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In the current paper, we investigate the effect of spin slip conditions for the Couette-Poiseuille flow of a couple stress fluid between two parallel plates. In the study, the motion of the fluid is considered to be steady, incompressible and unidirectional. At the interface between the fluid and the plates (both the upper and lower), we consider the non-zero tangential and couple stress spin slip relationships as boundary conditions. We present analytical expressions for the velocity profile, volume flow rate, vorticity, and couple stresses. This paper discusses the numerical influence of the spin slip parameter, velocity slip parameter, couple stress parameter, and pressure gradient on the velocity, vorticity, couple stresses, and volume flow rate. Our results show that the presence of the spin slip parameter reduces the velocity, couple stress and volume flow rate of the fluid, while it enhances the vorticity. The limiting cases for each problem align well with previously published results regarding the vanishing of couple stresses at the boundaries. This research helps both researchers and engineers in understanding how to control the conditions to achieve an efficient fluid flow, particularly in applications involving couple stress effects, such as microfluidics systems, lubrication technology, and polymeric suspensions. [ABSTRACT FROM AUTHOR]

The aim of the current study is to investigate the stability analysis in case of the linear as well as nonlinear of a thermo-solutal chemically reactive couple stress fluid under uniform magnetic field convection. Investigations have been conducted on the impact of chemical reaction and external vertical magnetic field on the commencement of double diffusive convection in couple stress fluid between infinite horizontal parallel plates. Darcy's modified law governs the flow in porous media and the Oberbeck-Boussinesq approximation is accurate. For modelling the momentum equation, the modified Darcy equation with the time derivative and inertia terms is utilized. Expressions for the Rayleigh numbers with finite amplitude, oscillatory, and stationary states are found in accordance with the regulating factors. Graphics are used to illustrate how the couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio affect stationary, oscillatory and finite-amplitude convection. Stationary, oscillatory and finite-amplitude convection are found to be stabilized by the couple-stress parameter and the solute Rayleigh number. The normal mode analysis method is utilized to look into the linear stability of flow dynamics after the nonlinear mathematical problem has been linearized. When stationary and finite-amplitude modes are present, the diffusivity ratio has a destabilizing effect; when oscillatory convection is present, it has a dual effect. Oscillatory convection develops earlier when the Vadasz number is higher. The couple-stress parameter and diffusivity ratio both increase with increasing solute Rayleigh number values, but the heat and mass transfer decreases as these values rise. Using double Fourier series, a generalized weakly nonlinear stability analysis is done. The research illustrates how various regulating parameters support and destabilize the flow dynamics. The influence of finite-amplitude convection on stability is also examined. Furthermore, the best conditions for stationary and oscillatory convection are based on altering the couple stress flow stability by controlling the applied magnetic field. [ABSTRACT FROM AUTHOR]

Nanofluids have improved thermophysical properties compared to conventional fluids, which makes them promising successors in fluid technology. The use of nanofluids enables optimal thermal efficiency to be achieved by introducing a minimal concentration of nanoparticles that are stably suspended in conventional fluids. The use of nanofluids in technology and industry is steadily increasing due to their effective implementation. The improved thermophysical properties of nanofluids have a significant impact on their effectiveness in convection phenomena. The technology is not yet complete at this point; binary and ternary nanofluids are currently being used to improve the performance of conventional fluids. Therefore, this work aims to theoretically investigate the ternary nanofluid flow of a couple stress fluid in a vertical channel. A homogeneous suspension of alumina, cuprous oxide, and titania nanoparticles is formed by dispersing trihybridized nanoparticles in a base fluid (water). The effects of pressure gradient and viscous dissipation are also considered in the analysis. The classical ternary nanofluid model with couple stress was generalized using the fractal–fractional derivative (FFD) operator. The Crank–Nicolson technique helped to discretize the generalized model, which was then solved using computer tools. To investigate the properties of the fluid flow and the distribution of thermal energy in the fluid, numerical methods were used to calculate the solution, which was then plotted as a function of various physical factors. The graphical results show that at a volume fraction of 0.04 (corresponding to 4% of the base fluid), the heat transfer rate of the ternary nanofluid flow increases significantly compared to the binary and unary nanofluid flows. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Ternary hybrid nanoliquid is employed in various engineering and science applications including electronic heaters, pharmaceutical, nuclear safety, and solar energy production. Hence, the current study focused on the thermal and entropy analysis of water-based ternary couple stress hybrid nanoliquid and couple stress hybrid nanoliquid flow in an oblique channel. The significance of heat flux, porous media, buoyant force, magnetic field, and convective condition on the couple stress ternary liquid has been scrutinized. The governing partial differential equations are transferred into ordinary differential equations with the help of dimensionless terms. In the next step, the ordinary differential equations were solved by utilizing the RKF-45 numerical method. The outturn elucidated that the inflated Brinkman number greatly promotes the thermal field. The flow profile declines with enhanced permeability parameters. The outcome of the scrutiny of the couple stress parameter concludes that highly reinforced by ternary fluid than hybrid couple stress nanofluid. [ABSTRACT FROM AUTHOR]

