Generalized Couette Flow Research Articles

Annular generalized Couette flow of immiscible viscous fluids in an anisotropic porous medium

Annular generalized Couette flow of immiscible viscous fluids in an anisotropic porous medium

Generalised Couette flow of nanoliquid among two concentric channels with particles injection

In the presence of nanoparticle injection, buoyancy power, constant pressure gradient, variable viscosity coefficient, magnetic field, mass diffusivity of thermophoresis, and Brownian motion, the hydrodynamic nanoliquid conducted with electric current flows through the gap between two concentric cylindrical channels of infinite length. The focus of this article was on generalised Couette flow that is flow in which the outer channel plate moves at a uniform velocity while still being subjected to a pressure gradient. Here we use the RKF45 numerical method and the shooting technique to solve dimensionless momentum, energy, and concentration equations. How the obtained parameters controlled on flow rate, temperature and concentration of the fluid have been investigated and appearances through respective graphs. The high magnitude of nanoliquid flow rate with outer channel wall motion and pressure gradient parameters has been observed. The nanoliquid temperature declines with an annular gap parameter while amplified thermophoresis and magnetic parameter values enrich the fluid temperature. In addition, loftier values of variable viscosity and Brownian motion parameters boost the nanoliquid concentration.

Influence of induced magnetic field and chemically reacting on hydromagnetic Couette flow of Jeffrey fluid in an inclined channel with variable viscosity and convective cooling: A Caputo derivative approach

In this study, the influence of induced magnetic field and chemically reacting on hydromagnetic generalized Couette flow of Jeffrey fluid in an inclined channel through a porous medium with variable viscosity and convective cooling has been investigated using the Caputo fractional order derivative operator. The mathematical formulation used for the hydromagnetic Couette flow of Jeffrey fluid takes into account the effects of viscous dissipation, Soret, and Dufour. The system of nonlinear partial differential equations governing the flow were solved numerically using the explicit finite difference method. The numerical results for the behavior of various physical parameter on the flow variables are obtained and represented graphically. Moreover, effects of the flow parameters on heat and mass transfer rates are obtained and discussed numerically through tabular forms. The graphical findings show that velocity, concentration, induced magnetic field, and thermal field profiles decline with progressively increment of Jeffrey parameter. The velocity, and temperature of the fluid decline with higher values of fluid viscosity parameter. An increase in the chemical reaction parameter recede the concentration field profiles while increase with raises the values of Soret number. Increasing Biot, and Dufour numbers significantly grows the thermal field profiles. Induced magnetic field grows with larger values of fluid viscosity parameter. The findings of this study are important due to its application in magnetohydrodynamics pumps, polymer manufacturing, fins designs, and food processing.

Joule heating and induced magnetic field on magnetohydrodynamic generalised Couette flow of Jeffrey fluid in an inclined channel with Soret and Dufour effects

In this study, the influence of Joule heating and induced magnetic field on magnetohydrodynamics generalised Couette flow of Jeffrey fluid in an inclined channel through a porous medium with Soret and Dufour effects has been investigated. The mathematical model in Cartesian coordinate system takes into account the effect of viscous dissipation. The nonlinear partial differential equations governing the flow are approximated numerically using the finite difference method. The profiles of the flow variables such as velocity, induced magnetic field, thermal field and concentration field are studied and the results are presented through graphs. The values for Sherwood number, Nusselt number and skin friction coefficient are computed and represented in tabular form. Concentration field grows with an increment of the Soret number. Velocity profiles grow significantly with larger values of inclination angle. Also, increasing Joule heating parameter leads to rise in the thermal field. The rate of mass transfer grows significantly with increasing the values of Soret number. The skin friction coefficient increases with raising the values of Dufour number and Joule heating parameter. The findings of this study are useful due to its application in the biological, natural and industrial systems.

