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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.

In this work, authors have studied peristaltic flow of immiscible type of couple stress and Newtonian fluid via an asymmetric horizontal channel filled with porous material by taking slippage into account at the channel wall which was ignored in previous published literature under the influence of thermal radiation and magnetic field. The study of peristaltic flow of considered immiscible fluids will play an important role in maximizing system efficiency, reducing energy losses, and improving performance of various fluid transport. In the present problem, the linearized form of governing equations has been solved by direct method with the use of Mathematica 14 software to obtained the closed form solutions of various flow variables. In this work, the impacts of various influencing factors on the model's flow, thermal, and concentration properties have been analyzed graphically. The work presented here leads to the significant result that large Schmidt number values in a porous filled duct reduces the mass diffusivity. Another key finding of this work is that the formation of entropy is reduced when low permeability porous material is used. Our research concludes that entropy creation in the asymmetric porous channel is decreased when the slip length increases on the channel's static borders. • We examine entropy generation, and concentration in peristaltic flow of immiscible fluids in a porous channel. • We obtain the closed form solutions for flow velocity, temeperature and concentration. • The concentration of the immiscible fluid diminishes as the Soret numbers increase. • The entropy generation number in the porous material filled channel can be reduced by raising the slip parameter. • This model is useful in thermal fusion reactors, cooling systems, and petroleum products. [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.

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]

In 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study investigates the thermal characteristics and irreversibility analysis of the combined electro-osmotic and electromagnetic flow of a couple stress fluid through a microfluidic channel with constant wall heat flux boundary condition. The analytical solutions for electromagnetohydrodynamic (EMHD) flow velocity, temperature field and entropy production distribution are obtained using the physically relevant boundary conditions. Results show the effects of several factors, including couple stress parameter, Hartmann number, lateral/transverse electric field parameter and Brinkman number on the temperature transport and entropy generation, particularly, the details of how the temperature, Nusselt number and entropy generation vary with these parameters. The results demonstrate that the entropy generation in the channel is strongly dependent on the flow velocity and thermal energy distribution. In this analysis, the primary focus is placed on the impact of the couple stress parameter on EMHD flow velocity, heat transfer and entropy generation. The results reveal that when the couple stress physical parameter increases, the magnitude of temperature and Bejan number decreases. However, the Nusselt number and entropy production rates have opposite effects towards the channel walls. The present research has enormous practical significance and can design efficient thermal micro/nanoequipment. [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]

The overall objective of the current analysis is to examine how electroosmotic flow combined with peristaltic pumping phenomenon could ably contribute to intracellular fluid flow. The biofluid is taken as non-Newtonian Couple stress fluid, while micro-passage is approximated as two-dimensional inclined channel comprehending complex peristaltic walls. Following a traditional approach of peristaltic fluid flow problem balance of mass and momentum is utilized. Beside channel waves, flow is also generated by Lorentz force triggered by electric and magnetic fields. To integrate electric potential term Poisson-Boltzmann and Nernst Planck equation are utilized. Finally, a sixth order BVP in term of stream function is obtained by employing creeping flow, long wavelength and Debye-Hückel assumptions. A numerical solution is calculated and analyzed by plotting fluid velocity and level curves in MATLAB 2021b. It is observed that couple stress fluid flows with greater speed (in central region of the channel) as compared to Newtonian fluid. Moreover, electro-osmotic parameter and Debye-Hückel length are assistive factors to the fluid velocity in the lower half of the passage. [ABSTRACT FROM AUTHOR]