The present flow problem analyzes the impact of radiative heat and mass transfer with inclined magnetic field on thermal exchange and entropy production of two immiscible nature of electrically conducting couple stress fluid in a static porous saturated conduit. In this model, the lower and upper porous regions of the rectangular channel are occupied by two different types of couple stress fluids. The static horizontal parallel plates of the porous duct are completely isothermal and the flow of immiscible fluid through the porous duct develops because of a constant pressure gradient at the entry zone of the duct. The Brinkman model is utilized in the modeling of fluid flow through porous saturated domain and Rosseland's approximation is utilized to compute the radiative thermal exchange effect on nonmiscible couple stress fluid. In this work, authors have analyzed the effect of various thermo-physical parameters such as the Hartmann number (Ha), permeability parameter (Da), Schmidt number (Sc), Soret number (Sr) and couple stress parameter ( s i , i = 1 , 2) on the entropy generation characteristics, Bejan number distribution, thermal behavior, concentration distribution and flow characteristics of immiscible couple stress fluid which passes through the porous channel. The parameters Ha, Da, s i , Sc, Sr correspond to magnetic field effect, permeability of porous media, couple stress, mass diffusion and thermal diffusion, respectively. The most significant findings of this research work are as follows: • In a porous saturated channel, the immiscible couple stress fluid velocity, entropy production number and thermal profile get enhanced on increasing the couple stress parameter. • On increasing the Hartmann number and decreasing the permeability of porous region, the thermal properties and entropy production number both decrease. • The couple stress fluid's concentration field and Bejan number distribution get decreased on enhancing Soret number Sr and Schmidt number Sc. • The entropy generation near the wall of the channel rapidly increases on increasing the Schmidt number and Soret number. The emerging finding of this research work exhibits excellent agreement with previously published work. This research work can be utilized in food processing, petroleum products and chemical process. [ABSTRACT FROM AUTHOR]

In this paper, the Poiseuille flow of non-isothermal couple stress fluid of Reynolds model between two heated parallel inclined plates has been studied. The strongly nonlinear coupled ordinary differential equations have been investigated using the Asymptotic Homotopy Perturbation method (AHPM) and the Optimal Homotopy Asymptotic Method with DJ Polynomials (OHAM-DJ). Employing both these techniques, the approximate solutions for velocity profile, temperature distributions, shear stress, average velocity and volumetric flow rate have been achieved. The results obtained using both these methods are in the form of infinite series, hence the results can be obtained easily. Comparison of various results, obtained through these methods, is carried out. Here, it is worth to mention that the results gained by both these approaches are in excellent resemblance. The effect of different parameters on the flow problem has been studied numerically as well as presented graphically. [ABSTRACT FROM AUTHOR]

In this paper, the study investigates the problem of the creeping flow of a non-Newtonian couple stress fluid through a linearly porous walled slit within a Darcy porous medium. The well-established approach, the Inverse Method approach, was employed to attain the precise solution of the governing equations. The inverse technique is utilized to transform the momentum equations into stream functions. The physical parameters are all computed: longitudinal velocity, transverse velocity, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. The data was also graphed, indicating that the initial flow rate affects longitudinal velocity but not transverse velocity. The streamlines are greatly affected by the initial flow rate, resulting in straighter and more uniform patterns as the flow rate increases. Parameters like permeability and the couple stress parameter also have an impact on physical quantities. Because of the porosity parameter, backward flow occurs at the slit's end. The novelty of this research lies in the investigation of couple stress fluid flow within both linear channel walls and a porous medium. The present research focuses on how kidney disease affects fluid flow in renal tubules. It's critical because fibers, lipids, and waste particles can clog or disrupt these channels, lowering kidney performance. Understanding this helps in the management of kidney disease and provides insights for better biomedical engineering in the development of improved renal medicines. [ABSTRACT FROM AUTHOR]

