion of Jeffrey Fluid in a Ciliated Channel Under the Effect of Nonlinear Radiation and Heat Source/Sink,” [ASME Journal of Biomechanical Engineering, 2021, 143(5), p. 051008; DOI: 10.1115/1.4049810]

Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

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