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Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. [ABSTRACT FROM AUTHOR]

A mathematical model is developed to analyse the peristaltic flow of couple-stress fluid in an inclined asymmetric channel with convective conditions. Soret and Dufour and Hall effects are taken into account. Analysis has been carried out in a wave frame of reference. Expressions for velocity, pressure gradient, temperature and concentration are constructed. Pumping and trapping phenomena are examined. Impact of sundry parameters on the velocity, temperature and concentration is discussed. [ABSTRACT FROM AUTHOR]

We make an effort to analyze the behavior of squeeze film characteristics of different finite plates with couple stress fluid in the presence of a transverse magnetic field. On the basis of the Stokes couple stress fluid model and hydromagnetic flow model, a modified Reynold's equation is derived, which is solved by using appropriate boundary conditions to obtain squeeze film pressure, load-carrying capacity, and squeeze film time. The graphical representation of the results suggests that the different bearing systems register an enhanced performance with couple stresses compared to that of a bearing system working with a conventional lubricant in the presence of a transverse magnetic field. It is observed that the effect of applied magnetic field on the squeeze film lubrication between different finite plates with conducting couple stress fluids is to increase the load-carrying capacity significantly and to delay the time of approach compared to the corresponding nonconducting Newtonian case. It is seen that for all of the finite plates of different shapes, the circular shape gives the maximum load and time. [ABSTRACT FROM PUBLISHER]

In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steady-state of the present flow are developed. The solution of the time dependent nonlinear and coupled governing equations is obtained with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the time histories of the skin-friction coefficient, Nusselt number, and Sherwood number as well as the steady-state velocity, temperature, and concentration are presented graphically and discussed. Also, it is observed that time required for the flow variables to reach the steady-state increases with the increasing values of Schmidt and Prandtl numbers, while the opposite trend is observed with respect to the buoyancy ratio parameter. To analyze the flow variables in the steady-state, the heatlines and masslines are used in addition to streamlines, isotherms, and isoconcentration lines. When the heat and mass functions are properly made dimensionless, its dimensionless values are related to the local and overall Nusselt and Sherwood numbers. Boundary layer flow visualization indicates that the heatlines and masslines are dense in the vicinity of the hot wall, especially near the leading edge. [ABSTRACT FROM AUTHOR]

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads. [ABSTRACT FROM AUTHOR]

The standard decoupled method with Newton-generalized minimum residual procedure performs poorly or may break down when used to solve certain elastohydrodynamic lubrication problems. The authors Zargari et al., 2007 presented decoupled and coupled methods in which the limitations of the decoupled method for some set of physical parameters and slight variation in these values (physical parameters) give a non-convergence solution. To overcome this aspect the wavelet-based preconditioners technique is used in this paper to solve the elastohydrodynamic lubrication problem. The effect of coupled stress fluids on elastohydrodynamic lubrication behavior in smooth, as well as rough, contact is investigated using the proposed method, numerically, in a low-speed-high load condition. The elastohydrodynamic lubrication characteristics computed for couple stress fluids are found to have strong dependence on the couple stress parameter, which shows the versatility and applicability of the proposed method.

The article offers information on the study conducted on the effect of the double stratification on the convection heat and mass transfer in porous medium. The result of the boundary layer analysis showed that temperature and concentration increases but velocity decreases in the presence of couple stresses in the fluid and on increasing thermal stratification parameter heat transfer coefficient increases but mass transfer coefficient decreases.