Peristaltic transport of couple stress fluid with heat transfer is investigated through flexible walls of the channel furnished with hair‐like structures. Locomotion of biological fluid is the result of the simultaneous propagation of metachronal waves (MCWs) and peristaltic waves. MCW emerges due to multi‐movement of cilia, while the elastic‐walls of the channel are responsible for the peristaltic wave. The two‐dimensional rheological flow experiences the resistive behavior of applied magnetic fields, besides, the role of viscous dissipation and entropy generation. A closed‐form solution is achieved for the nonlinear coupled differential equation, which is vetted through graphs. Finally, the theoretical analysis introduces the manufacture of a ciliate bronchial tube that can efficiently; remove mucus out of the lungs and bloodstream. [ABSTRACT FROM AUTHOR]

One significance of the fluid flow in a curved channel is the generation of centrifugal forces. However, nothing is known on the hydrodynamic study of a couple stress fluid flowing in a porous curved channel. The proposed work, concerns with the flow of couple stress fluid in a porous curved channel and analysing the generating centrifugal force. Here, the flow of fluid in the porous curved channel takes place due to the constant pressure gradient. In this work, the effect of the radius of curvature and permeability parameters are examined on the flow velocity and temperature profiles of the considered fluid. The aim of this study is to analyse the flow pattern of the couple stress fluid, measure the rate of heat transfer, and volumetric flow rate, when fluid flow through porous curved channel. The proposed model is useful in the biofluid mechanics, nuclear reactors, and in oil and chemical industries. The present model, i.e., the flow of couple stress fluid in a porous curved channel, governs by the highly non-linear coupled differential equations which are solved by using Homotopy Analysis Method (HAM). Through this work, it is concluded that couple stress fluid's velocity and temperature is smaller in magnitude than that of the Newtonian fluid. Further, it is noticed that the fluid's flow velocity and temperature in porous curved channel is reduced significantly on increasing the curvature parameter, permeability parameter, and on reducing the couple stress parameter. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 ∞ attractor for the model. [ABSTRACT FROM AUTHOR]

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

The effect of velocity slip with viscosity variation between porous rough circular stepped plates with couple stress fluid is examined. A stochastic random variable having a non-zero mean, variance, and skewness is used to model a more general type of surface roughness equation also the modified Reynolds equation accounting for pressure dependent viscosity is analytically derived. The numerical solution obtained for the non-dimensionless pressure, load carrying capacity and time. It is observed that the impact of roughness and viscosity variation using a couple stress fluid between circular stepped plates has been discussed. These effects improved the ability of load carrying capacity as compared to the corresponding Newtonian case. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The present level of literature on the subject matter indicates that nothing is known on the heat transfer across the couple stress rheological fluid flowing over a vertical avenue with Robin (mixed) wall conditions. The obtained conservation equations of the model are solved through DTM (differential transform method) and RPM (regular perturbation method). The nondimensional parameters obtained are a couple stress parameter, Brinkman number, mixed convection parameter, and Biot number. The computations reveal that flow acceleration and thermal enhancement is induced with increasing mixed convection parameter and Brinkman number for symmetric and asymmetric conditions. Increasing couple stress parameters dwindle the velocity and temperature for symmetric and asymmetric cases. The large values of the mixed convection parameter and Brinkman number increase the Nusselt values at the left wall and reduces at the right wall. The mass flow rate is augmented with the mixed convection parameter and Brinkman number but it is reduced with the couple stress parameter. The DTM, RKSM, and RPM solutions are in good agreement. [ABSTRACT FROM AUTHOR]

The present work concerns to study of the steady, axisymmetric slow flow of couple stress fluid through a rigid sphere in the transverse magnetic field. Boundary conditions on the sphere surface are the zero couple stress condition and tangential slip condition. The stream function, vorticity vector, and pressure term are obtained. The drag acting on the sphere in the presence of MHD is calculated. Here, we graphically represented the Hartmann number, couple stress, and slip parameters effect on the drag coefficient. Some well-known results of the drag are deduced. [ABSTRACT FROM AUTHOR]

