Couple Stress Fluid Research Articles

Drag Over A Fluid Sphere Filled With Couple Stress Due to Flow of A Couple Stress Fluid with Slip Condition

In this article, the exact solution for a couple stress fluid flow past a fluid sphere filled with a couple stress fluid is considered using interfacial slip on the boundary. The velocity is expressed with regard to the stream function. The external velocity and internal velocity are alongside the drag coefficient. It was noticed that with the increases in slip parameter, the drag coefficient is decreasing and the inflow pattern has more circulations with more area appearing near the poles and internal flow disappears gradually. The special cases of viscous fluid, no-slip condition, and solid sphere are evaluated. A good understanding of the current and literature outcomes have been obtained, including the special case of a viscous fluid past a couple stress fluid sphere. HIGHLIGHTS The flow of couple stress fluid flow past a fluid sphere filled with couple stress fluid with slip over the surface is reported In case of no-slip condition, results are captured as s→∞. and also as μ→∞, fluid sphere can reduce to the case of a solid sphere For the case of viscous fluid can be recovered as a limiting case of the analysis by taking λ_e→∞, λ_i→∞, and χ_1→∞, χ_2→∞ GRAPHICAL ABSTRACT

Non-Uniform Temperature Gradients Impact on Rayleigh-Darcy Convection : A Composite System with Couple Stress Fluid

The impact of non-uniform temperature gradients on Rayleigh-Darcy convection in a composite system of couple stress fluid is discussed. The composite system is bounded by stress-free surfaces and adiabatically insulated, and the fluid-porous layers are coupled by employing appropriate interfacial boundary conditions. To determine the eigen value, the regular perturbation method is used. The effect of dimensionless parameters on Rayleigh-Darcy convection is analysed graphically, and it is demonstrated that the couple stress parameter and couple stress viscosity ratio stabilise the system, while the opposite effect is observed for the Darcy number and thermal diffusivity ratio.

Linear, Parabolic, and Inverted Parabolic Temperature Gradients Impact on Double-Diffusive Rayleigh-Darcy Convection : A Composite System with Couple Stress Fluid

The influence of linear, parabolic and inverted parabolic temperature gradients on the onset of double-diffusive Rayleigh-Darcy convection is theoretically investigated. The composite system is constrained horizontally by adiabatic and free-free thermal boundaries, and appropriate interfacial boundary conditions are used to connect fluid-porous layers. The regular perturbation approach is used to determine the critical Rayleigh number expression for different temperature gradients. Graphs are used to investigate the significance of a variety of dimensionless characteristics. The couple stress parameter, couple stress viscosity ratio, solute Rayleigh number, and solute diffusivity ratio clearly have a stabilizing effect on the system, whereas the Darcy number and thermal diffusivity ratio destabilize it.

Rheology of peristaltic flow in couple stress fluid in an inclined tube: Heat and mass transfer analysis

The recent investigations ensure that the effect of an endoscope on the peristaltic flow is very important for medical diagnosis and it has many clinical applications such as gastric juice motion in the small intestine when an endoscope is inserted through it. Therefore, we have studied the problem of peristaltic flow with heat and mass transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave traveling down its wall. The inner tube fulfilled the slip condition while the outer tube has a no-slip condition. The lubrication approximation theory is utilized to simplify the normalized equations. The perturbation procedure is employed to concede the results for the pressure gradient and velocity field, whereas exact outcomes are established for the energy and concentration fields. Frictional forces and pressure rise per wavelength are calculated numerically. The impacts of embedded parameters are portrayed through graphs. It is found that fluid velocity reduces by increasing the couple stress parameter however the inverse effect is noted for the slip parameter. Furthermore, better pumping is viewed in the vertical tube as compared to the horizontal tube. A validity of perturbation solutions for velocity distribution is made with the finite element method and an admirable comparison is also noticed with previously published results.