In this paper, we have investigated the effect of channel inclination on the peristaltic transport of a couple stress fluid in the presence of externally applied magnetic field. The slip velocity at the channel wall has been taken into account. Under the long wave length and low-Reynolds number assumptions, the analytical solutions for axial velocity, stream function, pressure gradient and pressure rise are obtained. The computed results are presented graphically by taking valid numerical data for non-dimensional physical parameters available in the existing scientific literatures. The results revealed that the trapping fluid can be eliminated and the central line axial velocity can be reduced with a considerable extent by the application of magnetic field. The flow phenomena for the pumping characteristics, trapping and reflux are furthermore investigated. The study shows that the slip parameter and Froude number play an important role in controlling axial pressure gradient. [ABSTRACT FROM AUTHOR]

In this paper the dynamic mathematical model of blood flow through a stenosed tapered artery in the presence of a catheter has been studied. Blood is modelled as a homogeneous and incompressible couple stress fluid. The analytical solution for the velocity component ( v z ) is obtained in terms of Bessel functions of various kinds. The effects of tapering angle ( θ ), slip velocity ( u ), catheter radius ( r c ), Reynolds number ( R e ), pulsatile parameter ( σ ), maximum height of the stenosis ( ϵ ) and couple stress fluid parameters ( β , ω ) on physiological parameters such as Impedance and Wall shear stress (at the maximum height of the stenosis) are discussed. The locations of the maximum height of the stenosis and the annular radius which are dependent on both tapered parameter ( ζ ) and shape parameter ( n ) are computed. It is identified that the impedance and wall shear stress are increasing as the tapered parameter ( ζ ) and the couple stress fluid parameters are decreasing while the behaviour is reverse in the case of the radius of the catheter ( r c ) and ϵ . It is also observed that the impedance is more in the case of symmetric stenosis. Further the effect of tapering angle on physiological parameters shows that the impedance and wall shear stress are maximum in the case of converging tapered arteries. To validate the results obtained using the present model, the results are compared with the experimental results of Back (1994). [ABSTRACT FROM AUTHOR]

The stability of buoyancy-driven parallel shear flow of a couple stress fluid confined between vertical plates is investigated by performing a classical linear stability analysis. The plates are maintained at constant but different temperatures. A modified Orr–Sommerfeld equation is derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c , critical wave number a c and critical wave speed c c are computed for wide ranges of couple stress parameter Λ c and the Prandtl number Pr . Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number, at which the transition from stationary to travelling-wave mode takes place, increases with increasing Λ c . The couple stress parameter shows destabilising effect on the convective flow against stationary mode, while it exhibits a dual behaviour if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state. [ABSTRACT FROM AUTHOR]

The onset of double diffusive convection in a couple stress fluid saturated porous layer with an internal heat source is studied using linear and weak nonlinear stability analyses. The linear analysis is based on the classical normal mode technique. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. In the present context, double diffusive convection is of particular interest in the study of extraction of metals from ores where a mushy layer is formed during solidification of a metallic alloy. Further, internal heating of the system is used as an external means to influence the transport process, thereby controlling the quality and structure of the resulting solid. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of governing parameters such as internal Rayleigh number, couple stress parameter, solute Rayleigh number, Darcy-Prandtl number, normalized porosity and Lewis number and their effects on the stability of a system are shown graphically. It is observed that the onset of both stationary and oscillatory convection is advanced by the internal Rayleigh number. The nonlinear analysis is based on the truncated representation of Fourier series which provides the quantification of heat and mass transfer. Heat transport is reinforced while mass transport is suppressed by the internal Rayleigh number. The transient behavior of Nusselt and Sherwood numbers is studied by solving numerically a fifth order Lorenz type system using Runge–Kutta method. Some known results are recovered as the particular cases of the present study. [ABSTRACT FROM AUTHOR]

Effect of Hall current on peristaltic transport of couple stress fluid in an inclined asymmetric channel is investigated. An incompressible fluid is conducting in the presence of inclined magnetic field. Problem formulation is developed through heat and mass transfer aspects. Soret and Dufour effects are present. Long wavelength and low Reynolds number approaches are adopted. Closed form expression for longitudinal velocity, pressure gradient, temperature and concentration are presented. Important results reflecting the influence of embedded parameters in the problems have been pointed out. Pumping and trapping phenomena are especially focused. [ABSTRACT FROM AUTHOR]