A theoretical study on the asymptotic suction/injection magnetohydrodynamic flow as a result of a uniform freestream couple stress fluid flowing over a flat surface is undertaken in the current study. It is targeted to obtain exact flow and temperature solutions representing the permeable couple stress fluid flow. Analytical expressions are extracted to derive interesting engineering tools such as momentum layer thickness, thermal layer thickness, wall shear stress, and heat transfer rate. The physical parameters leading to the existence of wall suction/injection solutions are determined with their thresholds. Momentum and thermal layer analysis from the present results clearly reveal how they are influenced by the presence of electrically conducting couple stress fluid. Further flow studies of similar kind will certainly benefit from the presented formulae. [ABSTRACT FROM AUTHOR]

The transport of water contaminants with chemical reactions in the presence of an electric field is investigated in this article. In this analysis, we look at potential contaminations and their routes. Efforts to remove contaminants from water have resulted in the development of several processes/technologies. The movement of chemically reactive pollutants in a couple stress fluid in the presence of an electric field is described using the generalised dispersion model. For various values of electric number, couple stress parameter, and response rate parameter, analytical findings of dispersion coefficient were obtained. Graphs are used to illustrate the analytical results, and conclusions are drawn. Dispersion rises as the electric number and couple stress parameters rise, but falls when the reaction rate parameter rises. [ABSTRACT FROM AUTHOR]

This article addresses the influence of double-diffusivity convection in nanofluids in relation to peristaltic flow of magneto couple stress fluid in a nonuniform channel. Firstly, mathematical formulations of magneto couple stress fluid in the presence of double-diffusivity convection in nanofluids for 2-dimensional and 2-directional flows are described in detail. The highly nonlinear equations are simplified using approximation of long wavelength and low but finite Reynolds number. Exact solutions of stream function, axial induced magnetic field, axial pressure gradient, nanoparticle volume fraction temperature and concentration are computed. Graphical representations of numerous physical parameters of interest are presented to explain the conduct of flow quantities. It is observed from graphical plots that temperature profile and solutal concentration increases by increasing values of thermophoresis, Brownian motion, Soret and Dufour parameters. [ABSTRACT FROM AUTHOR]

Being motivated from the recent developments in biomicrofluidics, a mathematical model is presented to analyze the two-layered electrothermal flow via peristaltic propulsion of couple stress fluids caused by velocity and thermal slip conditions. An asymmetric microchannel is considered for the flow regime with different zeta potential moving with wave velocity. Couple stress fluid has been taken for aqueous solution to represent the non-Newtonian characteristics of physiological fluids. A lubrication approach with Debye H u ¨ ckel linearization is taken to obtain the analytical solution. Furthermore, heat transfer analysis is performed to analyze the thermal characteristics and variations in Nusselt number in the presence of thermal radiation. The study shows that the temperature reduces with increasing the electrical double layer thickness, thermal radiation, couple stress parameter, and magnitude of Brinkman number, however, it enhances with increasing the Joule heating and thermal slip effects. The rate of heat transfer enhances with Joule heating effects, while the trend is reversed due to the presence of two-layered electroosmotic flow and couple stress effect. [ABSTRACT FROM AUTHOR]

The impact of lateral walls and partial slip with different waveforms on peristaltic pumping of couple stress fluid in a rectangular duct with different waveforms has been discussed in the current article. By means of a wave frame of reference the flow is explored travelling away from a fixed frame with velocity c. Peristaltic waves generated on horizontal surface walls of rectangular duct are considered using lubrication technique. Mathematical modelling of couple fluid for three-dimensional flow are first discussed in detail. Lubrication approaches are used to simplify the proposed problem. Exact solutions of pressure gradient, pressure rise, velocity and stream function have been calculated. Numerical and graphical descriptions are displayed to look at the behaviour of diverse emerging parameters. [ABSTRACT FROM AUTHOR]

The presented article addresses the electro-osmotic peristaltic flow of a couple stress fluid bounded in an inclined asymmetric microchannel. The viscous dissipation, Joule heating and chemical reaction effects are employed simultaneously in the flow analysis. Heat and mass transfer have been studied under large wavelength and small Reynolds number. The resulting nonlinear systems are solved numerically. The influence of various dominant physical parameters is discussed for velocity, temperature distribution, concentration distribution and the pumping characteristics. Electro kinetic flow of fluids by micro-pumping through micro channels and micro peristaltic transport has accelerated considerable concern in accelerated medical technology and several areas of biomedical engineering. Deeper clarification of the fluid dynamics of such flow requires the continuous need for more delicate mathematical models and numerical simulations, in parallel with laboratory investigations. [ABSTRACT FROM AUTHOR]

