Secondary Shear Stress Research Articles

Carina: A major determinant in the pathophysiology and treatment of coronary bifurcation lesions.

Over the last decade, several in vivo and computational investigations have significantly advanced our understanding of the pathophysiology of coronary bifurcations, contributing to the enhancement of their percutaneous revascularization. The carina of the coronary bifurcations plays a substantial role in generating their main hemodynamic features, including distinctive flow patterns with secondary flows and specific shear stress patterns. These factors play a pivotal role in determining the susceptibility, development, and progression of atherosclerosis. The underlying pathophysiological mechanisms of atherosclerosis in coronary bifurcations are complex and multifactorial. Understanding these mechanisms is fundamental to comprehending lesions at the bifurcation level and informing future treatment strategies. This review aims to present the currently available data regarding the pathophysiological and prognostic role of the carina in coronary bifurcations, offering an interpretation of these findings from the perspective of interventional cardiologists, providing valuable insights for their clinical practice.

MHD gyrating stream of non‐Newtonian modified hybrid nanofluid past a vertical plate with ramped motion, Newtonian heating and Hall currents

AbstractIn this modern era, the thermal efficiency of susceptible systems is a major concern in many scientific and technical operations. Hybridized nanomaterials have innovative behaviours, which make them significant in various applications. Hybrid nanofluids (HNFs) are primarily utilized to address heat transfer concerns efficiently. Keeping view of these facts, the main motive of the current investigation is to address the critical role of magnetohydrodynamics with Hall currents on a time‐dependent gyrating stream of non‐Newtonian modified hybrid nanofluid (MHNF) with Casson fluid model past a vertically fluctuating plate with ramped motion, and Newtonian heating in a porous environment. As a counter‐example to Casson fluid, sodium alginate (SA) is considered. Graphite oxide, alumina and copper oxide nanoparticles are dispersed in the host fluid (SA) to constitute a MHNF. Thermal transportation is analysed under the physical consequence of thermal radiation. Darcy's law is utilized to counterfeit the porous medium's resistance in the flow field. The modelled problem is initially expressed in terms of physical conditions and partial differential equations (PDEs). The resulting dimensionless PDEs are solved analytically by dint of the Laplace transform technique. The physical consequences of significant physical and geometrical parameters on the profiles of associated flow quantities of industrial concern are visualized and explained in‐deep via several graphs and tables. Our simulation reveals that the fluid motion is noteworthy amended due to the existence of Coriolis and Lorentz forces with Hall currents. Hall currents and Darcian drag force have a dominating attribute on the primary shear stress, while they expose a positive response to the secondary shear stress. Comparative analysis suggests that the heat migration rate at the plate is superior for MHNF due to higher thermal conductivity than usual HNF. The ongoing research is relevant to hybrid nanolubricants in thermal management systems, dynamics of nanopolymers, industrial procedures and so forth.

Numerical study on flow pattern in meandering channels: The effect of hydraulic conditions and meander geometry

Natural rivers are one of the main sources of water and energy for humans. The design and management of exploitation of natural rivers systems will require a complete understanding of flow and sediment transport mechanics. Meanders are one of the most common types of rivers in nature, which have a very complex flow. The three-dimensional (3D) and complex characteristics of flow in meanderings bring up the necessity of investigating the flow pattern in this channel with 3D numerical models. This study aimed to investigate the flow pattern and predict the erosion and sedimentation site in the meandering. Also, the effect of the Froude number (Fr), the ratio of width-to-depth ([Formula: see text]/[Formula: see text] and meander angle parameters on the flow field are investigated. In this study, the turbulent flow pattern in a sine-generated channel and the angle of 50∘ with a rectangular section with width = 40 cm and the rigid bed is studied using the 3D mathematical model SSIIM1.1. The primary and secondary flow patterns were studied using the turbulence models of [Formula: see text]-[Formula: see text] and SST [Formula: see text]-[Formula: see text]. Comparison of numerical models and experimental results showed that the flow pattern is predicted well by both turbulence models of turbulence. But in some cases, the SST [Formula: see text]-[Formula: see text] model has provided closer results to the experimental results. The results show that the shear stress pattern depends on the changes in the Fr. But, the secondary flow pattern does not change much by changing the Fr. Also, changes in the [Formula: see text]/[Formula: see text] ratio affect the secondary flow pattern and shear stress pattern, so that for [Formula: see text]/[Formula: see text], a small rotary cell is made in addition to the main rotary cell near the outer coast. The results also show that the flow pattern and shear stress depend on the channel angle.