The heat and mass transfer characteristics of mixed convection flow of a chemically reacting couple stress fluid between vertical parallel plates in the presence of Dufour and Soret effects are studied. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are solved using Homotopy Analysis Method (HAM). Profiles of dimensionless velocity, temperature, and concentration are shown graphically for various values of Dufour number, Soret number, Couple stress parameter, and chemical reaction parameter. [ABSTRACT FROM AUTHOR]

This paper explores the mathematical model for couple stress fluid flow through an annular region. The above model is used for studying the blood flow between the clogged (stenotic) artery and the catheter. The asymmetric nature of the stenosis is considered. The closed form expressions for the physiological parameters such as impedance and shear stress at the wall are obtained. The effects of various geometric parameters and the parameters arising out of the fluid considered are discussed by considering the slip velocity and tapering angle. The study of the above model is very significant as it has direct applications in the treatment of cardiovascular diseases. [ABSTRACT FROM AUTHOR]

The steady flow of an incompressible couple stress fluid in a two dimensional uniform channel with stenosis under the influence of a magnetic field has been investigated. Assuming the stenosis to be mild, the flow equations have been analytically solved using the slip condition and expressions for the resistance to flow and wall shear stress have been derived. The effects of various parameters on these flow variables have been studied. It is found that the resistance to flow as well as the wall shear stress increase with the height of the stenosis and decrease with the couple stress and magnetic parameters. The effects of other parameters on resistance to flow and the wall shear stress have been considered. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical study of heat and flow of couple stress MHD fluids over permeable stretching/shrinking surfaces is undertaken in the present paper. Exact solutions for both flow and temperature fields under a boundary layer approach are targeted. In the absence of couple stress field the results completely collapse onto the special cases available in the literature. Obtained closed form solutions provide valuable knowledge for the velocity and temperature profiles as well as skin friction coefficient and Nusselt number. Dissimilar to the already known for a noncouple Newtonian fluid, double solutions exist over a stretching sheet, and triple solutions are present over a shrinking sheet, if couple stress effects are taken into consideration. [Copyright &y& Elsevier]

This article deals with a numerical investigation of fluid inertia effects on inclined slider bearings lubricated by couple stress fluids. Convective inertial forces are considered in the film fluid. A reduced version of the Navier-Stokes equations is thus derived. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing partial differential equations are discretized by finite differences based on boundary layer–type equations. The resulting algebraic equations are solved using a Gauss-Seidel method. Compared to the case of the non-inertia Newtonian lubricant, the couple effects of fluid inertia forces and non-Newtonian couple stresses provide a significant improvement in slider bearing load capacity. [ABSTRACT FROM AUTHOR]

Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical analysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping. [ABSTRACT FROM AUTHOR]

The paper presents analytical solution of squeeze film characteristics in wide parallel rectangular conjunctions with incompressible electrically conducting couple stress fluids subjected to a magnetic field. Analytical expressions are obtained by combined solution of modified Reynolds equation and Stokes micro-continuum for couple stress fluids with averaged inertia. Various cases of magneto-hydrodynamic, conducting and non-conducting fluid characteristics with and without convective inertial contributions are investigated. It is shown that, in general, couple stress fluids enhance the load carrying capacity of the contact and inhibit the incidence of thin films which can result in direct contact of surfaces. Convective inertia also significantly improves the load carrying capacity. However, with impulsive loading the response time of couple stress fluids deteriorates relative to Newtonian lubricants on account of their increased viscosity. An important conclusion of the study is that magneto-hydrodynamic couple stress fluids are best suited to applications with high relatively steady load applications. [ABSTRACT FROM PUBLISHER]

In this article couple stress fluid have been considered for the peristaltic flow of chyme in intestine. Problem under consideration have been formulated assuming that two non-periodic sinusoidal wave of different wavelength propagate with same speed c along the outer wall of the tube. Governing equations have been simplified under the assumptions of long wavelength and low Reynolds number approximation (such assumption are consistent that Re (Reynold number) is very small and long wavelength approximation also exists in the small intestine). Exact solutions have been evaluated for velocity and pressure rise. Physical behaviour of different parameter of couple stress fluid have been presented graphically for velocity, pressure rise, pressure gradient and frictional forces. The stream lines are also made against different parameters. [ABSTRACT FROM AUTHOR]