The present article deals with theoretical analysis on the peristaltic transport of a couple stress fluid with lubrication on the walls of the channel. The walls are coated with thin layer of power-law lubricant and the condition arised by the coating is modelled by taking the continuity of velocity and shear stresses of both the fluids at the fluid–fluid interface. The flow problem is discussed in two-dimensional asymmetric medium assuming long wavelength and low Reynolds number. Closed form solutions for velocity, stream function and flow rate are discussed. The numerical solutions for pressure rise, trapping and reflux are discussed. The effects of lubricant parameter, couple stress parameter, phase difference, wave amplitudes and flow rate are discussed for symmetric and asymmetric channels. It is observed that by increasing the lubrication effects, pressure rise increases in the pumping region and for trapping, boluses disappear and streamlines become parallel to the walls of the channel. From the given flow problem, the limiting cases of no-slip and viscous flow are presumed and found to be in excellent agreement with the existing literature. [ABSTRACT FROM AUTHOR]

Swimming of spermatozoa through couple stress fluid in an asymmetric human cervical canal is investigated in the present theoretical analysis. A couple of fourth-order partial differential equations arising from the mathematical modelling of the proposed model is solved analytically. Flow variables like pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for the pertinent parameters. Conspicuous features of the pumping characteristics are explored. It is found that pressure rise facilitates the motion of spermatozoa to fertilize an ovum in the female reproductive tract, whereas pressure drop by inverting the direction of spermatozoa controls the probability of pregnancy. Maximal propulsive velocity of the spermatozoa is reported in the absence of travelling waves along the cervical walls. Minute impact of phase difference on propulsive velocity is evident. An analogy of the current analysis with the existing literature is also made. [ABSTRACT FROM AUTHOR]

This article aims to explore the spiraling motion of a couple stress fluid over a disk rotating and radially stretching simultaneously. The spiraling motion is developed through the uniform rotation of the disk in addition to radial stretching. The logarithmic spirals in the disk velocity are produced due to the combined effects of stretching and rotation. The similarity transformations are invoked to obtain the coupled ordinary differential equations representing the flow. A Legendre wavelet spectral collocation method (LWSM) is employed for obtaining numerical solutions to analyze the effects of the pertinent parameters on the flow. The quantities of physical interest, i.e., radial and azimuthal skin friction coefficients, the wall shear stress, and the heat transfer rate are computed for the various values of the spiral angle, spiraling parameter, and couple stress parameter. It is found that enhancing the spiral angle declines the radial skin friction while enhancing azimuthal skin friction and the total wall shear stress. The temperature of the fluid is decreased for increasing the spiraling parameter and spiral angle, but increases for large couple stress parameter. [ABSTRACT FROM AUTHOR]

This paper looks at the MHD natural convection flow through a vertical porous channel of couple stress fluid nanoparticles under convective heat conditions at the wall of the channel. Incorporated Soret and Dufour effects lead to strong coupled and highly nonlinear differential systems. To describe accurately all the physical phenomenon, the nanoparticle’s volume fraction is taken into account. The useful technical of the similarity transformations is used to produce an ordinary system which is numerically solved. Graphical illustrations containing non-dimensional velocity, temperature, concentration and concentration of nanoparticles are extensively presented for different values of various thermophysical parameters. Main quantities of interest as Nusselt and Sherwood numbers at both the walls are tabulated. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional non-Newtonian couple stress fluid flow over the upper horizontal surface of a paraboloid (uhsp) (shaped like a submarine or any aerodynamical automobile) is investigated. At the freestream, a stretching of the fluid layer is assumed along with catalytic surface reaction which tends to induce the flow in the fluid-saturated domain. The problem is modeled by engaging laws of conservation for mass, momentum, heat and concentration. Velocity components are converted to stream functions and similarity transformations to reduce the dependent and independent variables in the partial differential equation describing the flow. Stream functions ideally satisfy continuity equation and transformation to reduce the PDEs to the system of coupled nonlinear ODEs. The numerical solution of these equations is obtained using the shooting-RKF method. The graphical results show that both the lateral and horizontal velocities decrease by increasing the couple stress material parameter and cause the temperature to rise. The thermal boundary layer decreases subject to the thickness parameter and has appositive effects on concentration boundary layer. Finally, numerical results have also been tabulated. [ABSTRACT FROM AUTHOR]