Prediction of Mechanical Properties of Thin-Walled Bar with Open Cross-Section under Restrained Torsion

Thin-walled bars with an open cross-section are widely used in mechanical structures where weight and size control are particularly required. Thus, this paper attempts to propose a theoretical model for predicting the mechanical properties of a thin-walled bar with an open cross-section under restrained torsion. Firstly, a theoretical model with predictions of shear stress, buckling normal stress, and secondary shear stress of the thin-walled bar with open cross-section under the condition of restrained torsion was developed based on torsion theory. Then, physical test and finite element modeling data were employed to validate the theoretical predictions. The results indicate that the theoretical predictions show good agreements with data of finite element modeling and experiments. Therefore, the proposed theoretical model could be used for the prediction of the mechanical response of a thin-walled bar with an open annular section under restrained torsion.

Secondary Currents with Scour Hole at Grade Control Structures

Most studies on local scouring at grade control structures have principally focused on the analysis of the primary flow field, predicting the equilibrium scour depth. Despite the numerous studies on scouring processes, secondary currents were not often considered. Based on comprehensive measurements of flow velocities in clear water scours downstream of a grade control structure in a channel with non-cohesive sediments, in this study, we attempted to investigate the generation and turbulence properties of secondary currents across a scour hole at equilibrium condition. The flow velocity distributions through the cross-sectional planes at the downstream location of the maximum equilibrium scour depth clearly show the development of secondary current cells. The secondary currents form a sort of helical-like motion, occurring in both halves of the cross-section in an axisymmetric fashion. A detailed analysis of the turbulence intensities and Reynolds shear stresses was carried out and compared with previous studies. The results highlight considerable spatial heterogeneities of flow turbulence. The anisotropy term of normal stresses dominates the secondary shear stress, giving the impression of its crucial role in generating secondary flow motion across the scour hole. The anisotropy term shows maximum values near both the scour mouth and the scour bed, caused, respectively, by the grade control structure and the sediment ridge formation, which play fundamental roles in maintaining and enhancing the secondary flow motion.

Homotopy Simulation of Dissipative Micropolar Flow and Heat Transfer from a Two-Dimensional Body with Heat Sink Effect

Non-Newtonian flow from a wedge constitutes a fundamental problem in chemical<br /> engineering systems and is relevant to processing of polymers, coating systems, etc. Motivated by such applications, the homotopy analysis method (HAM) was employed to<br /> obtain semi-analytical solutions for thermal convection boundary layer flow of incompressible micropolar fluid from a two-dimensional body (wedge). Viscous dissipation<br /> and heat sink effects were included. The non-dimensional boundary value problem<br /> emerges as a system of nonlinear coupled ordinary differential equations, by virtue of<br /> suitable coordinate transformations. The so-called Falkner-Skan flow cases are elaborated. Validation of the HAM solutions was achieved with earlier simpler models, as well as with a Nakamura finite difference method for the general model. The micropolar model employed simulates certain polymeric solutions quite accurately, and features rotary motions of micro-elements. Primary and secondary shear stress, wall couple stress, Nusselt number, microrotation velocity, and temperature were computed for the effect of<br /> vortex viscosity parameter (micropolar rheological), Eckert number (viscous dissipation),<br /> Falkner-Skan (pressure gradient) parameter, micro-inertia density, and heat sink parameter. The special cases of Blasius and stagnation flow were also addressed. It was observed from the study that the temperature and thermal boundary layer thickness are both suppressed with increasing wedge parameter and wall heat sink effect, which is beneficial to temperature regulation in polymer coating dynamics. Further, strong reverse spin was generated in the microrotation with increasing vortex viscosity, which resulted in<br /> increase in angular momentum boundary layer thickness. Also, both primary and secondary skin friction components were reduced with increasing wedge parameter. Nusselt number was also enhanced substantially with greater wedge parameter.

