Flow Of Couple Stress Fluid Research Articles

Thermal enhancement of couple stress fluid flow through anisotropic porous media

This study examines forced convective heat transfer via an anisotropic porous channel in a couple stress flow. The flow field is assumed to be fully developed and governed by the Darcy Brinkman Forchheimer equation. The thermal field is assumed to be developing. The channel walls are subjected to constant heat flux. Since the momentum equation is non-linear and the thermal energy equation is linear, coupled equations are solved numerically using the finite difference method. The variation in the bulk mean temperature is linear with the axial distance for all values of the couple stress parameter and Darcy number. In the absence of axial conduction and heat sources or sinks in the flow field, it is easy to see that the energy gained by the fluid up to an axial distance is twice the axial distance. The parameters, anisotropic permeability ratio, and anisotropic angle enhance the heat transfer. The couple stress parameter lessens the enhancement in heat transfer. Anisotropy is critical in heat transmission for Darcy number, DaH≤0.8. The heat transfer rate decreases by more than 40% due to couple stress fluid and anisotropic effects in the channel, as opposed to the Newtonian isotropic situation. This investigation's findings have been compared with previous experimental and numerical research.

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

AbstractThe 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.

Flow and Thermal Characteristics of Couple Stress Fluid over a Stretching Surface with Hybrid Nanoparticles

In the current research, a mathematical analysis of couple stress fluid flow and heat characteristics through a stretchable permeable surface with hybrid nanoparticles is conducted. The solid nanoparticles of the aluminium alloys (AA7072 and AA7075) are suspended in methanol to create the hybrid nanofluid. The similarity approach is used to reduce the governing equations into the similarity equations. Then, MATLAB's bvp4c function is employed to solve the resulting equations. The solutions for the flow and temperature fields, as well as the skin friction coefficient and Nusselt number are presented in table and graphical forms. The results demonstrate that hybrid nanofluids excel as thermal conductors, significantly augmenting the heat transfer rate. The heat transfer rate is increased by 0.38% for the nanofluid, while 0.89% increment for the hybrid nanofluid compared to the base fluid. Furthermore, a larger couple stress parameter is found to be associated with a decrease in the fluid temperature and an enhancement in fluid velocity.

A NANOFLUID COUPLE STRESS FLOW DUE TO POROUS STRETCHING AND SHRINKING SHEET WITH HEAT TRANSFER

The analysis of current work portrays the exact solution of couple stress fluid flow with heat transfer. Three varieties of nanoparticles are placed inside the flow to achieve better thermal conductivity. A porous sheet inside the fluid flow is considered to yield new results of the study. With the use of similarity variables, the controlling partial differential equations of the issue are converted into ordinary differential equations. Analytical analysis is used to determine the domain and solution of the momentum and energy equations in terms of the Laguerre polynomial. In addition, skin friction and Nusselt number are also verified using nondimensional different controlling parameters, such as thermal radiation, the couple stress fluid parameter, solid volume fractions, mass transpiration, and so on, to verify the results of this work. The present work is very good argument with a previously published paper, and it also covers many industrial applications, namely entropy generation, polymer production, automotive cooling systems, and microelectronics.

Comparative study of couple stress fluid flow using OHAM and NIM

Comparative study of couple stress fluid flow using OHAM and NIM

CREEPING FLOW OF COUPLE STRESS FLUID OVER A SPHERICAL FIELD ON A SATURATED BIPOROUS MEDIUM

This problem emphasizes the dynamic interaction between a biporous medium and a couple stress fluid of laminar flow. The flow around a permeable field engulfed in a couple stress fluid is examined. When examining the motion of an oil droplet in a porous collector that is surrounded by an aqueous medium (oil-in-water emulsion) and is subject to an external pressure drop, this formulation of the problem is typical. A similar issue arises when lymph enters the tissues of humans or animals: the inside permeable spherical field saturated with viscous fluid and outside region saturated with couple stress fluid. The Brinkman equations are utilized to characterize the couple stress fluid flow in a saturated biporous medium. The couple stress tensor and velocity fields are expressed using Gegenbauer polynomials and Macdonald functions. For the axially symmetric motion, both pressure distribution and the stream function solution are explicitly solved. The method of variable separation is used to investigate an analytical resoluteness for the flow field. The drag force on a saturated biporous medium and the drag coefficient <i>D<sub>N</sub></i> are calculated, and the impacts of the permeability κ, the ratio of viscosity (γ<sup>2</sup> = μ<sub>1</sub> /μ<sub>2</sub>), the couple stress viscosity ratio (τ = η'/η), and the parameter of couple stress (λ = √μ/η). The appropriate dependencies are graphically delineated and reviewed, including the permeability κ, couple stress parameter λ, viscosity ratio γ<sup>2</sup>, and couple stress viscosities (η, η'). According to the findings, increasing permeability gradually raises the drag coefficient, which is used to describe a spherical field’s surface with a high level resistance of flow. Limits statements are used to illustrate specific cases that are well-known. The current study is significant primarily in the course through a layer formed by penetrable particles and has very important and compelling applications in both nature and innovation, with a variety of potential outcomes.