The current study concentrated on the analysis of entropy generation in three dimensional mixed convection flow of couple stress nanofluid under the effect of high order velocity slip flow, passive and active control conditions. The problem advances more significance with the effect of non-Fourier's heat, and non-Fick's mass flux model to scrutinize the heat and mass transport rate. The high-order partial differential equations obtained from the designed problem are transmuted into higher order ordinary differential equations using similarity conversion and lastly solved by using bvp4c. Through this investigation how governing parameters have affected the flow problem were examined and offered in graphical and tabular form. It is discovered that the occurrence of couple stress inflow problem upsurges the velocity of the fluid and on the other hand it causes a reduction in the entropy production. Likewise, it is detected that temperature improves by snowballing the Hartman parameter. Moreover, the temperature and concentration disseminations are greater all for the situation of an active control while correlated with a case of passive control. Also, the same is true for numerical results of Nusselt number and Sherwood number that is due to an active control is greater than all for the case of passive control. Furthermore, this theoretical and numerical deliberation bears the potential to beneficial in the field of bio-fluid dynamics. [ABSTRACT FROM AUTHOR]

This paper concerns the analytical investigation of the axisymmetric and steady flow of incompressible couple stress fluid through a rigid sphere embedded in a porous medium. In the porous region, the flow field is governed by Brinkman's equation. Here we consider uniform flow at a distance from the sphere. The boundary conditions applied on the surface of the sphere are the slip condition and zero couple stress. Analytical solution of the problem in the terms of stream function is presented by modified Bessel functions. The drag experienced by an incompressible couple stress fluid on the sphere within the porous medium is calculated. The effects of the slip parameter, the couple stress parameter, and permeability on the drag are represented graphically. Special cases of viscous flow through a sphere are obtained and the results are compared with earlier published results.

Contemporary investigation studies the silent features of the dissipative free convection couple stress fluid flow over a cylinder under the action of magnetic field, thermal radiation and porous medium with chemical reaction effect. Present two-dimensional viscous incompressible physical model is designed based on the considered flow geometry. Present physical problem gives the highly complicated nonlinear coupled partial differential equations (PDE's) which are not amenable to any of the known techniques. Thus, unconditionally stable, most accurate and speed converging with flexible finite difference implicit technique is utilized to simplify the dimensionless flow field equations. It is apparent from the current results that; the velocity profiles are diminished with enhancing values of magnetic field. Temperature profile increases with enhancing values of thermal radiation parameter. Velocity contours deviates away from the wall with enhancing magnetic parameter. Also, the effects of magnetic field, porous medium, thermal radiation, chemical reaction, buoyancy ratio parameter and Eckert number on couple stress flow velocity, temperature, and concentration profiles are studied. However, the present study has good number of applications in the various fields of engineering such as; polymer processing, solidification of liquid crystals, colloidal solutions, synovial joints, geophysics, chemical engineering, astrophysics and nuclear reactors etc. Finally, the current solutions are validated with the available results in the literature review and found to be in good agreement.

A theoretical study of MHD with viscosity variation on the squeeze film attributes of a curved circular plate and a flat porous plate using couple stress fluid is examined in this paper. The Reynolds equation in modified is inferred and same is solved to get the expression for film pressure, load supporting capacity and response time in non-dimensional form. As per the computed results, the squeeze film attributes are improved by using a non-Newtonian fluid as a lubricant in association with a magnetic effect. Also, the impact of viscosity variation enhances the squeeze film attributes in comparison with constant viscosity whereas the permeability factor declines the pressure, load supporting capacity and response time as compared to non-porous case.

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.

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]

In the present study, the physical features of the bioconvective MHD flow of a couple stress fluid over an upper horizontal surface (i.e. surface shaped like a submarine or any (uhsp) aerodynamical automobile) is analysed by considering radiation and viscous dissipation effects. In the fluid-saturated domain flow is induced due to the reaction of catalytic surface, double diffusion and stretching fluid layers. In fact, couple stress fluid is electrically conducted because non-uniform magnetic field is imposed. With the assistance of appropriate similarity transformations governing equations of the study are reduced to set of ordinary differential equations. Thereafter, built-in MATLAB solver bvp4c is implemented to solve the system numerically. By means of graphs and tables variations of the velocity, temperature, concentration, friction factor, local heat and mass transfer rates are observed thoroughly by varying the flow controlling parameters. From this analysis, main observations are, for rising values of couple stress and magnetic parameter velocity is decline, whereas temperature rises for the same parameters and increase in the thermal boundary layer is noted for the Brinkman number, whereas reverse trend is noted in the concentration boundary layer. Finally, comparison is done and a good correlation is identified between the present analysis and perversely recorded analysis. [ABSTRACT FROM AUTHOR]