An exact asymptotic solution for a non-Newtonian fluid in a generalized Couette flow subject to an inclined magnetic field and a first-order chemical reaction

<abstract><p>Understanding generalized Couette flow provides valuable insights into the behavior of fluids under various conditions, contributing to the advancement of more accurate models for real-world applications including tribology and lubrication, polymer and food processing, water conservation and oil exploration, microfluidics, biological fluid dynamics (blood flow in vessels), and electrohydrodynamic, and so on. The present study provided the exact asymptotic solution for the generalized Couette flow of a non-Newtonian Jeffrey fluid in a horizontal channel immersed in a saturated porous medium.The governing partial differential equations were transformed into a dimensionless form using the similarity technique and the resulting system of equations is solved by the Perturbation technique, as well as the method of the separation of variables, and computed on MATLAB (ode15s solver).The behavior of fluid velocity was investigated and presented through 2-D and 3-D graphs for two cases (ⅰ) when the implication of the magnetic field was strengthened and (ⅱ) when the magnitude of the magnetic field was fixed but its degree of inclination was altered. The first-order chemical reactions and thermal radiation were also considered. Additionally, the effect of numerous emerging quantities on momentum, temperature, and concentration contours characterizing the fluid flow was depicted graphically and discussed. Furthermore, the skin friction (at different angles of inclination and magnetic strength), Nusselt number, and Sherwood number (at different time intervals) were evaluated at both boundaries and presented tabularly. The findings revealed that there was a decrease in the velocity profile with an increasing degree of inclination and strength of the magnetic field. Moreover, we observed an increment in thermal and mass flux when it was measured over time at both of the channels. Also, the outcomes predicted an oscillatory nature of shear stress at both of the boundries.</p></abstract>

Physics of generalized couette flow of immiscible fluids in anisotropic porous medium

This study presents an investigation on the generalized Couette flow of two immiscible Newtonian fluids in an anisotropic porous medium. The flow occurs between two parallel plates, driven by the combined effects of an axial pressure gradient and the movement of the upper plate. The region between the plates is filled with an anisotropic porous medium characterized by directional permeability. An exact solution is derived for the proposed problem by considering appropriate boundary and interface conditions. The slip condition is employed at the lower plate of the channel which has a significant role in the flow mechanics of fluids flowing through porous medium. The effects of directional permeability on the flow of immiscible fluids are explored, and specific cases are presented. This study reveals a significant influence of directional permeability on the flow velocity of both fluids. Furthermore, quantitative conclusions are drawn regarding the shear stress at the lower and upper wall of the channel, with implications for the anisotropic nature of blood arteries. The findings contribute to a deeper understanding of fluid flow in anisotropic porous media and have potential applications in various engineering domains.

Effects of Ohmic heating, induced magnetic field and Newtonian heating on magnetohydrodynamic generalized Couette flow of Jeffrey nanofluid between two parallel horizontal plates with convective cooling

In this article, the effects of Ohmic heating, induced magnetic field and Newtonian heating on MHD generalized Couette flow of Jeffrey nanofluid between two horizontal plates with convective cooling has been investigated. The mathematical model used for the magnetohydrodynamic generalized Couette flow of pure water as the fluid phase containing Copper (Cu) as nanoparticles takes into account the effects of viscous dissipation, Soret and Dufour. The numerical solution of the system of nonlinear partial differential equations controlling the flow was performed using the finite difference method. To acquire the flow variable profiles, such as velocity, induced magnetic field, temperature, and concentration profiles graphically, the resulting numerical schemes are simulated in MATLAB software. The findings reveal that an increase in the Schmidt number causes a decrease in the concentration profiles, rise in the Jeffrey parameter causes a decrease in the velocity profiles. The temperature profiles also rise as a result of an increase in the Ohmic heating parameter and the heat generation parameter. Induced magnetic field profiles decreases with an increase in magnetic Prandtl number. The results demonstrate that Cu - water shows significant impact over nanofluid on temperature and velocity in the generalized Couette channel. The results of this study are valuable because they can be applied to the development of many chemical technologies, such as the production of polymers, MHD pumps, food processing, chemical catalytic reactors, MHD flow meters, astronomy, and lubrication. The results are compared with standard literature and show good agreement.

Effects of Chemical Reaction and Joule Heating on MHD Generalized Couette Flow between Two Parallel Vertical Porous Plates with Induced Magnetic Field and Newtonian Heating/Cooling

In this article, the effects of chemical reaction and Joule heating on MHD generalized Couette flow between two vertical porous plates with induced magnetic field and Newtonian heating/cooling have been investigated. The mathematical model used for the MHD generalized Couette flow takes into account the effect of viscous dissipation. The system of nonlinear partial differential equations governing the flow was solved numerically using the finite difference method. The resulting numerical schemes are simulated in MATLAB to obtain the profiles of the flow variables such as velocity, induced magnetic field, temperature, and concentration profiles graphically. Also, the effects of the flow parameters on the skin‐friction coefficient, Nusselt number, and Sherwood number are obtained and discussed numerically through tabular forms. The findings show that an increase in the chemical reaction parameter leads to a decrease in the concentration profiles. Also, increase in the Joule heating parameter and heat generation parameter leads to an increase in the temperature profiles. Induced magnetic field profiles increase with an increase in Reynold’s number. The findings of this study are important due to its application in developing a variety of chemical technologies, including polymer manufacturing, MHD pumps, food processing, chemical catalytic reactors, astronomy, MHD flow meters, and lubrication.

