Couple Stress Fluid Research Articles

Statistical Analysis of Non-Newtonian Couple Stress Fluid Induced in Stretching Cylinder

The paper provides the impact of suction and injection on convection laminar incompressible couple stress fluid flow and magnetic field using spectral quasi linearization methods as the major novelty of our work. This work is to addresed heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyze the effect of MHD and non-Newtonian couple stress fluid runs over a permeable stretched cylinder. The leading formulation is transmuted into ordinary differential equations via similarity functions. The coupled equations with non-linearly terms are resolved numerically through utilization of MATLAB code for spectal quasi linearization methods (SQLM). Convergence regions for solutions are discussed. Graphical results illustrating the impacts of various emerging parameters are presented in discussion. The statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at the cylindrical surface for higher values of couple stress parameter and Reynolds number. Nusselt number or heat transfer rate also enhances at the surface of cylinder in the presence of Reynolds number.

Heat transfer analysis in hydromagnetic flow of couple stress fluid in presence of homogeneous and heterogeneous chemical reactions over a porous oscillatory stretchable sheet

The prime objective of this theoretical study is to investigate the flow, mass, and heat transfer in the time-dependent couple stress fluid over a permeable stretching oscillatory surface. The effect of applied magnetic field is also taken in the momentum equation. In addition, the energy equation is modeled by incorporating thermal radiation and heat generation. Furthermore, the concentration equation is designed in presence of homogenous and heterogeneous chemical reactions. The flow mechanism occurs because of the to and fro motion of the surface about a fixed point. For similar solution of the developed flow problem suitable similarity transformations is adopted. The analytical solution of the obtained flow equations in the form of partial differential equations (PDEs) is attained by utilizing a valuable method called Homotopy analysis method (HAM). An extensive assessment is performed to study the influence of various involved parameters namely the couple stress parameter, the relation of the parameter of the surface oscillatory frequency to its stretched rate constant, the Prandtl number, the strength of heterogeneous and homogeneous chemical reactions parameters, Schmidt number, heat production parameter and magneto-porosity parameter on the flow, concentration and temperature distributions, skin friction coefficient, and rate of heat transfer via tables and graphs and are discussed in detail. It is observed that the amplitude of velocity and skin friction coefficient shows a declining response with varying values of the couple stress parameter and it increases for higher values of the magneto-porous parameter.

Dynamics of Soret and Dufour effects on oscillatory flow of couple stress fluid due to stretchable curved surface

In this theoretical study, we have discussed the impacts of Soret and Dufour on the flow of time-dependent couple stress fluid across a stretchable curved oscillatory surface with magnetic field. The to and fro motion of the surface causes the flow phenomenon. The boundary layer flow equations depicting the flow phenomena are expressed in mathematical form by means of a curvilinear coordinates system along with some suitable similarity variables. The developed flow equations in the form of partial differential equations are then solved analytically by utilizing a valuable method called the homotopy analysis method (HAM). A detailed examination is performed to evaluate the influence of various involved parameters namely, the non-dimensional radius of curvature, couple stress parameter, magnetic parameter, the relation of the parameter of the surface oscillating frequency to its stretching rate constant and Soret and Dufour numbers on velocity field, pressure distribution, concentration and temperature distribution, rate of heat transfer, coefficient of skin friction, and rate of mass transport via graphs and are explained in detail. It is confirmed that the amplitude of velocity and pressure distribution exhibits reducing behavior with higher values of the couple stress parameter. The concentration and temperature profiles also diminish with varying time instants.

Entropy Generation Optimization in Couple Stress Fluid Flow with Variable Viscosity and Aligned Magnetic Field

This study explores the influence of an inclined magnetic field and variable viscosity on the entropy generation in steady flow of a couple stress fluid in an inclined channel. The walls of the channel are stationary and non-isothermal. The fluid flow is driven due to pressure gradient and gravitational force. Reynold’s model for temperature-dependent viscosity was used. The dimensionless, non-linear coupled equations of momentum and energy was solved, and we obtained an analytical solution for the velocity and temperature fields. The entropy generation and Bejan number were evaluated. The variation of pertinent parameters on flow quantities was discussed graphically. The rate of volume flow, skin friction coefficient, and Nusselt number at the surfaces of the channel were calculated and their variations were discussed through surface graphs. From the results, it is noticed that the entropy generation rate can be minimized by increasing the magnetic field and the temperature difference parameters. The findings of the current study in some special cases are in precise agreement with the previous investigation.

