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This paper carries out numerical simulation for pressure driven microscale gas flows in transition flow regime. The relaxation time of LBM model was modified with the application of near wall effective mean free path combined with a combination of Bounce-back and Specular Reflection (BSR) boundary condition. The results in this paper are more close to those of DSCM and IP-DSCM compared with the results obtained by other LBM models. The calculation results show that in transition regime, with the increase of Knudsen number, the dimensionless slip velocity at the wall significantly increases, but the maximum linear deviation of nonlinear pressure distribution gradually decreases.

This theoretical work explores the effect of the magnetic field on the liquid thin film flow of a non-Newtonian Powell–Eyring fluid. The thermocapillarity phenomenon in association with the effect of slip velocity is studied. In our research, we cannot ignore the important role of the numerical shooting method which employed to get the solution for our problem. This method helped us to sketch both the dimensionless velocity and the dimensionless temperature for several parameters. Furthermore, the authentication on the correctness and effectiveness for our method is checked by performing a comparison between this problem in the absence of some parameters and the previously published work, which confirms the robustness for the shooting method. Finally, an overview of the effect of the emerging parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number is done.

This research attempts to draw a fuller understanding of the magnetohydrodynamic flow of Williamson fluid owing to a continuously moving permeable surface. A detailed illustration of the importance of the effects of viscous dissipation and the variable fluid properties phenomena are also given. Meanwhile, this work has also revived the interest of the slip velocity phenomenon. The success is met after formulating the thorough equations which describe this model, thus it is no longer difficult to get into the numerical solution for this model via the shooting method. By analogy, this interesting subject also stimulates us to pursue further details which can be obtained from both the drag force or the skin-friction coefficient and the rate of heat transfer. Based on our apparent results, the presence of magnetic field, suction phenomena and slip velocity was the reason to reduce the surface velocity. Also, the same parameters can serve as a helpful guide for governing the rate of heat transfer.

A numerical solution for steady-state, incompressible, laminar Casson fluid flow and heat transfer in the combined region of a boundary layer is presented for the case of mixed convection and slip velocity. Before introducing the present technique of non-Newtonian Casson model, reviewing the literature has been carefully performed, an improved technique for this model is studied, which has not been previously reported. The presented analysis involves the harness of a magnetic field, viscous dissipation, internal heat generation/absorption and the slip velocity. Finite difference method (FDM) has been used to get an accurate and complete numerical solution. In this novel study, it is proved by means of a finite difference technique, that the velocity and the thermal field may be influenced with the presence of mixed convection phenomenon. The results show that both the fluid velocity and temperature may be predicted from the values of the controlling parameters. Finally, the graphical output reveals that the fluid velocity is diminished by strengthening both the Hartman number and the Casson parameter while the reverse characteristics are observed for the Grashof number.

In this paper, the influence of velocity slip and the Newtonian heating parameters on Williamson Nanofluid across a variable stretching sheet is studied. The basic fluid flow equations are turned into a system of coupled ordinary differential equations with appropriate conditions, which are solved numerically with the Keller-box approach. The outcomes show that, increasing Williamson parameter, due to the viscosity velocity of the fluid slowdown. As a result, it is noticed that the velocity slip parameter reduces Williamson Nanofluid velocity, while increasing shear stress, according to the results. Furthermore, it has been discovered that unlike velocity profiles, the slip influence is more pronounced on temperature and concentration profiles. Furthermore, the Newtonian heating parameter may be shown to have rising functions for velocity and dimensionless temperature. Newtonian heating has uses in the petroleum industry, heat exchangers, conjugate heat transfer around fins and solar radiation. It is discovered that the Joule heating parameter improves the thermal boundary layer thickness and slows down the velocity of the fluid, which aids in maintaining system temperature. Additionally, it has been found that the temperature profile exhibits a stronger slip effect compared with the velocity profile. To prepare toffee, chocolate and other delicacies as efficiently as possible, it is crucial to investigate the flow of Williamson fluids (such as drilling muds, clay coatings, various suspensions and some lubricating oils, thermoplastic melts, and a variety of colloids) in the incidence of heat transfer. The novelty of this paper is the effect of joule heating, Newtonian heating parameter and velocity slip on Williamson fluid velocity and temperature gradient. Furthermore, the heat and mass transfer rates are calculated for various parameters numerically and shown in tabular form.