Motility is defined as the movement of cells by some form of self-propulsion. Some organisms motile by using long flagella that quickly rotate to propel them over various surfaces (in swarming and swimming mechanism), while few motile without the aid of flagella (in twitching, sliding and gliding mechanism). Among these modes, gliding motility is adopted by a rod-shaped organism famously known as gliding bacteria. It is hypothesized that in such type of motility, organism motile under their own power by secreting a layer of slime on the substrate. In this study, an active wall is considered as a substrate and a two-dimensional wavy sheet as an organism. Slip effects are also employed in the current work. The physical properties of the slime are governed by a suitable constitutive equation of couple stress model. A sixth order BVP is obtained by utilizing lubrication assumption. For an appropriate fixed pair of flow rate and organism speed the BVP is solved by MATLAB built-in function bvp-5c. This solution is utilized in the mechanical equilibrium conditions which are obviously not satisfied yet. To satisfy these conditions, the pair of flow rate and gliding speed is refined by a root finding algorithm (modified Newton-Raphson method). By employing this numerical scheme, various figures are shown to demonstrate the effect of several associated parameters on organism speed, flow rate, energy expended by the glider, streamlines and longitudinal velocity. It is observed from the graphical results that organism speed and energy consumption is directly proportional to the couple stress parameter and slip effects., Competing Interests: Declaration of competing interest There is no conflict of interest with anyone., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

The unsteady three-dimensional flow of couple stress fluid over a stretched surface is investigated. Analysis has been performed in the presence of mass transfer and chemical reaction. Nonlinear flow analysis is computed by a homotopic approach. Plots are presented and analyzed for the various parameters of interest. A comparative study with existing solutions in a limiting sense is made.

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically.

Consider the flow of an incompressible fluid between two parallel plates, initially induced by a constant pressure gradient. After steady state is attained, the pressure gradient is suddenly with drawn while the plates are impulsively started simultaneously. The arising flow is referred to as run up flow and the present paper aims at studying this flow in the context of a couple stress fluid. Using Laplace transform technique, the expression for velocity is obtained in Laplace transform domain which is later inverted to the space time domain using a numerical approach. The variation of velocity with respect to various flow parameters is presented through graphs.

Stokes’ first and second problems for an incompressible couple stress fluid are considered under isothermal conditions. The problems are solved through the use of Laplace transform technique. Inversion of the Laplace transform of the velocity component in each case is carried out using a standard numerical approach. Velocity profiles are plotted and studied for different times and different values of couple stress Reynolds number. The results are presented through graphs in each case.

Abstract: The effect of couple stresses on linear and weakly nonlinear stability of a triply diffusive fluid layer is investigated. Several departures not observed either in singly or doubly diffusive couple stress fluid layer have been identified while analyzing the linear stability of the problem. In contrast to the doubly diffusive couple stress fluid system, oscillatory convection is found to occur even if the diffusivity ratios are greater than unity. The presence of couple stress is to increase the threshold value of solute Rayleigh number beyond which oscillatory convection is preferred. Moreover, disconnected closed oscillatory neutral curves are identified for certain choices of physical parameters indicating the requirement of three critical values of Rayleigh number to specify the linear stability criteria instead of the usual single value. Besides, heart-shaped oscillatory neutral curves are also found to occur in some cases and the effect of couple stress parameter on some of these unusual behaviors is analyzed. A weakly nonlinear stability analysis is performed using modified perturbation technique and the stability of steady bifurcating non-trivial equilibrium solution is discussed. Heat and mass transfer are calculated in terms of Nusselt numbers and the influence of various physical parameters on the same is discussed in detail. [Copyright &y& Elsevier]

