Couple Stress Fluid Research Articles

Thermodynamic survey of a reactive MHD couple stress fluid through saturated porous substances with convective boundary conditions

This study explores the thermodynamic behavior of a reactive hydromagnetic liquid flowing through permeable materials, with convective cooling applied to the walls. This study holds practical significance in optimization of thermal management systems and it is crucial for enhancing the efficiency of controlling thermal runaway. The flow is modeled as a system of partial differential equations which are numerically solved. The modified Adomian Decomposition Method and Pade approximation technique are utilized in solving the equations. The results acquired for velocity and temperature distributions are thereby employed to estimate entropy generation rate with critical values over numerous effects of various boundaries over improvement of thermal runaway utilizing Pade approximation technique to show the significant impact of convective cooling term (Biot number) and other thermophysical parameters on the fluid flow. The outcomes show that fluid velocity continuously increases with rising values of inverse couple stress and fluid temperature increases Biot number.

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.

Impact of porous material and slip condition on the MHD flow of immiscible Couple stress-Newtonian fluids through an inclined channel: Head loss and pressure difference

Nowadays, non-Newtonian and Newtonian non-miscible fluid flow problems are much more effective in real-life physical problems. The understanding of flow behavior of magneto-hydrodynamic non-miscible fluids through a porous region playing an important role in the areas of biochemical sciences, crude oil extraction, transport issues and biomedicine. The aim of the present study is to know the impact of inclination angle of the channel, porous material used in the channel, slip boundary condition and applied magnetic field on the flow variables such as velocity profile, wall shear stress, pressure differences, head loss and volumetric flow rate of the two electrically conducting non-miscible couple stress and Newtonian fluids flowing through an inclined channel occupied with porous material of different porosity and permeability. An inclined channel is divided into two sub-regions of equal width through which the Newtonian and Couple stress fluids flow, respectively. Here, Brinkman’s model has been used to study the flow of immiscible fluid in their respective porous region. The equations that govern the flow of non-miscible fluids are solved using a well-defined analytical method and Mathematica 10.3 software. The present study concludes that the porous materials can be used to control the velocity of immiscible fluids in an inclined channel. It is also concluded from the present study that the use of slip condition promotes the values of velocity, volumetric flow rate, pressure differences and head loss. This work is validated with the previously published research work. Such models can be helpful in industries for filtering or refining immiscible oils.

A theoretical analysis of rotating electromagnetohydrodynamic and electroosmotic transport of couple stress fluid through a microchannel

AbstractThe main motivation behind this research work is the electroosmotic flow (EOF), which characterizes the movement of charged particles in a fluid when subjected to an external electric field, which offers precise control over fluid movement without mechanical components. The study of bio‐fluids in rotating microfluidic platforms is becoming much more significant. Hence, it is important to discuss the non‐Newtonian fluids in such environments. This paper analytically investigates the hydrodynamic characteristics of combined electromagnetohydrodynamic (EMHD) and EOF transport of non‐Newtonian fluid through a rotating microchannel with Navier‐slip boundary conditions at the walls. The couple stress fluid model is considered a non‐Newtonian fluid in the flow domain. The linearized Poisson‐Boltzmann equation is considered inside the electric double layer (EDL). The modified Stokes equation is governed by a combined imposed magnetic and EOF field. Closed form expressions are obtained for electrical potential, flow velocity, and volume flow rate in the channel using analytical methods. The dependence of rotating electromagnetic flow velocity and flow rates on appropriate parameters is explained. It is found that the rotational flow velocity displays an opposite pattern when the couple stress parameter and electric field intensity parameters are varied due to the influence of channel rotation. It is also found that the secondary flow rate ratio is amplified with the Hartmann number and slip length parameter, due to the stronger impact of the non‐Newtonian behaviour than the Newtonian situation on the volume flow rate at a relatively higher rotational value. The findings of this study may aid in the design and analysis of practical thermal micro/nano‐equipment for transporting biofluids.

EHD instability of a cylindrical interface separating two couple-stress fluids

This article is an attempt at examining the axi-symmetric and asymmetric streaming flows described by the CSF framework. A liquid that has microfibers implanted in it, like a fiber-reinforced composite substance, is so-called CSF. It is a system that consists of an endless vertical cylindrical interface that separates the two CSF structure. The CSFs are increasingly growing significant in modern manufacturing and technology, necessitating greater research into these fluids. An axial EF acts over the cylindrical contact in addition to the influence of CSF. The VPT is employed for the sake of convenience to minimize mathematical complexity. Combining the elementary linear equations of motion and the proper linear related BCs is the major procedure of the linear technique. A collection of physically dimensionless numbers is produced using a non-dimensional process. Subsequently, the requirements for hypothetical linear stability are developed. With the aid of the Gaster's theorem, the MS is applied in computing the dispersion relationships. After carefully examining a variety of effects on the stability investigation of the system at issue, it has been shown that the system is more unstable when a porous material is present than it would be without one. The resulting axisymmetric disturbance situation is more unstable. The linear techniques are depicted throughout a number of graphs.