The present article deals with the effects of nanoparticles and magnetic field on the peristaltic flow of a couple stress fluid in an asymmetric channel with different wave forms. Mathematical modelling for 2-D and two directional flows of a couple stress fluid along with nanofluid are first given and then simplified under the assumptions of long wavelength and low Reynolds number approximation. After invoking these approximations we get coupled non-linear differential equations. The exact solutions of temperature distribution, the nanoparticle concentration, velocity, stream function and pressure gradient are calculated. Finally graphical results of various physical parameters of interest are discussed to examine the behavior of flow quantities. [ABSTRACT FROM AUTHOR]

In this paper, the effect of Coriolis force is explored on convective instability of a doubly diffusive incompressible couple stress fluid layer with gravity acting downward. A linear stability analysis is used to obtain the conditions for the onset of stationary and oscillatory convection in the closed form. Being a multiparameter instability problem, results for some isolated cases have been presented to illustrate interesting corners of parameter space. It is found that the neutral curve for oscillatory onset forms a closed-loop which is separate from the neutral curve for stationary onset indicating the requirement of three critical thermal Rayleigh numbers to specify the linear instability criteria instead of the usual single value. Besides, the simultaneous presence of rotation and the addition of heavy solute to the bottom of the layer exhibit an intriguing possibility of destabilizing the system under certain conditions, in contrast to their stabilizing effect when they are present in isolation. The implication of couple stresses on each of the aforementioned anomalies is clearly brought out. The spatial wavelength of convective cells at the onset is also discussed. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to present the effect of the preload on the static characteristics of three-lobe bearings lubricated with a fluid blended with high polymer additives modeled as a couple stress fluid. Design/methodology/approach: Based on the micro-continuum theory, the modified Reynolds equation for couple stress fluids is solved using a finite difference method to obtain the distribution of the pressure, the load-carrying capacity, the attitude angle, the friction coefficient and the side leakage for various values of the couple stress parameter and the preload factor. Findings: The results show that the presence of a couple stress in the lubricants improves the static characteristics of this type of bearing compared to those lubricated with Newtonian fluids for any value of the preload factor. Thus, it is found that the preload significantly affects the performance of the three-lobe journal bearing lubricated with a couple stress fluid or a Newtonian fluid. Moreover, the investigation showed that increasing the preload factor exhibits an increase in the load carrying capacity and the attitude angle, but it decreases the friction coefficient and the side leakage especially at a lower preload factor. Furthermore, using a couple stress fluid and a higher preload factor led to a significant rise in the load carrying capacity and a significant reduction in the friction coefficient. Practical implications: This study helped improve the performance characteristics of the three-lobe journal bearing. Originality/value: The presence of couple stress in the lubricants improves the static characteristics of this type of bearing compared to those lubricated with Newtonian fluids for any value of the preload factor. The usage of the couple stress fluid and the higher preload factor led to a significant rise in the load carrying capacity and a significant reduction in the friction coefficient. [ABSTRACT FROM AUTHOR]

This paper considers the steady translational motion of two collinear rigid spheres in an incompressible couple stress fluid. The two spheres are assumed to be of different sizes and are moving with two different speeds along a line axis connecting their centers. First, the general solution for the steady motion of an incompressible couple stress fluid past an axially symmetric particle is obtained analytically in the form of an infinite series. Second, the obtained solution is employed to construct the general solution for the steady motion of a couple stress fluid flow past two translating spheres using the principle of superposition. The boundary collocation technique is then used to satisfy the imposed boundary conditions on the surfaces of the two spheres. The normalized drag force acting on each of the two spherical particles is evaluated and presented numerically through tables and graphs. The tabulated results show that the convergence of the numerical results is achieved rapidly. In addition, it is observed that the increase in the couple stress viscosity parameter increases the values of the normalized drag force on each of the spherical particles. [ABSTRACT FROM AUTHOR]

The viscosity variation on circular stepped plates with MHD in Couple Stress fluid is analyzed. The modified Reynolds equation applicable to couple stress fluid is obtained by considering Viscosity Variation along with the film thickness. The expressions are obtained for dimensionless Pressure, Work load and time. The outcomes indicate that the viscosity variation reduces the pressure and squeeze film time. But, the Magnetic effect with couple stress fluid increases the Work load. [ABSTRACT FROM AUTHOR]