In nanofluids, the effect of convection in the presence of double diffusivity on a magneto couple stress fluid with the peristaltic flow of a model in a non-uniform channel (MCSFM) is reviewed in this article. This research discusses MCSF in a non-uniform channel by applying the Levenberg–Marquardt procedure via an artificial backpropagated neural network (LMP-ABNN). For two-dimensional and two-directional flows, mathematical formulations of double-diffusivity convection of a magneto couple stress fluid in nanofluids are developed. The partial differential equations are reduced to ordinary differential equations by using appropriate transformations. The assessment of the Hartmann number, thermophoresis parameter, Dufour parameter, Soret parameter, and magnetic Reynolds number over concentration profiles and temperature profiles is made by generating a dataset for LMP-ABNN based on the ND solve method for different variations of MSCFM. To examine the approximate solution validation, training and testing procedures are interpreted, and the performance is verified through error histogram and mean square error results. The extremely nonlinear equations are reduced by employing a long-wavelength approximation and a low but finite Reynolds number. To describe the behavior of flow quantities, graphical representations of a variety of physical characteristics of importance are shown. The impact of the Hartmann number and magnetic Reynolds number over axial magnetic field and current density is also studied. The concentration increases as the thermophoresis parameter and Dufour parameter values increase. This occurs because the concentration and both these parameters have a direct relationship. We observed opposite behavior for both the magnetic Reynolds number and the Hartman number. The behavior of current density J z increases with increasing values of R m. Both the temperature distribution and solute concentration increase. The final outcome of this study is to provide the potential for these techniques to provide new insights and solutions to challenging problems in nanofluids and other areas of fluid mechanics and to facilitate the design of more efficient and effective microfluidic devices.

• Creeping sinusoidal flowing and diffusion of solute material in incompressible couple-stress fluid are examined. • Both homogeneity and heterogeneity chemical interactions are taken into considered. • Surface properties, long wavelength hypothesis and dynamic periphery situations are elaborated. • Mean active diffusion factor is improved with wall features and amplitude ratio. • Suggesting peristalsis is promoted dispersion. A mathematical model has been constructed to examine the creeping sinusoidal flowing and diffusion of a solute material of an incompressible couple-stress fluid across a porous medium with wall features in the existence of heterogeneous-homogeneous chemical reaction. The mean effective diffusion factor is calculated using the long wavelength hypothesis, Taylor's limit criteria, and dynamic periphery restrictions. The graphs have been used to study the effects of important constraints on the mean effective diffusion coefficient. The mean effective diffusion factor is found to rise with wall characteristics and amplitude ratio, indicating that peristalsis causes an increase in scattering. Additionally, scattering increased with the permeability constraint but decreased with the couple-stress constraint, homogeneous reaction rates, and heterogeneous reaction rates. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of three‐dimensional magnetohydrodynamic flow for a couple of stress fluids on an exponentially stretching sheet. The magnetic field is implemented normally to the surface. To observe the transfer of heat phenomenon, the Cattaneo–Christov flux model of heat is employed. Using similarity transformation, the substantial differential equations are reformed into ordinary differential equations. Eventually, the effects of different physical parameters are studied graphically. The drawback in Fourier heat flux model is removed by adding a new paramter known as thermal relaxation time by Cattaneo. This perimeter allows heat transportation by way of propagation of waves thermally at a defined speed. After this, the Cattaneo law is further modified by Christov–Christov to replace the ordinary derivative along Oldroyd's upper‐convective derivative. [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]

In this paper, we have explored the steady Poiseuille flow of couple stress fluid between two parallel plates under ‎the influence of non-isothermal effects of Reynold viscosity model, using Optimal Homotopy Asymptotic Method ‎‎(OHAM) and New Iterative Method (NIM). We obtained expressions for velocity profile, temperature distribution, ‎average velocity, volume flux and shear stress. The solutions obtained using these methods are in the form of ‎infinite series; therefore, they can be easily computed. Comparative results of solutions obtained by both methods ‎are given using different tables and graphs.