Hydrophobic effects on a solid sphere translating in a Brinkman couple stress fluid covered by a concentric spherical cavity

In this study, a fluid flow with an incompressible axisymmetric steady couple stress translated through a porous media is analyzed between a hollow sphere and a concentric rigid sphere. In the permeable region, the flow field is regulated by Brinkman's equation. The slip and spin slip conditions are applied on both the rigid sphere and spherical cavity surfaces. Modified Bessel functions provide a systematic approach to the problem by utilizing the principle of a stream function. On the inner sphere, the wall correction factor that an incompressible couple stress fluid encounters is calculated. The effects of the slip, spin slip, coupling stress parameter, separation distance, and permeability parameter on the field functions and the normalized drag force are also graphically shown. The corresponding results are contrasted with the outcomes reported for particular cases of couple stress fluid and viscous fluid flow in two permeability-free concentric circles. Furthermore, graphs of the streamlines for various values of the relevant parameters have been included.

Natural convective and Cattaneo–Christov model for couple stress nanofluid at the middle of the squeezed channel with sensor surface

The aim of this work is to present a natural convective and squeezing flow model of two-dimensional couple stress nanofluid which is flowing on the sensory surface with variable fluid viscosity. The fluid flowing on a microcantilever sensory surface and squeezing is happening at free stream. The sensor is also useful to detect the movement of fluid and the variations in thermal and solutal rates. The Cattaneo–Christov model is adopted along with nanoparticle and chemical reaction to explore the transmission of heat and mass rates. The analysis of heat transmission in non-Newtonian couple stress fluid flowing on squeezed sensory surface by using the Cattaneo–Christov heat conduction model has various industrial and scientific applications including the polymer processing, wastewater treatment, chemical reactors, biomedical flows, cooling and heating processes in industries, heat exchangers, microfluidics, oil and gas industries. All the assumptions are applied in the basic governing laws laws and then we get the model of the partial differential equations. The governing model of equations is transmuted into ordinary differential equations form via the transformations and then the numerical results of these ODE’s are examined with a well-defined numerical technique “Shooting Method”. For higher inputs of couple stress, squeezing index and permeability velocity, the fluid’s internal velocity decreases. Because of the Prandtl number and thermal relaxation coefficient, the heat transfer mechanism slows down. Mass transfer increases for greater inputs of the thermal diffusivity coefficient and decreases due to concentration relaxation. Further, the numerical dependency of emerging parameters on the skin friction is illustrated in tabular form. The parametric effects on the model (velocity, temperature and concentration) are introduced using numerical values shown in the table.

The profound effect of heat transfer on magnetic peristaltic flow of a couple stress fluid in an inclined annular tube

In this study, we explore the analysis of peristaltic flow with heat transfer occurring within the gap between coaxial inclined tubes. The inner tube’s wall is rigid, while the outer tube’s wall features a sinusoidal wave propagating through it. The cylindrical system is employed to formulate the problem. The flow is characterized using continuity, momentum, and energy equations. We apply the assumption of long wavelength and the low Reynolds number approximation to simplify the nonlinear governing equation, subsequently solving it through perturbation techniques. We investigate the impact of crucial parameters, such as the magnetic field, porous media, slipping conditions, and others, on the peristaltic flow of a couple stress fluid. Our focus lies on assessing their influence on axial velocity, pressure gradient, and flow streamlines. The outcomes are visually presented through graphical representations. Notably, an increase in the slipping parameter results in a reduction of fluid velocity, attributed to the reverse slipping of the flow. The introduction of a magnetic field leads to an augmentation of the pressure gradient. Moreover, elevating the peristaltic amplitude and heat source induces the formation of a vortex within the flow. The presence of porous media leads to an increase in the pressure difference of the fluid flow. The primary objective of this research is to enhance our understanding of the peristaltic motion of non-Newtonian fluid dynamics, specifically incorporating a couple stress fluid. This contributes to a deeper understanding of crucial fluids, such as blood, within the human circulatory system. The implications extend to biological and industrial applications like magnetic resonance imaging (MRI) and radiosurgery, advancing our scholarly understanding of fluid behavior, especially in non-Newtonian scenarios.

Impact of inconsistent viscosity on the stability of a rotating layer of couple stress fluid

The present model considers viscosity of a couple stress fluid to be dependent on temperature and pressure. The stability of the rotating horizontal layer is analyzed by utilizing the normal mode technique and energy technique. The critical threshold obtained by the two theories is found to be the same and no subcritical region is found for the considered values. The couple stress and rotation are seen to stabilize while the viscosity variation is found to destabilize the system. The critical Rayleigh number values are found to depend on the reference pressure and temperature chosen at the top surface in the current work, and thus the convection can be controlled by controlling the reference temperature and pressure.