Fluid flow in micro-channels has been considered as one of the important research areas in the field of continuum mechanics due to its vast applications in biological sciences such as blood flow in arteries and capillaries. The channel walls of such fluid flows may exhibit some degree of roughness which influences the flow field functions such as rate of flow and fluid velocity. These flow problems can be modeled as couple stress fluid flows in axially corrugated pipes. This paper investigates the effect of surface roughness on the rate of flow and mean velocity of a couple stress fluid flow through a sinusoidal corrugated tube. The fluid motion is assumed to be steady and the Stokesian assumption of low Reynolds number is applied. Both longitudinal corrugations and transverse corrugations across the cross-section of the tube are studied. The boundary perturbation technique is employed to obtain the solution in each case. The total rate of flow and the mean velocity are obtained analytically in terms of the perturbation parameter up to order two. The results are represented graphically for different values of the couple stress viscosity coefficient, perturbation parameter and wave number of the corrugations. It is observed from the numerical results that the rate of flow decreases monotonically with the increase in the wave number for the case of longitudinal corrugations. For transverse corrugations, it is noticed that the wave number has a slight effect on the rate of flow. In addition, it is observed that the increase in the couple stress viscosity parameter results in a decrease in the flow rate for both cases. Finally, if the couple stress viscosity parameter is taken zero the case of classical viscous fluid flow is recovered. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study theoretically explores the electroosmotic and electromagnetohydrodynamic (EMHD) transport of couple stress fluid in a microchannel subjected to an applied magnetic and electric field simultaneously to predict the flow dynamics, thermal transport, and entropy generation in a thermofluidic system with slip-dependent (SD) zeta potential. Solving the linearized Poisson-Boltzmann equation gives a closed-form solution for the slip-dependent (SD) electrical potential distribution established in the Electrical Double Layer (EDL). Using suitable boundary conditions and the SD zeta potential, analytical expressions for flow velocity, temperature, and entropy generation rate are determined. There are a variety of important parameters that have been considered, including the couple stress, slip length, Hartmann number, pressure gradient, and transverse electric field. The findings for each of these parameters are graphically displayed. After accounting for the SD zeta potential for the slip parameter and Hartmann number, the fluid velocity is shown to rise; however, the normalized velocity for the couple stress parameter exhibits the reverse trend owing to its strong resistive influence. It is noticed that with a higher Brinkman number, the magnitude value of the temperature is larger for SD zeta potential than for slip-independent (SI) zeta potential owing to an increase in viscous dissipation effect. The results reveal that the flow velocity and thermal energy distribution have a substantial effect on the quantity of entropy generated in the channel under SD zeta potential. [ABSTRACT FROM AUTHOR]

In this article, an exact solution for couple stress fluid flow past a contaminated fluid sphere, filled with couple stress fluid was formed by using interfacial slip boundary condition. It's involved with internal and external cap and no cap regions. The velocity is expressed in terms of stream function. The external velocity and internal velocity are obtained. The Drag coefficient is computed. The special cases of a viscous fluid with a no-slip condition, solid sphere case are evaluated. The obtained results are in good agreement with the results from the literature. Additionally studied viscous fluid past a contaminated couple stress fluid sphere and couple stress fluid past a contaminated viscous sphere, also done. The results of special cases are also agreeing with the results from the literature. [ABSTRACT FROM AUTHOR]

• Debye thickness has vitol role in EOF. • Electrical strength can be utilized to increase fluid velocity. • Large bolus are generated near walls due to electro-osmosis and couple fluid parameter. • Magnetic field controls the pumping performance overall. • Heat transfer rate is accelerated due to Hall effect, Joule heating and magnetic field. The effect of heat transfer on Couple-Stress fluid's unsteady peristaltic motion is theoretically studied in this paper using applied electric and magnetic fields. Thermal analysis is carried out in the presence of fluid friction-induced viscous dissipation and Joule heating. The potential distribution is examined using the Debye-Huckel linearization approximation. The governing equation's complexity is decreased using the lubrication theory. The dynamics of electroosmosis and peristaltic pumping are examined for the velocity field, temperature field, pressure distribution, and streamlines. The effects of electrical double layer (EDL) on flow, pumping, and thermal properties have been calculated. Numerical computations have been done to provide the graphical depiction and to explain the model's outcomes. This model can be used to design a variety of microfluidic gadgets and intelligent micropumps for combining chemicals and ionic liquids. [ABSTRACT FROM AUTHOR]