In this article, the generalized plane Couette flow of Vogel’s model of incompressible, non-isothermal, couple stress fluid flowing steadily between two parallel walls is investigated. The governing equations are reduced to ordinary differential equations. To investigate the non-linear coupled system of differential equations, the optimal homotopy asymptotic method with DJ polynomial and asymptotic homotopy perturbation method have been used. Important flow properties are presented and discussed. We have obtained expressions for velocity, average velocity, shear stress, volume flux and temperature. The results gained employing these techniques are in the form of infinite series; thus, the results can be easily calculated. Comparison of various results, obtained through the suggested approaches, is carried out and an excellent agreement is achieved.

The paper deals with a theoretical study on blood flow in a stenosed segment of an artery, when blood is mixed with nano-particles. Blood is treated here as a couple stress fluid. Stenosis is known to impede blood flow and to be the cause of different cardiac diseases. Since the arterial wall is weakened due to arterial stenosis, it may lead to dilatation /aneurysm. The homotopy perturbation technique is employed to determine the solution to the problem for the case of mild stenosis. Analytical expressions for velocity, shear stress at the wall, pressure drop, and flow resistance are derived. The impact of different physical constants on the wall shear stress and impedance of the fluid is examined by numerical simulation. Streamline patterns of the nanofluid are investigated for different situations.

In this study, the dynamic behavior of three-lobe noncircular hydrodynamic journal bearings lubricated with couple stress fluid is presented. Currently, application of journal bearings with different geometries such as lobed bearings and using non-Newtonian lubricants, including various additives, are the common suggested solutions by tribology researchers to improve the performance of rotor-journal bearing systems. Due to the incompatibility of new lubricant behaviors including polymer chains or other types of suspended particles with considerable size from the classic Navier–Stokes equations, different models such as couple stress fluid theory have been proposed to evaluate their performance. To investigate the self-excited rotor disturbances caused by various factors, like operating in critical speeds, simultaneous solution of governing Reynolds equation of oil lubricant and the rotor motion equations has been done. The result of dynamic analyses using linear and nonlinear approaches indicates the possibility of enhancing the stiffness and damping ability of the three-lobe bearings by strengthening the couple stress properties of lubricant. It is seen from the results that by increasing the couple stress parameter of oil, the type of rotor perturbations in the bearing clearance space changes from divergent oscillations, as a leading cause of collision between the rotor surface and the bearing shell, to limit cycle motion around the rotor stable position or convergent fluctuations to the static equilibrium point. This improvement in the stability range of three-lobe journal bearings using a couple stress lubricant appears in the results of a linear analysis model in terms of increasing the critical mass parameter and decreasing the whirl frequency ratio. In addition, bifurcation diagram results show that using noncircular three-lobe bearings instead of circular types and replacing the Newtonian lubricant with the couple stress fluid improve the dynamic stability of rotor- bearing supports. [ABSTRACT FROM AUTHOR]

Peristalsis is the most dynamic phenomenon that is significant in the biomedical domain and offers considerable promise in microscale fluids. For the past few years, this biomimetic (peristaltic) phenomenon attracted the attention of the research community because of its massive applications in numerous medical and industrial domains. In the present study, the steady, laminar rheology of biological fluid from a biomimetic (peristaltic) channel is considered. The rheological equations are expressed in the Cartesian system, and the porosity effects are modelled (added) on a body force term of the momentum equation. The current analysis depends on the creeping phenomena and long wavelength. The closed-form solutions are acquired by using integration on the rheological equations subject to suitable boundary conditions. The rheology is controlled by two embedded parameters, the porosity and non-Newtonian parameters. It is shown using graphs that the magnitude of axial velocity is strongly affected by the larger strength of porosity (Darcy's number) and non-Newtonian (couple stress) parameters. We noticed the impacts of involved rheological constraints on pumping and trapping phenomena in the light of porous effects. Additionally, the wavy pattern of sinusoidal waves is utilised in the present analysis to increase the efficiency of the peristaltic pump. By increasing the porosity impacts, the magnitudes of velocity profile and pressure gradient of a biofluid are increased. The porosity has a dynamic role in the augmentation of peristaltic pumping. The impacts of couple stress parameter reduces the viscous effects. These outcomes may be useful in bioengineering (drug delivery schemes) and chemical processes. [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]