The study of central cracking mechanism and criterion in cross wedge rolling

Cross wedge rolling (CWR) is an innovative metal forming process to manufacture axisymmetric stepped shafts used in the transport industry. Central cracking, also called the Mannesmann Effect, consistently occurs in the central region of the CWR workpiece. This results in reduced product quality and increased costs due to rejected and failed parts. However, the understanding of central cracking mechanism and criterion is limited due to the complex stress states in CWR and the experimental limitations. A large number of CWR tests and different die geometries are required in the identification of the potential mechanistic factors such as the axial tensile stress, secondary tensile stress, shear stress and cyclic loading. Also, there is as yet no efficient method of determining the material constants associated with the central cracking fracture criteria. These problems are addressed in the present study. A physical model was built to reproduce the industrial CWR process. A newly designed model material (plasticine/flour composite) was used to mimic the material flows and internal fracture behaviours found in commercial CWR workpieces. This allowed a variety of die shapes to be rapidly and cost-effectively 3D printed, thereby enabling specific stress states to be achieved within the workpiece. Via experimental observations and the corresponding finite element modelling under different die geometries, the maximum shear stress was identified as the dominant factor for central cracking. The fracture criterion involving the maximum shear stress was quantitatively verified to be accurate and robust in predicting central cracking moments and locations. A novel approach using simplified die geometries to determine the associated material constants was proposed and validated. The high accuracy and cost/time efficiency of this new approach will be a significant benefit to fundamental research and also in industrial applications.

A priori tests of eddy viscosity models in square duct flow

We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number {text {Re}}_tau =1055. We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components a_{ij} responsible for turbulent secondary flows, namely the normal stress a_{22} and the secondary shear stress a_{23}. A priori tests on constitutive relations for a_{ij} are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of a_{ij}. We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to DNS data {widetilde{C}}_{ij}, which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress a_{12} ({widetilde{C}}_{12}>0.99), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress ({widetilde{C}}_{22}=0.911, {widetilde{C}}_{23}=0.743). Unfortunately, RANS models rely on additional assumptions and a priori analysis carried out on popular models, including k–varepsilon and v^2–f, reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the v^2–f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models.

Coupling of strike-slip faulting and lacustrine basin evolution: sequence stratigraphy, structure, and sedimentation in the North Yellow Sea Basin (West Bay Basin offshore North Korea), eastern China

The North Yellow Sea Basin in offshore areas of eastern China provides a unique opportunity to document the interaction between the paleo-Eurasian and circum-Pacific tectonic domains and the coupled relationship between Tanlu Fault strike-slip activity, intrabasinal tectonics and sedimentation. This study combines well data, three-dimensional (3-D), and two-dimensional (2-D) seismic data to make regional tectonics interpretations, and delineate the sequence stratigraphy, geological structure and sedimentary history of the basin's Eastern depression, particularly focusing on the influence of Tanlu Fault strike-slip activity on basin evolution. The Eastern depression data record the development of five second-order stratigraphic sequences, both the Mesozoic and the Cenozoic fault systems with basement F1, F2 and F3 faults, and the deposition of various deltaic, fan delta, lacustrine, and subaqueous fan facies associations. The F1 and F3 faults controlled the NW- and NE-trending secondary faults and associated Mesozoic sedimentation within the depression, while the F1 and F2 faults jointly controlled the development of NE- and near-E-W-trending secondary faults and associated Cenozoic sedimentation. The results indicate that the plate movements and Tanlu episodic, strike-slip faulting generated a left-lateral stress field in the Early Cretaceous, that switched to a right-lateral stress field during the middle Eocene to Oligocene. This transformation produced secondary shear stress fields in the North Yellow Sea Basin and generated NE-trending rifting superimposed on the previous NW-trending rift generation, and controlled the related structural geology and sedimentation in the Eastern depression of the basin. This proposed explanation of a tectonic regime transformation model, coupled with Tanlu strike-slip movements, could also provide new insights into the differences in gaps that occur in the stratigraphic record for the North Yellow Sea Basin and adjacent areas in eastern China.

