A Numerical study of the unsteady flow of two immiscible micro polar and Newtonian fluids through a horizontal channel using DQM with B-Spline basis function

Katta, Ramesh Kumar; Chandrawat, Rajesh Kumar; Joshi, Varun

doi:10.1088/1742-6596/1531/1/012090

Cited by 8 publications

(7 citation statements)

References 31 publications

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“…Thus, equations are reduced into a system of ordinary differential equations in time, that is, for i=1, 2, 3…, N, and the system is solved by the robust four-step third-order SSP RK43 [33]. The velocities and microrotation in both Zones are obtained as follows:…”

Section: Computation Of mentioning

confidence: 99%

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Numerical Study of Ion-Slip and Hall Effect on Couette Flow of Two Immiscible Micropolar and Micropolar Dusty Fluid (Fluid-Particle Suspension) with Heat Transfer

Chandrawat¹,

Joshi²

2021

IJHT

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In this paper, the unsteady magnetohydrodynamic (MHD) Couette flow of two non-Newtonian immiscible fluids micropolar and micropolar dusty (fluid-particle suspension) are considered in the horizontal channel with heat transfer. A comprehensive mathematical model and computational simulation with the modified cubic B-Spline-Differential Quadrature method (MCB-DQM) is described for unsteady flow. The coupled partial differential equation for fluid and particle-phase are formulated and the effect of viscous dissipation, Joule heating, Hall current, and other hydrodynamic and solutal parameters i. e. Reynolds number, Eckert number, particle concentration parameter, Eringen micropolar material parameter, time, viscosity ratio, and density ratio on the flow rate, micro rotation, and temperature characteristics were investigated. The analysis of obtained results reveals that the fluids and particle velocities are slightly decreasing with Hartmann number, and increasing with time, ion-slip, and Hall parameters. Microrotation declined with Microrotations dropped significantly with ion-slip and Hall parameter and grown Hartman number. The temperature begins to rise as time, Hartman number, and Eckert number grow and declined with Ion-slip and Hall parameter.

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Section: Computation Of mentioning

confidence: 99%

“…Ramesh and Joshi [32] simulated unsteady Jeffery liquid flow between two permeable plates utilizing the geometrical B-spline differential quadrature technique. Two immiscible micropolar and Newtonian liquids flow were simulated by the cubic B-Spline differential quadrature technique [33].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Ion-Slip and Hall Effect on Couette Flow of Two Immiscible Micropolar and Micropolar Dusty Fluid (Fluid-Particle Suspension) with Heat Transfer

Chandrawat¹,

Joshi²

2021

IJHT

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“…Two immiscible micropolar and Newtonian fluids were considered in the horizontal channel and the system of partial differential equations was solved by the modified cubic B-Spline differential quadrature method. 50 Researchers have presented multiple studies on the steady and unsteady flow of single and immiscible combination of micropolar, Newtonian fluids via different shapes and numerical simulation resulting in a variety of effects. To the best of the authors' awareness, no effort has yet been made to investigate the unsteady flow of two immiscible magnetohydrodynamic micropolar and micropolar dusty (fluid-particle suspension) fluids.…”

Section: Articlementioning

confidence: 99%

Ion Slip and Hall Effects on Generalized Time-Dependent Hydromagnetic Couette Flow of Immiscible Micropolar and Dusty Micropolar Fluids with Heat Transfer and Dissipation: A Numerical Study