Peristaltic mechanism of couple stress nanomaterial in a tapered channel

This paper addresses the analysis of chemical reaction for mixed convection peristaltic movement of electrically conducting couple stress nanomaterial in an asymmetric tapered porous channel under the influence of heat generation/absorption. The heat and mass performances of nanofluid are captured with an evaluation of the famous Buongiorno model, which enables us to determine the attractive features of Brownian motion and thermophoretic diffusion. The velocity slip and viscous dissipation effects are also be accounted. Mathematical modeling incorporates lubrication approximation. The expressions for temperature, pressure rise, concentration, velocity, pressure gradient, and streamlines are estimated numerically and scrutinized for dissimilar flow parameters such as magnetic parameter 1≤M≤4, Darcy number 0.1≤Da≤0.5, couple stress fluid parameter 3≤γ≤6, Brinkman number 1≤Br≤4, heat absorption parameter 1≤B≤2, Brownian motion parameter 1≤Nb≤4, thermophoresis parameter 1≤Nt≤4, Schmidt number 0.3≤Sc≤1.5 and chemical reaction parameter 0.4≤kc≤0.9. Furthermore, the skin friction and Nusselt number at the channel walls are established for a choice of assessments of significant parameters and which are exhibited in a tabular manner. Outcomes reveal that velocity and pressure gradient increase by enhancing the velocity slip parameter. Further, the thermophoresis parameter favors the nanofluid temperature and declines the concentration. To ensure the accuracy of the developed code, obtained results are compared with the results available in the literature and found in excellent agreement.

The Axisymmetric Migration of an Aerosol Particle Embedded in a Brinkmann Medium of a Couple Stress Fluid with Slip Regime

This study examined the relationship between stresses and couple stresses within the context of the couple stress fluid theory. The application of the effective medium approach, based on the Brinkman equation, is also discussed under the effect of slip and spin slip on the surface of the solid sphere immersed in porous couple stress fluid. The motion is generated by moving a solid sphere at a constant speed. Using Stokesian assumptions, the equation of motion ignores nonlinear terms. The surface conditions for slip and spin slip of couple stress fluids have been applied. Tables and graphs are used to represent the normalized drag force exerted by the fluid flow on the solid sphere. According to the numerical results, the drag force increases monotonically with permeability and couple stress. As a result, the results obtained are consistent with those found in the literature for viscous fluids, and the special cases are determined.

Unsteady Two Dimensional Mixed Convection MHD Couple Stress Fluid Flow through an Inclined Stretching Sheet with Chemical Reaction

In this work, the investigation has focused on the unsteady hydromagnetic mixed convection couple stress fluid through an inclined linearly stretching sheet. The model equations governing the flow are converted to ordinary differential equations employing appropriate similarity transformation variables. An efficient technique, Runge-Kutta 4th order (RK4) technique together with shooting method is deployed to tackle the dimensionless equations with relevant boundary conditions. The impacts of various parameters such as unsteadiness parameter , Hartman number , mixed convection parameter , concentration buoyancy parameter , angle of inclination , chemical reaction parameter and Schmidt number are analysed and discussed with plots. Fluid velocity decreases as the unsteadiness, Hartman number, Schmidt number, and chemical reaction parameters rise; while the angle of inclination, mixed convection, and concentration buoyancy parameters speed up the flow. Furthermore, the unsteadiness, angle of inclination and mixed convection parameters reduce fluid temperature, while all the parameters reduce flow concentration.

Static and Dynamic Characteristics of Rough Porous Rayleigh Step Bearing Lubricated with Couple Stress Fluid

In tribology, the Rayleigh step bearing has the maximum load capacity of any feasible bearing geometry. Traditional tribology resources have demonstrated that the Rayleigh step has an ideal geometry which maximizes load capacity. Both in nature and technology, rough and textured surfaces are essential for lubrication. While surface roughness enhances the performance of the bearings as an efficiency measure, it still has a significant impact on the load-carrying capacity of the bearing. In the present study, we investigate the dynamic characteristics of the Rayleigh step bearing with the impact of surface roughness and a porous medium by considering a squeezing action. Couple stress fluid is considered a lubricant with additives in both the film as well as the porous region. Based on Stokes constitutive equations for couple stress fluids, Darcy’s law for porous medium, and stochastic theory for rough surfaces, the averaged Reynolds-type equation is derived. Expressions are obtained for the volume flow rate, steady-state characteristics, and dynamic characteristics. The influence of surface roughness and the porous medium on the Rayleigh step bearing is analyzed. We investigated the static and dynamic characteristics of the Rayleigh step bearing. As a result, the couple stress fluid increases (decreases) the steady load-carrying capacity, dynamic stiffness, and dynamic damping coefficients, and decreases (increases) the volume flow rate negatively (positively) skewed roughness in comparison with that of the Newtonian case. The results are compared with those of the smooth case.