Couple Stress Fluid Flow in A Doubly Connected Region Bounded by Elliptic Cylinders

Couple Stress Fluid Flow in A Doubly Connected Region Bounded by Elliptic Cylinders

Non-Stationary Helical Flows for Incompressible Couple Stress Fluid

We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality α between velocity and the curl field of flow is investigated. In the given analysis for this given type of couple stress fluid flows, an absolutely novel class of exact solutions in theoretical hydrodynamics is illuminated. Conditions for the existence of the exact solution for the aforementioned type of flows were obtained, for which non-stationary helical flow with invariant Bernoulli-function satisfying to the Laplace equation was considered. The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli-function if components of the velocity of the flow are already obtained. Analytical and numerical findings are outlined, including outstanding graphical presentations of various types of constructed solutions, in order to elucidate dynamic snapshots that show the timely development of the topological behavior of said solutions.

Couple Stress Fluid Flow Through a Porous Media Past A Solid Sphere

A steady, two-dimensional, incompressible couple stress fluid flow over a rigid sphere of radius ‘a’ surrounded by infinite porous region specifying a constant velocity away from the boundary is considered. An exact solution is found for the governing equations which leads to the expression for the stream function and shearing stress. The impact of couple stress parameter and porosity on the flow patterns is examined through streamlines. Also shear stress is computed for various values of couple- stress parameter and porous parameter. The obtained results reveal that as coupling stress parameter increases for fixing the porosity, streamlines are symmetric and meandered near the rigid sphere. But for fixed coupling stress parameter and increase in porous parameter cause the streamlines to move away from the solid sphere. Also, the dimensionless shear stress increases as couple-stress parameter intensifies for fixed porous parameter and vanishes at two stagnation points. The amplitude of the shearing stress raises with raise in porous parameter for fixed coupling stress parameter.

Couple stress effects on the MHD triple-diffusive oscillatory flow in a fluid-saturated porous layer

The motivation of this paper is to explore an oscillatory flow of a magnetohydrodynamics (MHD) couple stress fluid with heat and mass transfer analyses through a porous medium. The modified Darcy–Brinkman couple stress fluid model is employed. There could be many potential applications of this study, such as thermal system, solidification of liquid crystals, cooling of metallic plates in a bath, exotic lubricants and colloidal solutions. In the wake of these potential applications, the study of MHD couple stress fluid flow with additional diffusing components has been found to be innovative and very interesting in the analysis of the influence of combined magnetic effects, couple stress fluid and two solutes. A governing coupled nonlinear partial differential equation with boundary constraints represents the modeled flow problem. In addition, these equations are converted into nondimensional form by employing the suitable nondimensionalizing quantities. It is possible to attain analytic solutions to the dimensionless equations that control the liquid flow, and the consequences of the flow’s confines on velocity, temperature, concentration and skin friction profile are examined and also the results are discussed through graphs. It is noteworthy that when the injection level on the heated plate is increased, the skin friction on each channel plate also increases.

Effects of Joule heating and reaction mechanisms on couple stress fluid flow with peristalsis in the presence of a porous material through an inclined channel

Abstract The objective of this study is to assess the flow behavior of the peristalsis mechanism of a couple stress fluid in incorporating a porous material. In addition, reaction mechanism and Ohmic heating are also taken into consideration with slip boundary conditions. For the purposes of mathematical simulation, we assume a long-wavelength approximation, ignoring the wave number and taking a low Reynolds number into account. The obtained outcome is shown in a graphical manner and then analyzed. The results of this investigation reveal that when the Hartmann number improves, the pattern of velocity noticeably decelerates. The Lorentz forces have a retarding impact on the velocity of the fluid from a physical standpoint. As the couple stress variable rises, so does the velocity of the fluid. As the couple stress component increases, the skin friction coefficient increases in one region of the fluid channel and falls in another region, between x = 0.5 and x = 1. As the thermal slip variable rises, more heat is transferred through the surface to the fluid, resulting in a rise in the temperature profile. When the couple stress variable is raised, the Nusselt number rises, while the thermal radiation factor causes the Nusselt number to decline. The results showed a positive relationship between the Sherwood number and the reaction mechanism parameter. This study demonstrates the potential use of this research in the fields of a career in engineering, namely, in enhancing hydraulic systems, as well as in medicine, particularly in optimizing gastrointestinal processes. The process of dissection facilitates the unimpeded circulation of blood and lymph inside the vascular system of the body, enabling the delivery of oxygen to tissues and the elimination of waste materials.