The effect of imposed time-periodic boundary temperature of small amplitude on electroconvection under AC electric field in dielectric couple stress liquids is investigated by making a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of sub-critical motions. The Venezian approach is adopted for obtaining eigen value of the problem. Three cases of oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in-phase, (b) asymmetric, corresponding to out-of-phase modulation and (c) only the lower wall is modulated. It is shown that the system is most stable when the boundary temperatures are modulated out-of-phase. [ABSTRACT FROM AUTHOR]

The current article discusses the influence of nanofluid on the peristaltic flow of an incompressible couple stress fluid in a two-dimensional uniform tube. The problem formulation is accessible in an upsurge structure of orientation for equations of momentum, energy, and concentrations. The continuity, linear momentum, energy, and nanoparticle equations lead to the mathematical development. HPM is used to get the solutions for velocity, temperature, nanoparticle, and pressure gradient. The solutions contain the Brownian motion number Nb, thermophoresis number Nt, local temperature Grashof number Br, and local nanoparticle Grashof number Gr. The physical features of different embedded parameters are analyzed and discussed physically in detail. [ABSTRACT FROM PUBLISHER]

Abstract: The flow visualization has been made using the heat function concept for the conjugate heat transfer effects on the transient free convective couple stress fluid flow over a vertical slender hollow circular cylinder with the inner surface kept at a constant temperature. The governing non-linear equations are solved numerically by using an unconditionally stable implicit method. Numerical results show that the deviations of flow variables of couple stress fluid from those of the Newtonian fluid turn out to be considerable. Boundary layer flow visualization indicates that the streamlines exist starting from the leading edge to the far downstream, while the heatlines terminate at a finite distance from the cylinder wall. It is noticed that the steady-state values of average skin-friction and heat transfer rate decrease as the conjugate-conduction parameter increases. [Copyright &y& Elsevier]

The present work investigates numerically the inherent irreversibility in a steady flow of a couple stress fluid through a vertical channel packed with saturated porous substances. The First and Second Laws of Thermodynamics are applied to analyze the problem. The nonlinear governing equations in Cartesian coordinates are obtained and solved numerically using shooting methods together with a Runge-Kutta Fehlberg integration scheme. The entropy generation number is computed by utilizing the velocity and temperature profiles. The effects of various physical parameters on the flow and heat transfer characteristics, as well as entropy generation rates and Bejan number, are investigated through graphs. [ABSTRACT FROM AUTHOR]

An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefficient and Nusselt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the non-isothermal Poiseuille flow between two heated parallel inclined plates using incompressible couple stress fluids. Reynold's model is used for temperature dependent viscosity. We have developed highly non-linear coupled ordinary differential equations from momentum and energy equations. The Perturbation technique is used to obtain the approximate analytical expressions for velocity and temperature distributions. Expressions for velocity field, temperature distribution, dynamic pressure, volume flow rate, average velocity and shear stress on the plates are obtained. The influence of various emerging parameters on the flow problem is discussed and presented graphically. [ABSTRACT FROM AUTHOR]

In this article, the influence of heat and mass transfer on peristaltic transport of a couple stress fluid in a uniform tube with slip conditions on the wall is studied. The problem can model the blood flow in living creatures. Under long wavelength approximation and zero Reynolds number, exact solutions for the axial velocity component, pressure gradient, and both temperature and concentration fields are derived. The pressure rise is computed numerically and explained graphically. Moreover, effects of various physical parameters of the problem on temperature distribution, concentration field, and trapping are studied and discussed graphically. [ABSTRACT FROM PUBLISHER]