In the existing investigation, impacts of slip and chemical reactions on mass and heat exchange on an incompressible and electrically conducting micropolar fluid past a porous wedge within the sight of Hall and ion slip are examined. By employing similarity conversion, the relevant highly nonlinear PDEs are reformed into a collection of nonlinear linked ODEs. The equations framed in this manner have been resolved by using the bvp5c, the in-build MATLAB. Examination of magneto-hydrodynamic micropolar fluid on stagnation point flow is significant due to its uses in the production of plastic substances, polymer extrusion, lubricants, etc. The influence of the magnetic field, heat generation, microrotation, along with Hall and ion slip on the liquid flow is analyzed. Examination with prior published research papers is performed and the outcomes are compared with each other. Numerical simulations for shear stress coefficients, Sherwood and Nusselt numbers are provided in tabular form, and in addition, the variations in axial and microrotation velocities, temperature and solutal profiles are evaluated visually for various parameters in detail. The ion slip and slip velocity both slow down the shear rate, whereas the elevated values of the Hall and magnetic parameters show an opposite trend. The profile shows thinning of the bounding surface and offers its greatest magnitude in the case of a Newtonian liquid.

This paper presents a theoretical analysis of the effects of a magnetic field, couple stress fluid, and slip velocity on squeeze film lubrication between a sphere and a flat plate. The modified Reynolds equation is derived using Stokes micro continuum theory of couple stress fluids. The nondimensional governing equations of the flow model are solved analytically for pressure, load-carrying capacity and squeezing time. The results are graphically presented and analyzed for various parameters. The study shows that the couple stress parameter and magnetic field significantly enhance the film pressure, load-carrying capacity, and squeeze film time compared to the Newtonian and nonmagnetic cases. Also from the results, it is observed that the squeeze film properties can be significantly reduced by the effect of the slip parameter.

The transfer of the liquid from groove to plate is significantly affected by the breakup process of liquid bridge, which is the core problem of gravure. In this paper, many-body dissipative particle dynamics method (MDPD) is used to simulate the behaviors of the stretching liquid cylinder between the plate and the groove, and the influence of surface wettability, stretching velocity and groove structure on the liquid cylinder rupture and the transfer rate of liquid are studied. The results show that both of the slipping velocity of the contact line on the plate and the thinning velocity of the liquid cylinder determine the breakup state of the liquid bridges and the liquid transfer rate from the groove to the plate. In the cases with the same surface wettability, at high hydrophilicity surface, the transfer rate increases firstly and then decreases with the increase of the stretching velocity. In the cases with different surface wettability of the plate and the groove, reducing the stretching velocity and the inclination angle of the groove are helpful to pull the liquid out of the groove and increase the transfer rate, and it could also be achieved by increasing the wettability of the plate and decreasing the wettability of the groove. This study provides some new insights into the effects of surface wettability, stretching velocity and groove structure on the dynamics of breakup process and liquid transfer in stretching.

This study investigates the interaction between fluid dynamics and electromagnetic fields, a complex problem that has not been extensively studied. The Lorentz force, which arises due to the interaction between magnetic fields and currents in a fluid is considered in this study. This research investigates the effects of a magnetic field, couple stress, and slip velocity on the behavior of a squeeze film (SF) formed between a porous flat and spherical plate. The Stokes equation for couple stress fluids is used to produce a generalized version of the Reynolds equation, which is then used to determine the film pressure. Also, this study considers the impact of a constant magnetic field orthogonal to the plate. The fluid in the porous region is governed by modified Darcy law. The effect of a uniform magnetic field perpendicular to the plate is considered. The bearing characteristics pressure, squeeze film time, and load-carrying capacity are graphically presented. The results revealed that the load-carrying capacity, pressure, and squeeze film time are reduced with a rise in slip and porousness parameters. The slip parameter decreases the values of film pressure, squeeze time, and load-carrying capacity as related to the no-slip case.