Characterizing Quadratic Convection and Electromagnetically Induced Flow of Couple Stress Fluids in Microchannels

Characterizing Quadratic Convection and Electromagnetically Induced Flow of Couple Stress Fluids in Microchannels

Entropy generation analysis in micropolar-couple stress fluid’s flow in an inclined porous channel using Homotopy Analysis Method

In this work, authors have presented the flow of the micropolar-couple stress fluids passage through an inclined channel. The inclined channel is occupied by the porous material. In the proposed problem, the channel is divided into two zones, zone-I contains the micropolar fluid and zone-II contains the couple stress fluid. The permeability of both zones is taken to be different and we have considered that the movement in the fluids occurs with the help of the constant pressure gradient. In this work, we have analysed the flow velocities, temperatures, and entropy generation when immiscible micropolar-couple stress fluids flow in an inclined channel filled with a porous medium. We have used the Homotopy Analysis Method (HAM) to solve the fundamental system of differential equations of the proposed problem. For both fluids, a graphic analysis is also done on the effects of various flow-affecting parameters, such as couple stress, micropolarity, inclination angle, viscous dissipation, etc., on the linear velocities, micropolar fluid’s microrotational velocity, temperatures, entropy generation, and Bejan numbers. The derived results are validated with the previously established results available in the literature. This work shows the effect of two polar fluids one containing microstructures (micropolar fluid) and another without microstructures (couple stress fluid) on the entropy generation. From the proposed work, it is found that in the flow of two polar fluids, the entropy production in the couple stress fluid flow region is smaller than that of the micropolar fluid flow region. The present model is useful in maintaining the entropy production to enhance the efficiency of electric devices such as, refrigerators, thermal engineering devices, heat regulatory devices, etc.

Effects of slippage and permeability of couple stress fluid squeezed between two concentric rotating spheres

This study investigates the rotation of two concentric spheres saturated by creeping single-phase couple stress fluid flow under the impacts of permeability and slippage. The slippage conditions are applied on the surfaces of the spheres. In addition, the couple stresses on the boundary are assumed to vanish. Moreover, the analytical solution to the problem is used to obtain the field functions velocity, tangential stress, and couple stresses. The torque experienced by the fluid on the inner solid sphere is evaluated and plotted. The contour lines of fluid velocity are sketched at specific values of the parameters. The results presented that the torque acting on the inside sphere decreases monotonically with the permeability and slippage parameters at certain values of the relevant parameters. Also, the rise of couple stresses inclined the torque.

Analysis of pressure load-carrying capacity and squeezing time on magnetohydrodynamic couple stress fluid flow between sphere and flat plate with slip velocity

This paper presents a theoretical analysis of the effects of a magnetic field, couple stress fluid, and slip velocity on squeeze film lubrication between a sphere and a flat plate. The modified Reynolds equation is derived using Stokes micro continuum theory of couple stress fluids. The nondimensional governing equations of the flow model are solved analytically for pressure, load-carrying capacity and squeezing time. The results are graphically presented and analyzed for various parameters. The study shows that the couple stress parameter and magnetic field significantly enhance the film pressure, load-carrying capacity, and squeeze film time compared to the Newtonian and nonmagnetic cases. Also from the results, it is observed that the squeeze film properties can be significantly reduced by the effect of the slip parameter.

Natural convection with variable fluid properties of couple stress fluid with Cattaneo-Christov model and enthalpy process

The geometry under consideration for this flow problem, namely paraboloid surface is similar to aircraft and car bonnet, bullet shape, front shape of submarine, rockets and these types of are useful in manufacturing of formula F1 cars and airplanes. The flow of fluid over paraboloid surface has several applications in space science, industries, mechanical works and architecture. The aim of this study is to explore the Cattaneo-Christov heat and mass flux model in steady 2D couple stress fluid flow with variable thermo-physical characteristics near the parabolic surface. The effects of enthalpy and activation energy are also taken into consideration. The stretching in the layers of fluid is assumed at the surface of body. The problem is amended by using the law of conservation of momentum, energy and mass transfer. The non-linear governing partial differential equations are converted into ordinary differential equations by using self-similar form with similarity transformation. The resulting ODE's are numerically solved by bvp4c method. The conclusion indicates that the fluid moves quickly due to higher inputs of couples stress parameter and buoyancy parameter while the viscosity coefficient creates restriction in the fluid motion. The transference analysis of temperature and concentration enhances for higher impacts of thermal conduction and mass diffusivity coefficient. The thermal concentration relaxation parameters are the source of decline in the concentration and temperature of fluid. The heat transmission rate is maximum and mass transfer is minimum due to raising values of Dramkholer number. The impression of all parameters on different fields is listed in discussion section.