• Dynamic transition theory is used on couple-stress fluid saturated porous media convection problem. • Complete description of the global dynamics on and during the onset of convection is obtained. • Approximate bifurcated solutions are given and corresponding roll structures are visualized. • Transition types are determined during the onset of convection. In this article, we study the stability and transition of couple stress fluid saturated porous media, heated from below and cooled from above by employing a thermal non-equilibrium model. Careful analysis shows that the thermal non-equilibrium model has a global attractor, and the global attractor only consists of the basic solution if the Rayleigh number is equal or below a threshold. In generic case where the transitioning eigenvalue has multiplicity one, we show that the transition involved is of continuous type, and the basic solution will be bifurcated to two stable convection solutions which attract globally. If the leading eigenvalue multiplicity is two, the transition is also continuous and a global attractor homeomorphic to the unit circle bifurcates. The attractor then contains four steady-state convection solutions, two of which are stable while the other two are unstable. Further numerical works give more details in the transition process including the bifurcated roll structure. [ABSTRACT FROM AUTHOR]

The non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient is obtained. While the pressure and flow rate are obtained numerically. The impact of involved parameters on important physical quantities such as temperature, pressure, and pressure gradient are elaborated through graphs and in tabular form. The pressure and pressure gradient decreases for variation of the couple stress parameter and velocity ratio parameter K. While the variation of the slip parameter increases the pressure and pressure gradient inside the flow geometry. Additionally, flow rate decreases for the variation of the slip parameter as fluid starts moving rapidly along the roller surface. The most important physical quantity which is responsible for maintaining the quality of the coating and thickness is flow rate. For variation of both the couple stress parameter and the slip parameter, the flow rate decreases compared to the Newtonian case, consequently the coating thickness decreases for the variation of the discussed parameter. [ABSTRACT FROM AUTHOR]

This study investigates the analysis of a reactive hydromagnetic fluid flow of a couple stress fluid through a saturated channel with porous materials. The analytical expressions for the fluid motion and heat transfer are obtained to find the rate of entropy generation with the use of modified Adomian decomposition method (mADM) as well as determining the critical values. The results are compared with previously obtained results to validate the use of mADM. Also, the impact of magnetic strength and other thermophysical parameters are presented and discussed in tables and graphs to show the impact of magnetic strength on fluid motion, heat transfer and rate of entropy generation. [ABSTRACT FROM AUTHOR]

Radiative–convective flow studies find wide range of applications in furnace design, solar fans, photochemical reactors, turbid water bodies, etc. The present article focusses on unsteady radiative–convective hydromagnetic couple stress fluid (CSF) flow from a vertical cylinder using the thermodynamic concept. The obtained governing equations of the present model are resolved by a well-organised numerical scheme. The unsteady nature of friction, entropy, coefficients of heat and mass transfer (HMT) along with the time-independent state pattern of flow-field profiles, are shown graphically for distinct values of governing radiation parameter, magnetic parameter, concentration parameter, and constant parameter to display important aspects of the solution. To analyse the HMT process in a 2D domain, Bejans flow visualisation is considered along with isotherms, streamlines, and isoconcentration lines. The Bejans HMT flow visualisation shows that the heat and mass function contours are denser in the foremost verge of the hot surface of the cylinder compared to other contours. The result indicates that the entropy generation (EG) parameter increases with decreasing values of radiation and magnetic parameters. Also, the entropy parameter increases for increasing values of concentration parameter or constant parameter. [ABSTRACT FROM AUTHOR]

The Couette–Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of spherical and homogeneous Hafnium particles was taken into account. The temperature dependent viscosity model, namely, Reynolds' model was utilized. The Runge–Kutta scheme with shooting was used to tackle a non-linear system of equations. It was observed that the velocity decreased by increasing the values of the Hartman number, as heating of the wall reduced the effects of viscous forces, therefore, resistance of magnetic force reduced the velocity of fluid. However, due to shear thinning effects, the velocity was increased by increasing the values of the viscosity parameter, and as a result the temperature profile also declined. The suspension of inertial particles in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids can be used to analyze the biphase flows through diverse geometries that could possibly be future perspectives of proposed model. [ABSTRACT FROM AUTHOR]