Computation of Non-isothermal Thermo-convective Micropolar Fluid Dynamics in a Hall MHD Generator System with Non-linear Distending Wall

A theoretical model for steady non-isothermal convective heat transfer in non-Newtonian magnetized micropolar gas flow from a non-linear stretching/contracting wall in the presence of strong magnetic field is presented, as a simulation of an MHD (magnetohydrodynamic) Hall energy generator. Subsonic flow is considered, and compressibility effects neglected. The strength of the magnetic field which is applied in the general case obliquely to the wall is sufficient to invoke the collective effects of Hall current and Ohmic heating (Joule dissipation). Viscous heating is also included in the energy balance. Deploying similarity transformations, the governing equations are normalized into nonlinear ordinary differential equations with associated boundary conditions. The non-linear boundary value problem thus posed is then solved computationally with Nachtsheim–Swigert iteration technique along with the fourth-fifth order Runge–Kutta integration method. Verification of solutions is obtained with the semi-analytical Homotopy analysis method. Further validation is conducted with the semi-numerical Adomian decomposition method. In both cases excellent agreement is obtained with the Runge–Kutta shooting quadrature solutions. Additional validation is conducted with earlier Newtonian studies in the absence of micropolar, Hall current and dissipation effects. The influence of local Grashof number, local Hartmann number, Eringen microrotational parameter, Eringen coupling vortex parameter, Prandtl number and Eckert number on non-dimensional velocity components (primary, secondary and angular) and temperature within the boundary layer are graphically illustrated and interpreted at length. Furthermore, the effects of the thermophysical (e.g. non-isothermal power law index), electromagnetic parameters (e.g. Hall parameter) and geometric parameter (wall extension/contraction parameter) on the skin-friction coefficient (i.e. primary and secondary shear stress and wall couple stress) and surface heat transfer rate (Nusselt number) are evaluated. The study is relevant to near wall transport phenomena in novel MHD Hall power generators.

Unsteady nonlinear magnetohydrodynamic micropolar transport phenomena with Hall and Ion-slip current effects: Numerical study

Unsteady viscous two-dimensional magnetohydrodynamic micropolar flow, heat and mass transfer from an infinite vertical surface with Hall and Ion-slip currents is investigated theoretically and numerically. The simulation presented is motivated by electro-conductive polymer (ECP) materials processing in which multiple electromagnetic effects arise. The primitive boundary layer conservation equations are transformed into a non-similar system of coupled non-dimensional momentum, angular momentum, energy and concentration equations, with appropriate boundary conditions. The resulting two-point boundary value problem is solved numerically by an exceptionally stable and well-tested implicit finite difference technique. A stability analysis is included for restrictions of the implicit finite difference method (FDM) employed. Validation with a Galerkin finite element method (FEM) technique is included. The influence of various parameters is presented graphically on primary and secondary shear stress, Nusselt number, Sherwood number and wall couple stress. Secondary (cross flow) shear stress is strongly enhanced with greater magnetic parameter (Hartmann number) and micropolar wall couple stress is also weakly enhanced for small time values with Hartmann number. Increasing thermo-diffusive Soret number suppresses both Nusselt and Sherwood numbers whereas it elevates both primary and secondary shear stress and at larger time values also increases the couple stress. Secondary shear stress is strongly boosted with Hall parameter. Ion slip effect induces a weak modification in primary and secondary shear stress distributions. The present study is relevant to electroconductive non-Newtonian (magnetic polymer) materials processing systems.

Unsteady Flow of a Nanofluid over a Sphere with Nonlinear Boussinesq Approximation

A theoretical study is presented for transient mixed convection flow of a nanofluid in the forward stagnation region of a heated sphere that is rotating with time-dependent angular velocity, taking nonlinear Boussinesq approximation into account. The nanofluid is treated as a two-component mixture (i.e., nanoparticles distributed homogenously in a base fluid). The effects of the Brownian motion and thermophoresis are included for the nanofluid flow. The first and second laws of thermodynamics are employed to study thermophysics as well as heat and mass transfer phenomena. The governing equations are transformed into a system of dimensionless, nonlinear, coupled, differential equations using suitable transformation, which are then solved numerically by applying the Keller box method. The accuracy of the obtained numerical results is validated via comparison to previously published results for special cases. Primary shear stress is boosted with increasing mixed convection parameter and Brownian motion effect, whereas secondary shear stress is depressed. Temperatures are suppressed with increasing nonlinear temperature parameter, whereas nanoparticle concentrations are elevated.