Thermal radiation effect of mixed convection of couple stress fluid in a vertical channel in the presence of heat source or heat sink

The fully developed mixed convection of couple stress fluid in a vertical channel in the presence of heat source or sink and thermal radiation effect is analyzed. The two boundaries of the channel are considered as isothermal-isothermal, isoflux-isothermal and isothermal-isoflux for the left and right walls and kept either at equal or at different temperature. The governing momentum and energy equations are coupled and nonlinear due to the viscous effects. The results are represented graphically for different values of buoyancy parameter , couple stress parameter 'a' and radiation parameter F on velocity and temperature distributions. We observe that for purely viscous fluid with the flow reversal was at the hot wall whereas for couple stress fluid there is a flow reversal both at left and right walls. The effect of on the flow for couple stress fluid is dominating compared to viscous fluid both on velocity and temperature. The profiles of temperature are significant for couple stress fluid for different values of whereas the profiles were not sensible for different values of for viscous fluid.

Effects of Slip and Inclined Magnetic Field on the Flow of Immiscible Fluids (Couple Stress Fluid and Jeffrey Fluid) in a Porous Channel

In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey fluid in a porous channel. Instead of the classical no-slip conditions on the boundaries, we used slip boundary conditions, which are more realistic and meaningful. In addition, we used inclined magnetic field effects on the fluid flow. The couple stress fluid and Jeffrey fluid are flowing adjacent to each other in the region I and in the region II, respectively, of the horizontal porous channel. The nondimensionalized governing equations are solved analytically by using slip conditions at the lower and upper boundaries and interface conditions at the fluid-fluid interface. The analytical expressions for the velocity components in both regions are obtained in closed form. The effects of slip parameter, Hartmann number, couple stress parameter, Jeffrey parameter, angle of inclination, and Darcy number on velocity components in both regions are investigated. In the absence of slip, couple stress parameter, and Jeffrey parameters, limiting cases are obtained and discussed.

Analysis of couple stress nanofluid flow under convective condition in the temperature‐dependent fluid properties and Lorentz forces

AbstractIn recent years, a great deal of interest has been generated in modern micro‐ and nanotechnologies for micro/nano‐electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro‐organisms. Motivated by bio‐nanofluid vertical channel oxygenators in medical engineering, in the current work, a mathematical model is developed to examine the flow of mixed convective couple‐stress nanofluids in a vertical channel with a transverse magnetic field, fluid viscosity that changes with temperature, and thermal conductivity. The non‐Newtonian model follows Brownian motion and heat spread by nanoparticles in a fluid under coupled stress. Highly linked, nonlinear regulating equations are translated into nondimensional equations using relevant variables. The governing equations are then turned into a form with no dimensions. The Keller‐box technique, a second‐order finite difference method for solving second‐order equations, is used to solve them numerically. On the other hand, the effects of different non‐Newtonian flow parameters, such as the couple stress fluid parameter, the magnetic parameter, the variable fluid viscosity, the variable thermal conductivity parameters, the Brinkman number, the nanofluid and buoyancy parameters, and the rate of chemical reaction parameter, are carefully studied. The velocity, temperature, and concentration fields are calculated over a wide range of possible values for the relevant parameters.