A note on the slip effects of an Oldroyd 6-constant fluid: Optimal homotopy asymptotic method

We study here the effectiveness of the optimal homotopy asymptotic method (OHAM) in solving non-linear differential equations of non-Newtonian fluids. To this consequence, we consider the Oldroyd 6-constant fluid when it demonstrates slippage between the plate and fluid generating non-linear boundary value problems. The problems of plane Couette flow, generalized Couette flow, and plane Poiseuille flow are considered. Graphs of the results are plotted to show the performance of the method in terms of velocity profile. It is observed that the method is quite easy to implement, having latent potential to handle such kinds of non-linear problems and yield accurate results at minimum to low computational work.

Differential transform method for couple stress fluid flow in a channel with a porous base

AbstractThe paper presents an application of the semi‐analytical differential transform method (DTM) to thermofluidics of generalized Couette flow of couple stress fluid inside a composite channel. The channel comprises a fluid‐saturated porous layer and a clear fluid region. The flow is caused by a uniformly favorable pressure gradient applied at the mouth of the channel and the shear of the moving upper wall of the channel. The matching conditions are taken such that the velocity, temperature, and respective gradients are continuous at a clear fluid–porous medium. The problem is novel because this is the first mathematical endeavor to treat fluidic systems involving composite channels. Besides the mathematical rigor, it presents an analysis of thermodynamic irreversibility and other quantities of interest, viz, skin friction and Nusselt number. The results derived from DTM are compared with those obtained by exact solution showing excellent agreement. The plots and tables are drawn and discussed.

A comparative analysis of multiple fractional solutions of generalized Couette flow of couple stress fluid in a channel

AbstractThis study provides the exact solutions of couple stress fluid (CSF) in a channel. The CSF is bounded by two plates in which the lower plate is moving with constant velocity Uo and the upper plate is fixed. The influence of the external pressure gradient is considered on the CSF fluid. To transform the classical CSF model, we have introduced three approaches to fractional derivatives, (a) Caputo (b) Caputo–Fabrizio (CF), and (c) Atangana–Baleanu (AB) fractional definitions. Exact solutions have been obtained using the Laplace and finite Fourier sine transforms jointly. Furthermore, the effect of different fractional derivatives is compared, and the results are shown in graphs. Moreover, parameters that affect the CSF motion are discussed in the graphs using the computational software MATHCAD. The most important outcome of the given study is the comparison of Caputo, CF, and AB fractional models with the classical CSF model. From the comparison, it can be noticed that AB fractional model discusses the dynamics of the CSF with a good memory effect as compared to Caputo and CF fractional operators. The CSF model can be reduced to Newtonian fluid as a limiting case and also investigated solutions in the absence of external pressure. Finally, Skin friction is evaluated for lower and upper plates, and the obtained results presented in tabular form.

Role of electromagnetic analysis in radiative immiscible Newtonian and non‐Newtonian fluids through a microchannel with chemical reactions

AbstractThe study of an immiscible fluid plays a significant role in the field of petroleum extraction, blood flow in arteries, hydrology, manufacturing process, and reservoir mechanics. These phenomena include immiscible fluids of different densities and viscosities in the same channel. Due to the various practical applications, in the current study, the generalized Couette flow of two immiscible fluids (Newtonian and non‐Newtonian fluids) of different viscosities between two infinite parallel plates under the presence of constant pressure gradient and electroosmosis is addressed. The effects such as electromagnetohydrodynamics, zeta potential, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been also considered into account. The dimensional system of equations has been nondenationalized with suitable dimensionless quantities. The resulting nondimensional system of coupled flow equations has been solved analytically. The solutions for the velocity, temperature, and concentration have been presented. The effect of various pertinent fluid flow parameters has been displayed graphically. The current study concludes that both the velocity and temperature profiles decrease with the increase in Hartmann number and radiation parameter, whereas an increase in chemical reaction parameter uplifts the concentration of both fluids.