Effect of Gravity and Throughflow on Double Diffusive Convection in a Couple Stress Fluid Saturated Porous Media

We have investigated effect of throughflow and gravity modulation on double diffusive convection with couple-stress fluid saturated porous media. Applying the Landau model, we have derived finite amplitude of couple-stress convection in the presence of gravity modulation. The presence of a couple-stress parameter produces both diminishing and enhancing heat mass transfer in the layer. To present the results we have used Mathematica to obtain the Nusselt number and Sherwood numbers numerically. Further, it is shown that, throughflow and modulation of gravity controls double diffusive convection through convective amplitude and alter transport phenomenon.

The Well-posedness and the Regularity of Global Attractor for a Couple Stress Fluid Through Porous Layer with the Local Thermal Non-equilibrium Effect

In the article, we aim to investigate the well-posedness of solution and the regularity of the global attractor for the couple stress fluid in saturated porous media with the local thermal non-equilibrium effect. To be more specific, we firstly show the existence and uniqueness of global weak solution to the model by making use of the standard Galerkin method. Second, relying on verifying the uniformly compact condition required, we prove the existence of the global attractor of the model in the space where the weak solution resides. Finally, we improve the regularity of global attractor by uniformly compact condition and obtain the \(C^{\infty}\) attractor for the model.

Three-Dimensional Thermohydrodynamic Analysis of Journal Bearing Lubricated by Magnetic Fluids with Couple Stresses

Couple stresses because of magnetic particles additives on the lubrication performance of a journal bearing system was embraced and scrutinized in the current examinations theoretically. The governing equations of Reynolds (pressure field), energy (temperature field), and heat conduction (temperature field through the solids) are coupled and solved instantaneously in term of temperature and viscosity. After these set of equation pressure is obtained, it is used to obtain the bearing characteristic. It was found that the load currying capacity and maximum pressure are increased due the employing of magnetic fluids along with the couple stresses, as well as side leakage flow and the friction coefficient are decreased. It can be also concluded that the magnetic fluids with couple stresses are better lubricant than magnetic fluid only (l = 0), Newtonian fluids, and couple stress fluid (ʎ = 0).

Hydromagnetic Flow of Two Immiscible Couple Stress Fluids in an Inclined Porous Channel: Effects of Slip Boundary

In this study, we investigated the effects of slip boundary and magnetic field on the flow of two immiscible couple stress fluids in an inclined porous media channel. The Stokes model was used to define the two couple stress fluids. The fluids in both the regions are assumed to be incompressible and immiscible and the transport properties in the two regions are assumed to be constant. The governing coupled linear ordinary differential equations are made dimensionless by using appropriate fundamental quantities. The expressions for the velocity components in both the regions are obtained in closed form using the undetermined coefficient method; by applying slip boundary condition at the boundary of the channel and at fluid‐fluid interface, the continuity of velocities, vorticities, shear stresses, and couple stresses are applied. The effects of the nondimensional parameters including the couple stress parameters, slip parameter, Hartmann number, Darcy number, and the ratio of basic fluid properties on the velocity components are presented graphically; the flow rate and shear stress are presented in table and discussed briefly. It is reported that the presence of couple stresses and magnetic field have a declining impact while slip boundary has an enhancement impact on the fluid velocity and the volumetric flow rate. In the absence of couple stress, the results for the liming case as s⟶∞(η⟶0) for Newtonian flow are achieved and further limiting cases are established and briefly addressed.