Soret and Dufour effects on MHD double-diffusive mixed convective heat and mass transfer of couple stress fluid in a channel formed by electrically conducting and non-conducting walls

A numerical investigation is carried out to study the significance of Soret and Dufour effects on magnetohydrodynamic double-diffusive mixed convective heat and mass transfer of couple stress fluid flow with induced magnetic field in a vertical channel. The flow field is governed by Brinkmann–Forchheimer extended Darcy’s momentum equation. The channel walls are electrically conducting and non-conducting; also the temperature of the channel wall increases or decreases linearly with in the direction of the fluid flow. The coupled non-linear governing equations are solved numerically using Galerkin finite element method. The influence of governing parameters on the flow variables along with heat and mass transfer is discussed. Obtained results indicate that increase in Darcy number increases the velocity profile due to higher permeability of the medium. Increasing the thermal and solute Rayleigh number enhances the velocity in the channel. The Dufour effect is more prominent on the temperature profile when compared to concentration. In the Soret phenomenon, the temperature gradient affected the concentration distribution. Higher values of the Soret number results in higher convective flow and, hence, increases the concentration. This study includes computational fluid dynamics (CFD) simulations as well as an artificial neural network (ANN) model.

Study of Thermal Stability in A Newtonian Fluids

In this present paper, we studied about thermal stability in a Newtonian fluid. A detailed account of thermal convection in a Newtonian fluid layer in the presence of magnetic field has been given by Chandrasekhar [11]. Stokes [79] has formulated the theory of couple-stresses in fluids. The theory due to Stokes allows for polar effects such as the presence of couple stresses and body couples. The theory has been applied to the study of some simple lubrication problems. According to the theory, couple-stresses are found to appear in noticeable magnitudes in fluids with very large molecules. Since the long chain hyaluronic acid molecules are found as additives in synovial fluid, Walicki and Walicka [80] modeled synovial fluid as a couple-stress fluid in human joints. A human joint is a dynamically loaded bearing which has particular cartilage as the bearing and synovial fluid as the lubricant. A synovial fluid is the natural lubricant of joints of the vertebrates. The synovial is obtained from the hyaluronic acid, a fluid of high viscosity, near a gel. Normal synovial fluid is clear or yellowish and is a non- Newtonian, viscous fluid. The shoulder, hip, knee and ankle joints are loaded with the synovial fluids and joints have a low friction coefficient and negligible wear.

An analytical study of couple stress fluid through a sphere with an influence of the magnetic field

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Mathematical modeling for peristalsis of couple stress nanofluid

The current article investigates the magnetohydrodynamic (MHD) radiative peristaltic flow of a couple stress nanoliquid in a symmetric channel. Thermally convective and zero mass flux conditions are imposed on flexible channel walls. Impacts of Joule heating and viscous dissipation are considered. Nanofluid model consists of important features Brownian motion and thermophoresis. First‐order chemical reaction is present in mass transportation. The resulting system of differential equations is numerically tackled after adopting large wavelength and low Reynolds number assumptions. Influences of pertinent variables of interest on concentration, temperature, coefficient of heat transfer, streamlines, skin friction coefficient, and Nusselt and Sherwood numbers are examined graphically. The findings of this study reveal that temperature enhances against Brownian motion and thermophoresis parameters, whereas it decays for radiation variable. Concentration of the fluid declines for a couple stress fluid variable. Further, the heat transfer coefficient shows increasing behavior for Eckert number.

Modelling and simulation of fluid flow through stenosis and aneurysm blood vessel: a computational hemodynamic analysis

In this article, the hemodynamics of nanofluid flow through the modelled stenosis-aneurysm models in the presence of the catheter has been studied. The eight stenosis-aneurysm models are developed to mimic biological observations and thus make the model more realistic. The mathematical understanding helps in treating the stenosis in the blood vessel by targeting the unhealthy region to the drug, which is coated on nanoparticles. The catheter achieves the active drug release to the aimed organs by coating on the catheter surface, which adds additional benefits. In the present hemodynamic study, the blood is modeled as a couple stress fluid; as a result, the highly non-linear momentum, temperature, and concentration equations were obtained. The fluid flow equations’ complexity is further increased by incorporating the variable viscosity effects that arose due to the suspension of nanoparticles. The resultant mathematical model is solved by using the homotopy perturbation method. The convergence of the perturbed solutions is studied and depicted the degree of deformation in the case of temperature and concentration. The effects of the porous nature of the stenosis, no-slip at the catheter surface, and the free slip at the blood vessel boundary in the non-stenotic region are also considered in the model. The essential physiological property like surface shear stress is computed, and various parameters’ influence on shear stress is analyzed. The present analysis can be helpful in understanding the enhancement in mass dispersion and heat transfer in unhealthy blood vessels, which could be used for drug delivery in the treatment of stenotic conditions.