Unsteady Generalized Couette Flow in a Horizontal Channel with Sudden Application or Removal of a Porous Material

The role of sudden application or removal of a porous material on generalized Couette flow in a horizontal channel is carried out. The governing momentum equation is obtained and solved with the necessary initial and boundary conditions. The well-known Laplace transform technique is employed to transform the PDEs into ODEs and then solved exactly in the Laplace domain. A numerical approximation based on the Riemann-sum is employed to transform the solutions obtained from the Laplace domain to the time domain. Based on the simulated results, it is found that the time taken to attain steady-state skin-friction and volumetric flow rate is strictly affected by the sudden application/withdrawal of porous medium. Also, despite the sudden application/withdrawal of porous medium, the velocities, skin-friction and volumetric flow-rates still attain steady state values.

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

The unsteady, magneto-hydrodynamic generalized Couette flows of two immiscible fluids in a rectangular channel with isothermal walls under the influence of an inclined magnetic field and an axial electric field have been investigated. Both fluids are considered electrically conducting and the solid boundaries are electrically insulated. Approximate analytical solutions for the velocity, induced magnetic, and temperature fields have been determined using the Laplace transform method along with the numerical Stehfest's algorithm for the inversion of the Laplace transforms. Also, for the nonlinear differential equation of energy, a numerical scheme based on the finite differences has been developed. A particular case has been numerically and graphically studied to show the evolution of the fluid velocity, induced magnetic field, and viscous dissipation in both flow regions.

Computation of unsteady generalized Couette flow and heat transfer in immiscible dusty and non‐dusty fluids with viscous heating and wall suction effects using a modified cubic B‐spine differential quadrature method

AbstractIn this paper, the unsteady flow of two immiscible fluids with heat transfer is studied numerically with a modified cubic B‐spine Differential Quadrature Method. Generalized Couette flow of two immiscible dusty (fluid–particle suspension) and pure (Newtonian) fluids are considered through rigid horizontal channels for three separate scenarios: first for nonporous plates with heat transfer, second for porous plates with uniform suction and injection and heat transfer, and third for nonporous plates with interface evolution. The stable liquid–liquid interface is considered for the two immiscible fluids in the first two cases. In the third case, it is assumed that the interface travels from one position to another and may undergo serious deformation; hence the single momentum equation based on the volume of fluid method is combined with the continuum surface approach model, and an interface tracking is proposed. The flow cases are considered to be subjected to three different pressure gradients, of relevance to energy systems—namely, applied constant, decaying, and periodic pressure gradients. For each case, the coupled partial differential equations are formulated and solved numerically using MCB‐DQM to compute the fluids velocities, fluid temperatures, interface evolution. The effects of emerging thermo‐fluid parameters, that is, Eckert (dissipation), Reynolds, Prandtl, and Froude numbers, particle concentration parameter, volume fraction parameter, pressure gradient, time, and the ratio of viscosities, densities, thermal conductivities, and specific heats on velocity and temperature characteristics are illustrated through graphs.

Heat transfer from a ferrofluid during generalized Couette flow through parallel plates in the presence of an orthogonal magnetic field

In the present work, we report heat transfer during the unidirectional laminar flow of ferrofluids in a parallel plate channel in the presence of a homogeneously applied magnetic field perpendicular to the flow direction. We have considered generalized Couette flow which results from the combination of shear stress, due to the relative motion between the parallel plates, and applied pressure gradient. For a comprehensive investigation, four different thermal boundary conditions have been considered. The application of magnetic field modifies the viscosity of the colloidal ferrofluid and thereby causes variations in the local flow field. Further, it also modifies the thermal conductivity of the fluid by changing particle orientation. As a consequence, the temperature distribution between the parallel plate channel is uniquely modified. The complex interplay between the hydrodynamics and the magnetics results in implicitly coupled governing differential equations, which have been solved numerically. We report that the local temperature in the domain could be reduced by increasing the applied field strength irrespective of the imposed thermal boundary conditions. However, the influence of the applied field finally gets saturated. We also discuss the effect of Brinkman number, loading of magnetic particles and pressure gradient on temperature distribution. Finally, analytical solutions, which presents closed-form expressions of the temperature profiles for four different types of boundary conditions, have been proposed.

Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method

In this research work, we have studied the steady generalized Couette flow of couple stress fluid between two parallel plates considering the non-isothermal effects. The governing equations that are, continuity, momentum and energy equations are reduced to ordinary differential equations. The Optimal Homotopy Asymptotic Method (OHAM) and New Iterative Method (NIM) are used to solve this coupled system of differential equations. Using the said methods, we have obtained expressions for velocity profile, temperature distribution, volume flux, average velocity and shear stress. The results of OHAM and NIM are compared numerically as well as graphically and a tremendous agreement is attained.

Regular perturbation solution of Couette flow (non-Newtonian) between two parallel porous plates: a numerical analysis with irreversibility

The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation. An irreversible process is a process in which the entropy of the system is increased. The second law of thermodynamics is used to define whether the given system is reversible or irreversible. Here, our focus is how to reduce the entropy of the system and maximize the capability of the system. There are many methods for maximizing the capacity of heat transport. The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy. The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel. For this, we choose two different fluid models, namely, the plane and generalized Couette flows. The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid. The present analysis shows the effects of the fluid parameters on the velocity, the temperature, the entropy generation, and the Bejan number. The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method. To validate the perturbation solution, a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0. The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters. It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number. When ηi → 0 (i = 1, 2, 3), the Eyring-Powell fluid is transformed into a Newtonian fluid.

On Criticality for a Generalized Couette Flow of a Branch-Chain Thermal Reactive Third-Grade Fluid with Reynold’s Viscosity Model

This research considers the third-grade liquid flow and criticality branched-chain of a thermal reaction in a Couette generalized medium with a nonlinear viscosity model. A dimensionless transformation of the system momentum and heat equations are carried out. Compared with the diffusion coefficient, the flow is stimulated by initiation reaction rate, reaction branch-chain order, non-Newtonian term, thermal Grashof number, and pressure gradient. The reactive fluid is fully exothermic with consumption of the material, and the heat exchange in the system is greater than the exchange of heat with the ambient. A semianalytical collocation weighted residual scheme is employed for the branch-chain slice bifurcation, dimensionless energy, and momentum solutions. The results show that exponential decreases in the thermal fluid viscosity can help in controlling the boundless heat produced by the Frank-Kamenetskii term and initiation reaction rate. Therefore, the results will help in stimulating positive combustion processes.

Computational study of solid-liquid supercritical flow of 4th-grade fluid through magnetized surface

This paper offers a comparative investigation of the multiphase flow of Newtonian and non-Newtonian dispersions passing through an inclined channel. Couette and Generalized Couette flow models are taken into account. A fourth-grade fluid is taken as non-Newtonian fluid, as well as base fluid. The stress tensor of fourth-grade fluid is used to formulate the problem. The relative motion between fluid and the upper plate is considered, while the relative motion between fluid and lower plate is mistreated. Crystal and Hafnium nano-sized particles are utilized to prepare dispersions. An external magnetic field is applied to the multiphase flows of dispersions in the channel and at the same time, the impact of gravitational force is also examined which has great mastery on flows. The governing equations for two-phase flows problem are determined by using Naiver-Stokes equations of continuity and momentum. Partial differential equations are reduced into ordinary differential equations by using appropriate transformations. The perturbation method is used to find out analytical solutions to these ordinary differential equations. Exact and approximation solutions are obtained by using MATHEMATICA Software. The impacts of salient parameters on each type of flow for velocity profile are discussed graphically. Furthermore, the comparison of velocity profiles of multiphase flows of dispersions is also presented in tabular forms. The variation in the magnitude of the fourth-grade non-Newtonian dimensionless parameter has great importance in non-Newtonian dispersions. The outcomes dispose of that the two-phase flows of Newtonian fluids suspended with crystal and hafnium particles are better one than the bi-phase flows of fourth-grade dispersions. Moreover, the Newtonian fluids suspended with hafnium particles are more consequential than the Newtonian fluids suspended with crystal particles. Similarly, the same behavior is observed in fourth-grade non-Newtonian dispersions. Then it is concluded that hafnium particles are a better option than crystal particles. These amalgams are very useful in every field of life, especially medicine as nanofluid drug delivery. In addition to this, no comparative analysis between Newtonian and fourth-grade non-Newtonian bi-phase flows has so far been reported in the existing literature.