This article presents an analysis of a long journal bearing with a double-layer porous lubricant film using couple stress and Newtonian fluids. The porous layer with infinite permeability analyzed in this study simulates the surface layer. The Brinkman model was utilized to model the flow in the porous region. The effects of couple stresses were analyzed based on Stokes microcontinuum theory. A double-layer porous lubricant film configuration, with a low-permeability porous layer on top of a high-permeability bearing adherent porous layer, improved the journal bearing performance characteristics. A surface porous layered lubricant film configuration increased the load-carrying capacity and reduced the coefficient of friction in a journal bearing. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to develop a new model of the interaction of a fluid film with a porous medium. The model takes into account the fluid inertia in both the lubricant and the porous matrix. Non-Newtonian behavior of the fluid, viscous effects in the porous matrix, and poroelasticity of the matrix are also considered. The main concerns are modeling and simulation of the squeeze film lubrication between two discs when one has a porous facing. The fluid flow is described using a reduced version of the Navier–Stokes equations in the fluid film, and the Darcy–Brinkman–Forchheimer generalized model in the porous matrix. The present study focuses on the combined effects of the non-Newtonian fluid lubricant and porous matrix deformation. The non-Newtonian behavior of the lubricant is described by the so-called couple stress model. The porous interface deformation is obtained using the thin elastic layer approach. The partial differential equations established in this study are discretized by finite differences. The resulting algebraic equations are solved using the Gauss–Seidel relaxation method. The numerical results of the present simulations show that all these effects have a significant influence on the porous squeeze film performance. [Copyright &y& Elsevier]

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number. [ABSTRACT FROM AUTHOR]

Abstract: The simultaneous effect of rotation and a vertical AC electric field on the onset of electrohydrodynamic instability in a horizontal couple stress dielectric fluid layer caused by the dielectrophoretic force due to the variation in the dielectric constant with temperature is investigated. The boundaries of the fluid layer are considered to be either free–free or rigid–rigid or lower rigid–upper free which are either isothermal or insulated to temperature perturbations. The resulting eigenvalue problem is solved exactly for free-free isothermal boundaries. It is observed that oscillatory convection is not a preferred mode of instability as far as the dielectric fluids are concerned and the necessary conditions for its occurrence are found to be independent of applied vertical AC electric field. For the other combinations of velocity and temperature boundary conditions, the problem is solved numerically using the Galerkin method. In contrast to the non-rotating case, it is shown that a rotating fluid layer becomes destabilizing in the presence of couple stress for all the boundary conditions considered. The effect of increasing AC electric Rayleigh number is to increase the transfer of heat more effectively and hastens the onset of convection, while rotation inhibits the onset of electrohydrodynamic instability. Although the rigid-rigid boundaries enhance the stability when compared to free-free boundaries up to certain values of Taylor number, the situation gets reversed at high Taylor number domain which in turn depends on the value of couple stress parameter and boundary conditions. Isothermal boundaries display more stabilizing effect than insulated ones. [Copyright &y& Elsevier]

The simultaneous effect of electric field and couple stress on the generalized dispersion of an unsteady convective diffusion in a poorly conducting fluid through a channel is investigated. A two dimensional flow has been considered and the resulting partial differential equation have been solved analytically using the mixture theory together with a regular perturbation technique. The solutions are computed and the results show that the solute is dispersed relative to a plane moving with the mean speed of couple stress poorly conducting fluid as well as the mean speed of coagulation of aerosols with a relative unsteady dispersion coefficient. The graphs for velocity, mean concentration and dispersion coefficient are presented for different values of electric number and couple stress parameter. They show that the effect of couple stress is predominate only for small values. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of boundary layer stagnation point flow and heat transfer of couple stress fluid containing nanoparticles and flowing over an exponentially stretching surface in a porous medium. The governing equations of the couple stress fluid model for velocity, temperature and nanoparticle profiles are given as part of the boundary layer approach. The nonlinear partial differential equations are simplified by using similar transformations. The analytical solutions of simplified equations are found using the homotopy analysis method. The convergence of the HAM solutions is discussed by plotting ħ-curves and also through homotopy padé approximation. The physical features of pertinent parameters are discussed through graphs. [ABSTRACT FROM AUTHOR]

Abstract: The Hall and Ion-slip effects on fully developed electrically conducting couple stress fluid flow between parallel disks has been considered. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using Homotopy Analysis Method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-Slip parameter, Prandtl number and couple stress fluid parameter on velocity and temperature are discussed and shown graphically. [Copyright &y& Elsevier]