Chandrawat

Joshi

Bég³

2021

j nanofluids

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The hydrodynamics of immiscible micropolar fluids are important in a variety of engineering problems, including biofluid dynamics of arterial blood flows, pharmacodynamics, Principle of Boundary layers, lubrication technology, short waves for heat-conducting fluids, sediment transportation, magnetohydrodynamics, multicomponent hydrodynamics, and electrohydrodynamic. Motivated by the development of biological fluid modeling and medical diagnosis instrumentation, this article examines the collective impacts of ion slip, viscous dissipation, Joule heating, and Hall current on unsteady generalized magnetohydrodynamic (MHD) Couette flow of two immiscible fluids. Two non-Newtonian incompressible magnetohydrodynamic micropolar and micropolar dusty (fluid-particle suspension) fluids are considered in a horizontal duct with heat transfer. No-slip boundary conditions are assumed at the channel walls and constant pressure gradient. Continuous shear stress and fluid velocity are considered across the interface between the two immiscible fluids. The coupled partial differential equations are formulated for fluids and particle phases and the velocities, temperatures, and microrotation profiles are obtained. Under the physically realistic boundary and interfacial conditions, the Modified cubic-Bspline differential quadrature approach (MCB-DQM) is deployed to obtain numerical results. The influence of the magnetic, thermal, and other pertinent parameters, i.e. Hartmann magnetic number, Eckert (dissipation) number, Reynolds number, Prandtl number, micropolar material parameters, Hall and ion-slip parameters, particle concentration parameter, viscosity ratio, density ratio, and time on velocity, microrotation, and temperature characteristics are illustrated through graphs. The MCB-DQM is found to be in good agreement with accuracy and the skin friction coefficient and Nusselt number are also explored. It is found that fluids and particle velocities are reduced with increasing Hartmann numbers whereas they are elevated with increment in ion-slip and Hall parameters. Temperatures are generally enhanced with increasing Eckert number and viscosity ratio. The simulations are relevant to nuclear heat transfer control, MHD energy generators, and electromagnetic multiphase systems in chemical engineering.

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“…[51] for the calculation of weighting coefficients in DQM. This technique is both easily applicable and efficient strategically, contributing to error reduction and simple to enforce as described by Katta et al 52 Katta and Joshi 34 used DQM to numerically analyze the hydromagnetic flow of a viscoelastic Jeffrey fluid in a porous medium. 53 Previous studies have been confined to examining the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes.…”

Section: Articlementioning

confidence: 99%

Numerical Study of Interface Tracking for the Unsteady Flow of Two Immiscible Micropolar and Newtonian Fluids Through a Horizontal Channel with an Unstable Interface

2021

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The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical separation techniques, etc. One of the most essential components of immiscible flow is the fluid interface, which must be consistently monitored. In this article, the unsteady flow of two immiscible fluids i.e., an Eringen micropolar and Newtonian liquid is considered in a horizontal channel. Despite the no-slip and hyper-stick shear stress condition at the channel edge, it is accepted that the liquid interface is dynamic, migrating from one position to the next and possibly get absolute change; as a result, The CS (continuum surface) model is integrated with the single moment equation based on the VOF (volume of fluid) approach to trace the interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant, decaying, and periodic) and flow is analyzed under seamless shear stress over the entire interface. The modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled partial differential equations for the fluid interface evolution. The advection and tracking of the interface with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of micropolar parameters affects the interface with time. The novelty of the current study is that previous studies (which considered the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes) are extended and generalized to consider the time-dependent flow of two immiscible fluids namely Eringen micropolar and Newtonian with a moving interface in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the steady-state, the peak of the waves resembles those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure gradient case i.e., weaker micropolar fluids encourage faster stabilization of the interface. With periodic pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

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A Numerical study of the unsteady flow of two immiscible micro polar and Newtonian fluids through a horizontal channel using DQM with B-Spline basis function

Cited by 8 publications

References 31 publications

Numerical Study of Ion-Slip and Hall Effect on Couette Flow of Two Immiscible Micropolar and Micropolar Dusty Fluid (Fluid-Particle Suspension) with Heat Transfer

Numerical Study of Ion-Slip and Hall Effect on Couette Flow of Two Immiscible Micropolar and Micropolar Dusty Fluid (Fluid-Particle Suspension) with Heat Transfer

Ion Slip and Hall Effects on Generalized Time-Dependent Hydromagnetic Couette Flow of Immiscible Micropolar and Dusty Micropolar Fluids with Heat Transfer and Dissipation: A Numerical Study

Numerical Study of Interface Tracking for the Unsteady Flow of Two Immiscible Micropolar and Newtonian Fluids Through a Horizontal Channel with an Unstable Interface

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