In this research, the combined effect of magnetohydrodynamics (MHD) and slip velocity on squeeze film lubrication of long cylinders and infinite plates with couple stress fluid has been studied. Combining the Stokes couple stress theory and the Lorentz force theory yields analytical solutions for the modified Reynolds equation. Using the Reynolds equation, the mathematical expressions for squeeze film pressure, load-carrying capacity and squeeze film time are obtained. The pressure, load carrying capacity and squeeze film time increase with the combined effect of MHD, couple stress fluids and slip velocity.

A mathematical model is developed in this paper for studying blood flow through a stenosed arterial segment by taking into account the slip velocity at the wall of the artery. Consideration of the non-Newtonian character of blood is made, where a constitutive relation of blood is described by the Herschel–Bulkley equation. The effect of slip at the arterial wall in the presence of mild, moderate, and severe stenosis growth at the lumen of an artery is investigated. Analytical expressions for skin friction, flow resistance, and the flow rate are derived by using the model. The derived expressions are computed numerically by considering an illustrative example. The study provides an insight into the effects of slip velocity on the volumetric flow rate of blood, flow resistance, and skin friction.

The present investigation deals with the application of Adomian decomposition method (ADM) to blood flow through an asymmetric non-uniform channel induced by peristaltic wave in the presence of magnetic field and the velocity slip at the wall. The ADM is applied with an aim to avoid any simplifications and restrictions, which changes non-linearity of the problem as well as to provide analytical solution. The blood flowing through the vessel is assumed to be Newtonian and incompressible with constant viscosity. The analytical expressions for the axial velocity component, streamlines and wall shear stress are presented. The numerical results of these physical quantities are obtained for different values of the Reynolds number, wave number and Hartmann number. The results obtained for different values of the parameters involved in the problem under consideration show that the flow is appreciably influenced by the presence of slip velocity as well as magnetic field. From this study, we conclude that the assumption of long wavelength and low Reynolds number overestimates the flow characteristics even for a small change in the parameters.

A new multidimensional drift flux mixture model was developed to simulate gas–liquid droplet two-phase flows. The new drift flux model was modified by considering the centrifugal force on the liquid-droplets. Therefore the traditional 1D drift flux model was upgraded to multidimension, 2D and 3D. The slip velocities between the continual phase (gas) and the dispersed phase (liquid droplets) were able to calculate through the multidimensional diffusion flux velocities based on the new modified drift flux model. Through the numerical simulations comparing with the experiments and the simulations of other models on the backward-facing step and the water mist spray two-phase flows, the new model was validated.

A conventional “recipe” for strong ground motion prediction has been applied to the seismic fault (deep fault; located within seismogenic layer). In order to perform assessments of strong ground motions and permanent displacements at sites very close to the fault trace, we proposed the method of modeling that takes the entire ruptured fault from the ground surface to the seismic fault into account. Our approach was validated by the simulation of observed records obtained at stations very close to the fault trace of the mainshock of the 2016 Kumamoto Japan, earthquake (M_w7.1). Also, through the ground motion assessment performed for a hypothetical strike-slip fault with a 90${}^{\circ }$ dip angle, we found that adding the shallow fault had virtually no effect on acceleration time history, but it had a clear effect on the fault-parallel component of velocity and displacement time histories in the area close to the fault trace.

A theoretical investigation concerning the influence of slip velocity on the flow of blood through an artery having its wall permeable has been carried out. Here blood is treated as a homogeneous Newtonian fluid. The flow is characterized by three parameters: β the ratio of radius to length of the arterial segment, Re the characteristic Reynolds number associated with the pressure outside the arterial segment and ϵ the filtration coefficient. The problem has been solved by the use of a perturbation technique. ϵ is considered to be very small, ensuring the validity of the perturbation method. The computed numerical results are presented graphically to depict the variations in velocity, volumetric flow rate, wall shear stress and flow resistance.

The slip velocity of the flow at the porous-fluid interface is studied using a 2D porous region, modeled as an array of circular cylinders in square and hexagonal arrangements to resemble the structure of real porous media. The Navier-Stokes and continuity equations are solved using a hybrid FEM-FVM solver by applying appropriate macroscopic boundary conditions. The existence of a slip velocity at the porous-fluid interface is demonstrated and it is observed that the slip velocity increases with increase in porosity and flow Reynolds number.