HEAT TRANSFER IN COUPLE STRESS TWO-FLUID FLOW MODEL: EFFECTS OF MODIFIED HEAT FLUX, ELECTROMAGNETIC FORCE, AND UNEVEN HEAT SOURCE/SINK

The aim of the present investigation is to study the variations due to uneven heat flux and an electromagnetic field on the couple stress fluid flow of a binary mixture traveling through a stretched cylindrical surface with developed heat flux. The partial differential equations governing the fluid transport system are derived into a set of ordinary differential equations using suitable nondimensional parameters and similarity transformations, which could then be computationally solved using the Runge-Kutta Fehlberg method. The main aspect of the current problem is that it discusses the entire scenario in terms of the liquid and dust phases. Using the MATLAB code, a graphical representation of the relevant parameters is obtained. The results were carried out for our system, and it reveals that the velocity and thermal gradient of both the phases of fluid and dust behave in an opposite trend for rising mass concentration, where the curvature parameter makes the rise in the same manner. Furthermore, the thermal transport profiles for both phases decline for the rising thermal relaxation parameters.

DRAG ON A POROUS SPHERE ENCLOSED IN A SOLID CORE EMBEDDED IN COUPLE STRESS FLUID

In this paper, the problem of steady and axisymmetrical creeping flow of couple stress fluid past a permeable sphere enclosed by a solid core is analyzed. The continuous case of normal velocity and tangential velocity, stress jump boundary condition, and couple stress to be vanishing conditions are applied on the surface of the porous sphere, and the nonpenetrability boundary condition is applied for solid sphere. The problem is expressed by using the Stokes and Brinkman equations, which describe both the flow outside and inside the porous sphere, respectively. Expressions for the couple stress tensor and velocity fields are obtained in terms of Gegenbauer polynomials and Macdonald functions. Both the pressure distribution and the stream function solution for the axially symmetric motion are explicitly solved. An analytical determination for the flow field in terms of stream function is examined by wielding the method of separation of variables. The drag force felt by a permeable sphere due to the external and internal flow is calculated. The impact of the viscosity coefficients and couple stress parameter on drag is investigated numerically, and the findings are displayed in graphical form. The findings show that the uniform flow of a couple stress fluid past a porous sphere enclosed by a solid core with stress jump condition has less drag than the flow of a couple stress fluid through a porous sphere with continuous case of shear stress, and the presence of stress jump coefficients reduces the drag force, pressure, and couple stresses. With reference to earlier, well-known cases, some unique cases of flow past a porous sphere have been validated.

Properties of Capturing of Peristaltic Flow to A Chemically Reacting Couple Stress Fluid Through an Inclined Asymmetric Channel with Variable Viscosity and Various Boundaries

Properties of Capturing of Peristaltic Flow to A Chemically Reacting Couple Stress Fluid Through an Inclined Asymmetric Channel with Variable Viscosity and Various Boundaries

Impact of couple stress and variable viscosity on heat transfer and flow between two parallel plates in conducting field

<abstract> <p>This study explores the flow properties of a couple stress fluid with the consideration of variable viscosity and a uniform transverse magnetic field. Under the effect of irreversible heat transfer, a steady fluid flow has taken place between two parallel inclined plates. The fluid flows due to gravity and the constant pressure gradient force. The plates are fixed and isothermal. The governing equations have been solved analytically for velocity and temperature fields. The total rate of heat flow and volume flow across the channel, skin friction, and Nusselt number at both plates are calculated and represent the impacts of relevant parameters through tables and graphs. The findings show that velocity, temperature, and the total rate of heat flow across the channel are enhanced by increasing the couple stress parameter and the viscosity variation parameter, while increasing the values of the Hartmann number reduces them.</p> </abstract>

Study of surface roughness with MHD and couple stress fluid on porous curved annular plates

The purpose of this article is to examine the effect of surface roughness on porous curved annular plates lubricated with couple stress fluid in the presence of magnetic field. The MHD-Stochastic Reynolds equation is derived using Christensen’s stochastic model and applied to predict the squeeze film characteristics of porous curved annular plates. The expressions for squeeze film pressure, load-carrying capacity, and squeeze film time are obtained analytically, the results are discussed for various values of operating parameters, and are plotted graphically. It is found that the squeeze film characteristics of porous curved annular plates are improved using a non-Newtonian fluid in the presence of an external magnetic field. The effect of roughness parameter is to increase (decrease) the squeeze film attributes for azimuthal (radial) roughness configuration as compared to the smooth case. Furthermore, the effect of permeability parameter is to decrease the pressure, load-carrying capacity, and squeeze-film time as compared to the non-porous case.