An investigation of 2D laminar magnetohydrodynamics couple stress hybrid nanofluid is performed with inclined magnetic field over the stretching/-shrinking surface embedded in porous media. The quiescent water-based nanofluid is subjected to the external force by pulling the two ends of the sheet with equal magnitude and opposite forces. The governing nonlinear partial differential equations (PDEs) are converted into nonlinear ordinary differential equation (ODE) by adopting the suitable similarity transformation and obtains the analytical solution for velocity. The hydrodynamic characteristics are investigated in the presence of different physical parameters such as couple stress parameter, magnetic parameter, mass transpiration, stretching/shrinking parameter, porosity and magnetic parameter with the help of graphs. The thermal properties are enhanced by adding the copper and alumina nanoparticles to the base fluid. The result of this study has important applications in industrial and scientific are such as polymer extrusion process, liquid crystal solidification, cement artificial foams production, ceramics, metal spinning, and roofing shingles and also have possible technological applications in fluid-based systems involving stretchable/shrinkable materials. [ABSTRACT FROM AUTHOR]

This paper investigates the electric properties of gold nanoparticles mixed with a convection dielectric couple stress fluid inside a vertical cylindrical tube with moving endoscope in the presence of Hall currents and thermal radiation. Under the long wavelength approximation and the use of appropriate conversion relationships between fixed and moving frame coordinates, the exact solutions have been evaluated for temperature distribution, gold nanoparticles concentration, electrical potential function and nanofluid pressure, while analytical solution is found for the axial velocity using the homotopy analysis method. The results show that the presence of the electric field enhances the effects of Brownian motion parameter, thermophoresis parameter, radiation parameter, Hall currents and wave amplitude ratio on the axial nanofluid velocity, while it was found that its presence reduces the effects of couple stress parameter, thermophoresis diffusion constant and Brownian diffusion constant. [ABSTRACT FROM AUTHOR]

In this paper, the mixed convective flow of an electrically conducting, viscous incompressible couple stress fluid through a vertical channel filled with a saturated porous medium has been investigated. The fluid is assumed to be driven by both buoyancy force and oscillatory pressure gradient parallel to the channel plates. A uniform magnetic field of strength B0 is imposed transverse to the channel boundaries. The temperature of the right channel plate is assumed to vary periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. Under these assumptions, the equations governing the two-dimensional couple stress fluid flow are formulated and exact solutions of the velocity and the temperature fields are obtained. The effects of radiation, Hall current, porous medium permeability and other various flow parameters on the flow and heat transfer are presented graphically and discussed extensively.

The study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

Hybrid nanofluid is an emerging field due to the rapid enhancement of heat transfer and stable nanoparticles in base fluid properties. A three dimensional hybrid nanofluid flow model is constructed over biaxial porous stretching/shrinking sheet with heat transfer, Radiative heat and mass flux (3D-HNF-RHF). Bayesian Regularization technique based on Backpropagated neural networks (BRT-BNNs) is employed to estimate the solution of proposed model. It is the mathematical process which converts nonlinear regression fitting into a well-posed statistical process in the form of ridge regression. This method diminishes length cross validation need and more robust then Backpropagation technique. The proposed flow system 3D-HNF-RHF is transferred to ordinary differential equations (ODEs) possessing physical variations through self-similar transformations. The effect of derived variations such as thermal relaxation parameter, mass flux parameter, Stretching/shrinking parameter, Prandtl number, Skin friction and Nusselt number observed over the velocity and temperature fields. Numerical results of these physical parameters have been presented in tabulated form obtained from a dataset constructed through Homotopy Analysis Method imposed on 3D-HNF-RHF model. Statistical tests through mean square error, histogram curve and regression fitting curves are employed to check the accuracy and convergences of the solution obtained through BRT-BNNs. It is observed that Stretching/shrinking quantity and mass flux parameter slow down the flow rate whereas, increase radiative heat flux upsurges the temperature gradient. The impacts of surface drag force and heat transfer are illustrated through the different graphical illustrations.