Influence of Hall Current on Hydromagnetic Flow Through a Uniform Channel Bounded by Porous Media of Finite Thickness

A steady two dimensional hydromagnetic flow through a uniform channel covered by porous media having finite thickness is considered. A uniform magnetic field is applied in the perpendicular direction of the motion of the fluid. Since, it is assumed that the thickness of the porous media is smaller than the width of the flow channel, analytical solutions are obtained by using Beavers-Joseph-Rudraiah slip condition. Expressions for primary and secondary velocities and the shear stress are obtained. These expressions have been computed for different values of the Hartmann number, Hall parameter, Darcy velocity, the porous parameter and width of the porous medium. The effects of these parameters on both primary and secondary velocities and shear stress have been investigated.

HALL CURRENT EFFECTS ON HYDROMAGNETIC FLOW THROUGH UNIFORM CHANNEL BOUNDED BY POROUS MEDIA

The steady, laminar, viscous, electrically conducting hydromagnetic flow through a channel of uniform width covered by porous media of infinite thickness is studied with Hall effects. The fluid is acted upon by the constant pressure gradient and a uniform magnetic field is applied in the direction perpendicular to the motion of the fluid. Closed form solution is obtained for the governing equations using Beavers–Joseph slip condition. Profiles of primary and secondary velocities and shear stress have been computed for different values of porous parameter, Darcy velocity, slip parameter, Hartmann number, and Hall parameter. It is observed that the porous parameter, slip parameter, and Hartmann number produce a retarding effect on both the primary and secondary velocities. The Hall parameter has an accelerating effect on both the velocities. It is noticed that the components of shear stress decreased in magnitude when the Hartmann number increases. It is also observed that the value of shear stress due to primary and secondary flows increases in magnitude when the Hall parameter and slip parameter increase.

Effects of finite-size neutrally buoyant particles on the turbulent flows in a square duct

Interface-resolved direct numerical simulations of the particle-laden turbulent flows in a square duct are performed with a direct-forcing fictitious domain method. The effects of the finite-size particles on the mean and root-mean-square (RMS) velocities are investigated at the friction Reynolds number of 150 (based on the friction velocity and half duct width) and the particle volume fractions ranging from 0.78% to 7.07%. Our results show that the mean secondary flow is enhanced and its circulation center shifts closer to the center of the duct cross section when the particles are added. The reason for the particle effect on the mean secondary flow is analyzed by examining the terms in the mean streamwise vorticity equation. It is observed that the particles enhance the gradients of the secondary Reynolds normal stress difference and shear stress in the near-wall region near the corners, which we think is mainly responsible for the enhancement in the mean secondary flow. Under a prescribed driving pressure gradient, the presence of particles attenuates the bulk velocity and the turbulent intensity. All particle-induced effects are intensified with increasing particle volume fraction and decreasing particle size, if other parameters are fixed. In addition, the particles accumulate preferentially in the near-corner region. The effects of the type of the collision model (i.e., if friction and damping are included or not) on the results are found significant, but not so significant to bring about qualitatively different results.

The effect of boundary layer fluctuations on the streamwise vortex structure in simulated plane turbulent mixing layers

This paper details the influence of the magnitude of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. The fluctuations are physically-correlated, and produced by an inflow generation technique. The imposed high-speed side boundary layer fluctuation magnitude is varied from a low-level, up to a magnitude sufficiently high that the boundary layer can be considered, in a mean sense, as nominally laminar. Cross-plane flow visualisation shows that each simulation contains streamwise vortices in the laminar and turbulent regions of the mixing layer. Statistical analysis of the secondary shear stress reveals that mixing layers originating from boundary layers with low-level fluctuations contain a spatially stationary streamwise structure. Increasing the high-speed side boundary layer fluctuation magnitude leads to a weakening of this stationary streamwise structure, or its removal from the flow entirely. The mixing layer growth rate reduces with increasing initial fluctuation level. These findings are discussed in terms of the available experimental data on mixing layers, and recommendations for both future experimental and numerical research into the mixing layer are made.