Velocity Slip with Viscosity Variation for Rough Porous Circular Stepped Plates Using Couple Stress Fluid

Velocity Slip with Viscosity Variation for Rough Porous Circular Stepped Plates Using Couple Stress Fluid

Time fractional model of free convection flow and dusty two‐phase couple stress fluid along vertical plates

AbstractCouple Stress Fluid (CSF) incorporates a new material constant whose, in contrast to a Newtonian fluid, regulates both couple stress and lubricant viscosity. Due to the fourth‐order spatial derivative term that this material constant introduces into the momentum equation, this fluid (CSF), even for classical fluid problems, has received limited research. The aim of this article is to examine the joint impact of heat transmission and magnetic field on a time‐fractional model of two‐phase free convection flow of dusty fluid that is electrically conducting. Among parallel plates, one of which is stationary and the other of which is oscillating with constant velocity, the CSF is supposed to flow. Heat is transferred by free convection and buoyant force, which generates the flow. Furthermore, all spherical dust particles are uniformly dispersed through the fluid. The flow is modeled mathematically in terms of PDEs. The provided derived system of PDEs is generalized by applying a recently invented fractional derivative, the Caputo‐Fabrizio fractional derivative. Finite sine Fourier and Laplace transformations are jointly applied to handle the problem. The velocity and temperature profiles have closed form solutions. The CSF outcomes for stimulating fluid parameters are shown in numerous graphs for CF time fractional derivatives. Additionally, the influence of various parameters has been discussed. Mathcad‐15 is used to plot the graphical outcomes for the CSF, dust particle, and temperature profiles. Furthermore, the skin friction and Nusselt number are calculated. Table 1 demonstrates how the rate of heat transmission reduces as the Peclet number's value rises. Similarly, Table 2 demonstrates that the skin friction increases as the magnetic parameter and couple stress parameter are raised. Table 3 and 4, shows the Regression analysis that the variation in the velocity for Couple stress and dusty fluid parameter are statistically significant. By increasing the couple stress parameter λ, retarde the both velocities profile.

Numerical Investigation of the Magnetized Reactive Viscous Couple Stress Fluid Flow Down an Inclined Riga Plate with Variable Viscosity

Accurate determination of optimum flow and heat transfer condition is one of the major challenges faced in the application of magnetic fluid in the field of medicine and engineering, especially when applied as ferrofluids for targeted drug deliveries, treatment of hyperthermia, sealants in computer hard drives, lubricants in car shafts. In view of these important applications, a mathematical investigation of the flow and heat transfer behavior of reactive magnetic fluids containing nanostructures is presented based on a couple of stress constitutive models. The reactive fluid is assumed to flow through inclined magnetized solid boundaries for energy conversion. The formulation leads to nonlinear coupled equations. The dimensionless equations are numerically solved using the spectral Chebyshev assumed solution for the weighted residual technique, and the correctness of the solution is confirmed using the shooting Runge–Kutta method. The effects of various fluid parameters on velocity, temperature, skin friction, and heat transfer rates are described in tabular and graphical form, along with suitable physical explanations. Thermal analysis computations are also presented. According to the findings, an enhanced couple of stress fluid and variable viscosity parameters reduced the skin drag and heat transfer rate at the bottom wall. Furthermore, the thermal stability of the flow can be achieved with increasing values modified Hartman number while increasing couple stress parameter encourages thermal instability in the flow domain.

Effect of Electric Field Modulation on The Onset of Electroconvection in a Couple Stress Fluid

The problem of a convectional instability in a horizontal dielectric fluid layer with electric field modulation under couple stress fluid is examined. The horizontal dielectric upper boundary fluid layer is cooled, and the lower boundary is subjected to an isothermal boundary condition. The regular perturbation method based on the small magnitude of modulation is used to compute the critical Rayleigh number and the corresponding wavenumber. The solidity of the system is the characterised by a correction Rayleigh number, which is computed as a function of thermal, electric, and couple stress parameters and the frequency of electric field modulation. Some of the known findings are retrieved as specific cases in this study. It is demonstrated that the onset of the convection may be advanced or delayed by the proper regulation of different regulation parameters. The outcomes of this study have potential implications for the control of electroconvection with a time-dependent electric field.

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.

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.