Analysis of heat and mass transfer of a non-linear convective heat generating fluid flow in a porous medium with variable viscosity

The present study addresses the significance of analyzing the heat and mass transfer characteristics of a non-linear convective fluid flow featuring variable viscosity within a porous medium. Our focus lies on understanding the impact of varying viscosity on the hydromagnetic coupling stress, particularly in the presence of internal heat generation. The fluid is confined within a porous medium, and convection cooling takes place at both wall of the fluid. A key assumption in our investigation is the nonlinearity nature of the buoyancy force, specifically when there is a substantial difference in temperature and concentration within the fluid and its surroundings, the buoyancy force becomes quadratic. The exploration of couple stress fluids, alongside considerations of temperature-dependent internal heat generation and mass transfer, contributes to advancing our understanding of thermal system performance. By accounting for nonlinearity in density, temperature, and concentration, the research aims to provide more accurate results than previous linear models, crucial for optimizing energy consumption in practical applications such as nuclear reactors and heat exchangers. Dealing with this type of problem often pose significant challenges, as they often lack analytical solutions, necessitating the use of more advanced numerical methods or approximation techniques. We employ Spectral Quasilinearisation Method (SQLM) to solve the coupled non-linear boundary value problems (PDE) arising from the model, momentum equation, energy equation, concentration equation, and entropy generation. The obtained results are then validated using the Runge–Kutta method and a good agreement is achieved. The findings for the dimensionless velocity, temperature, mass concentration and entropy generation are presented in graphics and in table manner, and effects of controlling parameters are extensively explained. The results highlight that an increase in variable viscosity leads to an enhancement in the velocity profile, while simultaneously reducing the temperature in the system. Furthermore, increments in the non-linear convection parameter and coupling stress parameter result in an appreciation of the velocity profile, temperature profile, and entropy generation rate.

MHD Couple stress fluid between two concentric spheres with slip regime

The problem of the axisymmetric steady flow of an incompressible couple stress fluid within two concentric spheres is analyzed analytically in this study. In the interior of the solid sphere, translation takes place with a uniform velocity, and in the exterior, translation takes place with a fixed velocity. A study of slip conditions was carried out on the surfaces of the two spheres. In terms of stream functions, modified Bessel functions provide an analytical solution to the problem. As the outer sphere remains stationary, the inner sphere experiences the normalized drag force. A graphic representation of drag is provided based on the slip and spin slip parameters, the couple stress parameter, the separation distance, and the MHD parameter. In addition, the results are compared with earlier results for special cases of translation of one rigid sphere through an unbounded magnetic medium, viscous fluid flow, and Couple stress fluid without MHD between two concentric spheres.

Surface Roughness Influence on the Dynamic Performance of Rayleigh Step Bearing Lubricated with Couplestress Fluid

Surface Roughness Influence on the Dynamic Performance of Rayleigh Step Bearing Lubricated with Couplestress Fluid

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.

Effect of magnetic field and slip velocity on the performance of bearings lubricated by couple stress fluid on long cylinder and infinite plate — A theoretical analysis

In this research, the combined effect of magnetohydrodynamics (MHD) and slip velocity on squeeze film lubrication of long cylinders and infinite plates with couple stress fluid has been studied. Combining the Stokes couple stress theory and the Lorentz force theory yields analytical solutions for the modified Reynolds equation. Using the Reynolds equation, the mathematical expressions for squeeze film pressure, load-carrying capacity and squeeze film time are obtained. The pressure, load carrying capacity and squeeze film time increase with the combined effect of MHD, couple stress fluids and slip velocity.

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.

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.

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.

Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field

Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field

Comparative study of couple stress fluid flow using OHAM and NIM

Comparative study of couple stress fluid flow using OHAM and NIM

Nonlinear flow of couple stress fluid layer over an inclined plate

The issue of stability of a thin couple-stress liquid layer flows on an inclined plane was inspected. The thin-film approximation was employed to obtain a Benney-like differential equation, that described the time record of the interface profile The linear transition state and reduction ratio of maximum classical (Newtonian) growth-rate were discussed. The complete evolution equation was solved numerically using the method of lines in order to support the novelty of the work. The linear stability could be enhanced by increasing the couple-stress coefficient and surface tension as well as reducing the inclination. However, the ordinary viscosity played an irregular role. The linear results predicted conditions (windows) in which the non-Newtonian film was more stable than its Newtonian counterpart. The nonlinear stimulation anticipated the existence of sock waves in certain situations. The appearance of instability through the linear subcritical region as well as irregular influences with respect to surface tension and couple-stress property was revealed. The nonlinear approach was more accurate in describing the stability issue than the linear one. Such results could be employed to attain the optimum statuses with regard to the film stability, and control the shock waves. They would not only enable accurate practical implementation in the design of inertial confinement fusion capsules and supernova explosions and implosions modeling, but also would allow for precise numerical simulation.