Numerical modeling of flow field in compound channels with non-prismatic floodplains

In this paper an attempt has been made to study flow field in compound channels with non-prismatic floodplains. A three dimensional computational fluid dynamic (CFD) model is used to calculate the velocity distribution, secondary flow circulation and boundary shear stress in non-prismatic compound channels with two different convergence angles of 3.81o and 11.31o. The ANSYS-CFX software and k-e turbulence model is used to solve Reynolds Averaged Navier-Stokes (RANS) equations. The results of the numerical modeling were then compared to the experimental data on non-prismatic compound channels with the same convergence angles. The study shows that, more or less, the k-e turbulence model is capable of predicting the velocity and boundary shear stress distributions along the flume fairly well, especially for convergence angle of 3.81o. Also by increasing relative depth, discrepancy between numerical and experimental data decreases. The results of modeling show that the k-eturbulence model is able to predict secondary flow circulations in the main channel, created by the mass exchange between the floodplains and the main channel.

On streamwise vortices in Large Eddy Simulations of initially laminar plane mixing layers

This paper details the influence of the nature of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. A simulation with imposed white-noise random fluctuations, commonly used in numerical simulations, produces mean-flow statistics that agree well with reference experimental data. Whilst flow visualisation images show evidence for streamwise vorticity in this simulation, quantitative statistics do not reveal the presence of statistically stationary streamwise vortices. A further simulation that uses physically-correlated inflow fluctuations also produces good mean-flow statistical agreement with reference data. From secondary shear stress contours it can be inferred that this simulation does, however, predict the presence of statistically stationary streamwise vortices. The properties of the streamwise vortices are in good agreement with experimental data. The data presented here indicate that, even for initially laminar conditions, plane mixing layer simulations require accurate physically correlated inflow conditions in order to reproduce the flow features found experimentally.

Hydrodynamic computational evaluation in solar tubular photobioreactors bends with different cross section

In this article, the hydrodynamic behavior of a single-phase flow in various solar collectors with different cross sections (circular, octagonal, hexagonal and square), with same hydraulic diameter and longitudinal profile was analyzed. Secondary flow, pressure drop and shear stress were evaluated, because the photosynthetic efficiency and microalgae endurance depend on these properties. These parameters were reviewed at six different culture inlet rates in the collector (from 0,25 to 0,5m/s), emphasizing in the bends regions. A higher speed and agitation was present in the square solar collector, contrary to what happened to the circular one. Despite this, the circular solar collector remains the best option for the industrial implementation phase. However, the shear stress generated in the culture -as it passes through the 180° bend of the solar collector- affects the microalgae growth, as stated in the literature.
 

Steady hydromagnetic Couette flow in a rotating system with nonconducting walls

Steady hydromagnetic Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system with non-conducting walls is studied. Exact solution of the governing equations is obtained in closed form. Expressions for the shear stress at the lower and upper plates due to primary and secondary flows and mass flow rates in primary and secondary flow directions are also derived. Asymptotic behavior of the solution for fluid velocity and induced magnetic field is analyzed for small and large values of rotation parameter K2 and magnetic parameter M2 to gain further insight into the flow pattern. Heat transfer characteristics of the flow are considered taking viscous and Joule dissipations into account. The numerical solution of energy equation and numerical values of rate of heat transfer at both plates are obtained with the help of MATLAB software. The numerical values of fluid velocity, induced magnetic field and fluid temperature are depicted graphically versus channel width variable c for various values of M2 and K2 while numerical values of primary and secondary shear stress at the lower and upper plates, mass flow rates in primary and secondary flow directions and rate of heat transfer at the lower and upper plates are presented in tabular form for various values of K2 and M2.