This paper concerns the analytical investigation of the axisymmetric and steady flow of incompressible couple stress fluid through a rigid sphere embedded in a porous medium. In the porous region, the flow field is governed by Brinkman's equation. Here we consider uniform flow at a distance from the sphere. The boundary conditions applied on the surface of the sphere are the slip condition and zero couple stress. Analytical solution of the problem in the terms of stream function is presented by modified Bessel functions. The drag experienced by an incompressible couple stress fluid on the sphere within the porous medium is calculated. The effects of the slip parameter, the couple stress parameter, and permeability on the drag are represented graphically. Special cases of viscous flow through a sphere are obtained and the results are compared with earlier published results. [ABSTRACT FROM AUTHOR]

The primary focus behind this research work is to unfold the heat and mass transfer characteristics of peristaltic transport of hydromagnetic couple stress fluid through a porous medium in an inclined channel of asymmetric kind. Consideration of both Dufour and Soret effects is one of the key factors of this investigation. Simultaneous convective conditions of mass and heat transfer are satisfied by the channel walls. Beneath the presumptions of small Reynolds number along with long wavelength, the governing two-dimensional coupled differential equations are simplified after incorporating dimensionless variables. To calculate the pressure difference, the technique of numerical integration has been employed. Graphical demonstrations for velocity, temperature, concentration profiles have been sketched out under the influence of pertinent flow parameters. Pumping characteristics and trapping phenomenon for some particular kind of waveshapes are also highlighted through contour plots. Noteworthy findings are that near the center of the channel the maximum value of the temperature is attained due to the intensification of heat generation parameter. Also, Dufour number tends to enhance the temperature of the fluid, whereas Soret effect results in a downfall in the concentration field. Heat and mass transfer Biot numbers lead to an elevation in the concentration and temperature profiles, respectively. It is also perceived that a reduction in concentration takes place due to the presence of destructive kind of chemical reaction while a reverse trend is being followed during a chemical reaction of constructive kind. Moreover, both the pressure gradient as well as pressure difference act as increasing functions of the angle of inclination of the channel. Additionally, the general propensity of couple stress fluid parameter is to diminish the volume of the trapped bolus. [ABSTRACT FROM AUTHOR]

This paper presents a computational modeling approach to analyze the peristaltic pumping of couple stress hybrid nanofluids regulated by the electroosmosis mechanism through a microchannel. The effects of applied magnetic field, Joule heating and buoyancy have also been computed. In this analytical model, water-based titanium dioxide (TiO2) and silver (Ag) hybrid nanofluids have been considered. For more relevant physical problem, the axial velocity slip and thermal slip conditions have also been introduced. The nonlinear differential equations are simplified by considering the Hückel–Debye approximations as well as lubrication theory, and then the equations have been solved numerically by Mathematica 10 software via the NDsolve commands. The pertinent influences of key parameters on the axial velocity, nanoparticle temperature, Nusselt number and streamlines in the microchannel have been visualized graphically. It is observed that an increase in the thermal Grashof number produces a maximum axial velocity, and temperature of nanoparticles for both water–titanium dioxide and water–silver nanofluids. The maximum axial velocity and nanoparticle temperature occur in water–titanium dioxide as compared with water–silver. The outcomes of this model shall be very useful in the designs of smart electro-peristaltic pumps for thermal systems and drug delivery systems. [ABSTRACT FROM AUTHOR]