Entropy minimization for variable viscous couple stress fluid flow over a channel with thermal radiation and heat source/sink

Entropy minimization for variable viscous couple stress fluid flow over a channel with thermal radiation and heat source/sink

Double-Layered Porous Rayleigh Step Slider Bearings Lubricated with Couplestress Fluids

Objective: To examine the performance of double-layered porous Rayleigh step slider bearings lubricated with couple stress fluid and to compare it with the performance of single layered porous Rayleigh step bearing. Methods: Based on the Stokes micro continuum theory of couple stress fluids, the modified Reynolds equation governing fluid film pressure is derived. Its analytical solution is and the closed form expressions for the fluid film pressure, frictional force and load carrying capacity are obtained. Findings: The numerical results for bearing characteristics such as pressure, load carrying capacity, frictional force are plotted graphically to study the effect of doublelayered porous facing. The effect of permeability of the porous layer is to decrease the load carrying capacity as it gives an easy path for the lubricant to pass through. This adverse effect can be compensated by introducing double layered porous facing with different permeabilities and the results presented here in this paper clearly shows the increase in load carrying capacity and decrease in co-efficient of friction for the double layered porous bearings as compared to that of single layered porous bearings. Novelty: Original research was conducted on double-layered porous Rayleigh step slider bearings with couple stress fluid by considering the effects of lubricant additives in the porous region and the results are compared with that of single layered porous bearings. Keywords: Rayleighstep slider bearing; permeability; Doublelayered porous; couple stress fluid Microcontinuum

Homotopy analysis method with application to thin-film flow of couple stress fluid through a vertical cylinder

Abstract This work solves the problem of thin-film withdrawal and drainage of a steady incompressible couple stress fluid on the outer surface of a vertical cylinder. The governing equations for velocity and temperature distributions are subjected to the boundary conditions and solved with the help of homotopy analysis method. The obtained expressions for flow profile, temperature profile, average velocity, volume flow rate, and shear stress confirmed that the thin-film flow of couple stress fluid highly depends on involved parameters say Stokes number St , vorticity parameter λ, couple stress parameter η, and Brinkman number Br presented in the graphical description as well.

Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium

Viscoelastic liquid sheet of couple-stress type streaming with relative motion into an inviscid gas through porous molium is studied theoretically and quantitatively in this project. To derive the differential equations that describe liquids, gases, and the electric field, we linearized the governing equations of motion and continuity, Maxwell’s equations in quasi-static approximation, and the appropriate boundary conditions at the two interfaces. Then we used the normal mode method. It was demonstrated analytically that the solutions to these differential equations can be found for both symmetric and antisymmetric disturbances, respectively. We could not obtain an explicit form of the growth rates since we could not solve the dispersion relations for both situations because they were obtained in highly complex forms. The Mathematica program is used to solve the dimensionless forms of the dispersion relations numerically using Gaster’s theorem. Various influences on the stability analysis of the considered system have been studied in detail, and it is determined that the system in the presence of a porous material is more unstable than it would be otherwise. In a two-dimensional system, the antisymmetric disturbance case is found to be more unstable than the corresponding symmetric disturbance situation. Some characteristics, such as Wabe number, Ohnesorge number, and electric field, have destabilizing effects, whereas others, such as porosity, medium permeability, viscoelasticity parameter, gas-to-liquid viscosity ratio, and dielachic constants, have stabilizing effects. Finally, it is discovered that the gas-to-liquid velocity ratio plays a dual role in the stability condition depending on whether the gas-to-liquid velocity ratio U ≶ 1. In the past, we have only found evidence of very few previous studies.