Oscillatory Flow of Couple Stress Fluid Flow over a Contaminated Fluid Sphere with Slip Condition

This research paper aims at finding the analytic solution for an oscillatory flow of couple stress fluid flow over a contaminated fluid sphere, filled with a couple stress fluid which is considered with interfacial slip on the boundary. The stream functions and drags related to the findings were analytically obtained. The special cases as a result of this are deduced for drag force which satisfies with the available data mentioned in the literature. The numerical values that were obtained are represented in both tabular and graphical forms for ease of representation. It has also been observed that in the case of viscous fluid, there is an inverse relation between real drag, slip parameter and viscosity ratio. It was also found that, there is a direct relation between imaginary drag, slip parameter and viscosity ratio respectively. For instance, in the case of the couple stress fluid, at lower values of the couple stress parameter there is a reduction in real drag, and an increase in imaginary drag respectively. These findings can result in future research considering body forces and other non-Newtonian fluids

Impact of an inclined magnetic field on couple stress fluid flow over a stretching surface with effect of Stefan blowing, radiation and chemical reaction

The present work focuses on the investigation of the couple stress nanofluid flow with the inclined magnetic field, heat, and mass transform effect. The impact of parameters such as the Schmidt number, the Prandtl number, the Stefan Boltzmann constant, and the magnetic field parameter is evaluated. The regular partial differential equations (PDEs) are mapped into ordinary differential equations (ODEs) and solved analytically, while the exact solution of heat and mass transfer is given in terms of confluent hypergeometric function. It is shown that the impact of the couple blowing effect has primitive impact on velocity, temperature and concentration profiles. The magnetic parameter, by posing a magnetic field normal to the stretching sheet, reduces the flow velocity, the couple stress fluid parameter increases the amplitude of oscillations in velocity and skin friction coefficient, the heat source/sink parameter increases the temperature of the fluid, the volume fraction of the nanoparticles increases the thermal efficiency of the fluid, the chemical reaction parameter decreases the temperature of the fluid, and, finally, the thermal radiation increases the nanofluid temperature.

Influence of Hall current & Lorentz force with nonlinear thermal radiation in an inclined slip flow of couple stress fluid over a Riga plate

Partially ionised fluids subject to an external magnetic field results in a completely different dynamical behaviour. Very few studies are conducted to explore the fascinating properties of Hall current and Ion slip in fluid flows. Flow over a Riga plate with MHD Ion and Hall currents, nonlinear thermal radiation is still rare. We aim to analyse the inclined stagnation point slip flow of Couple Stress fluid over a stretched horizontal Riga plate to close this gap. The flow problem is modelled using Navier stokes theory along with energy conservation and then principal partial differential equations are converted into ordinary differential equations. The governed system is solved mathematically by numerical technique RK Fehlberg method. The behaviour of fluid is described through graphs including fluid’s motion and energy. Local surface skin friction coefficients and local heat and mass flux at surface are the concerned physical magnitudes which are described through graphs and tables and are highly recommended in practical solicitations in numerous production plants and manufacturing workshops. Thermally radiative MHD flow with Ion Hall currents are broadly used in thermal controlling systems, spectro scopy, microchip technology, Magnetohydrodynamic energy conversion campaigns, exploration and expansion for high & low efficiency release, power-driven & power generation structures, MHD accelerations & thrusters, and drift regulator in hypersonic and automobiles.

Second law analysis of thermo-magneto-hydrodynamic couple-stress fluid flow in a cavity with heated fin

The objective of current study is to analyze the magnetohydrodynamic (MHD) natural convection flow of couple-stress fluid and entropy generation (second law analysis) inside the cavity with heated fin by using the Galerkin finite element method. The heated fin has been placed in middle of the heated bottom wall, the temperature T c is fixed on the vertical walls and an insulated situation is considered at the top wall. The irreversibility ratio and heat flux inside the enclosure are examined through entropy generation and Bejan heatlines, respectively. The obtained results show that the intensity of circulations of streamlines decrease from 3.9744 to 0.03148 and heatlines from 7 to 4.5 due to increasing couple-stress parameter ( K ) from 0 to 1.5 . It is noted that the heatlines bowls appear due to enhanced buoyancy-driven flow against high Rayleigh number. The reverse relation is noted between the entropy generation and the Hartmann number. The overall heat transfer rate along with the bottom and vertical side walls increase 111.65 % and 75.8297 % , respectively, with increasing the fin height from 0 to 0.25 . Obtained results could help to optimize heat transfer in engineering systems like heat exchangers, cooling processes of devices, chemical reactors, and solar collectors.