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The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.

Complicated motion of vortex is frequently observed in the wake of islands. These kinds of swirling fluid cause the trap of sediments or pollutants, subsequently inducing the dead zone, odor or poor water quality. Therefore, the understanding of flow past a circular cylinder is significant in predicting water quality and positioning the immersed structures. This study aims to investigate the flow properties around a structure using Navier-slip boundary conditions.

Boundary conditions are a major factor affecting the flow pattern because the magnitude of flow detachment on a surface can redistribute the tangential stress on the wall. Therefore, the authors performed an analysis of laminar flow passing through a circular structure to investigate the effect of boundary conditions on the flow pattern.

The authors examined the relationship between the partial-slip boundary conditions and the flow behavior at low Reynolds number past a circular cylinder considering velocity and vorticity distributions behind the cylinder, lift coefficient and Strouhal number. The amplitude of lift coefficient by the partial slip condition had relatively small value compared with that of no-slip condition, as the wall shear stress acting on the cylinder became smaller by the velocity along the cylinder surface. The frequency of the asymmetrical vortex formation with partial slip velocity was increased compared with no-slip case due to the intrinsic inertial effect of Navier-slip condition.

The ability to engineer slip could have dramatic influences on flow, as the viscous dominated motion can lead to large pressure drops and large axial dispersion. By the slip length control, no-slip, partial-slip and free-slip boundary conditions are tunable, and the velocity distributions at the wall, vortex formation and wake pattern including the amplitude of lift coefficient and frequency were significantly affected by slip length parameter.

This paper aims to better understand the dynamic characteristics of an aerostatic slider caused by a gas film, and the impact of a gas film slip on the load capacity, stiffness and dynamic stiffness of the guideway is studied.

In theory, the Navier velocity slip model is introduced for fluid continuous flow equation to calculate the flow state in the micro-state; in experimental techniques, the stiffness experiment of the guideway by digital inductance meter is performed under different loadings, which are used to inspect the simulation results.

The maximum value of bearing stiffness in the condition of considering that the gas slip is larger than that of not considering the gas slip, and the gas film clearance of maximum bearing stiffness in the condition of considering the gas slip is less than that of not considering the gas slip. This is verified by the measurement of the stiffness of the guideway.

This paper mostly studies the influence of the gas slip effects on the performance of the aerostatic guideway, which will make a certain contribution to the guideway stability and the machining precision of the machine tool.

This paper aims to explore the mechanism of the slip phenomenon at macro/micro scales, and analyze the effect of slip on fluid flow and heat transfer, to reduce drag and enhance heat transfer.

The improved tangential momentum accommodation coefficient scheme incorporated with Navier’s slip model is introduced to the discrete unified gas kinetic scheme as a slip boundary condition. Numerical tests are simulated using the D2Q9 model with a code written in C++.

Velocity contour with slip at high Re is similar to that without slip at low Re. For flow around a square cylinder, the drag is reduced effectively and the vortex shedding frequency is reduced. For flow around a delta wing, drag is reduced and lift is increased significantly. For Cu/water nanofluid in a channel with surface mounted blocks, drag can be reduced greatly by slip and the highest value of drag reduction (DR) (67.63%) can be obtained. The highest value of the increase in averaged Nu (11.78%) is obtained by slip at Re = 40 with volume fraction φ=0.01, which shows that super-hydrophobic surface can enhance heat transfer by slip.

The present study introduces and proposes an effective and superior method for the numerical simulation of fluid/nanofluid slip flow, which has active guidance meaning and applied value to the engineering practice of DR, heat transfer, flow control and performance improvement.

This study aims to investigate the thermohydrodynamic (THD) and thermoelastohydrodynamic (TEHD) performance of an air-lubricated thrust bearing under different slip conditions, especially the slip length effect.

In this study, a new modified boundary slip model was established to investigate thrust bearing performance. The THD and TEHD bearing characteristic distribution was analyzed with fluid–thermal–structure interaction approach. The effect of the slip length on the bearing performance was studied using various bearing structure parameters.

The increased slip length changed the classical feature distribution of the film pressure and temperature. The sacrifice of the bearing load capacity effectively compensated for the aerodynamic thermal effect and friction torque under the slip condition. The TEHD model has a lower film pressure and load capacity than the THD model. However, it also has lower film temperature, lower friction torque and smaller Knudsen number (Kn).

The bearing THD and TEHD performances of the modified boundary slip model were compared with those of a traditional no-slip bearing. The results help to guide the selection of the bearing surface materials and processing technology of rotor and foil, so as to fully control the degree of slip and make use of it.

The purpose of this paper is to investigate the combined effects of slip and rheological parameters on the flow and heat transfer of the Herschel-Bulkley fluid.

The combinative dimensionless parameter method is introduced into the equations of the slip flow and heat transfer to make the discussion more comprehensive. More specifically, the slip and rheological parameters are transformed into the dimensionless slip number as well as Herschel-Bulkley number. We solve the dimensionless equations and then focus on the effects of these parameters on the slip flow and heat transfer.

The results show that, for a given value of Herschel-Bulkley number, there is a finite critical value of slip number at which the pressure gradient reaches the lowest value and both the dimensionless yield radius and slip velocity become 1. Meanwhile, the Nusselt number tends to be infinite at this critical value of slip number. For the case of slip, the Nusselt number also approaches infinity at a finite critical value of Herschel-Bulkley number. Furthermore, the dimensionless velocity as well as temperature of the yield pseudoplastic fluid with higher slip number is lower within a small radius but becomes higher near the wall. Meanwhile, from the velocity and temperature profiles, the effect of Herschel-Bulkley number on these two parameters of the Bingham fluid at the smaller radius is opposite.

These associated expressions can be generalized to the flow and heat transfer of a Herschel-Bulkley fluid under slip boundary condition. It can provide a reference for the engineering application relating to the heat transfer and flow of a Herschel-Bulkley fluid. Meanwhile, it also suggests some revelations for dealing with this similar problem.

The paper aims to examine the boundary layers of a three-dimensional stagnation point flow of Al-Cu nanoparticle-suspended water-based nanofluid in an electrically conducting medium. The effect of magnetic field on second-order slip effect and convective heating is also taken into account.

The thermophysical properties of alloy nanoparticles such as density, specific heat capacity and thermal conductivity are computed using appropriate formula. The non-linear parabolic partial differential equations are transformed to ordinary differential equations and solved by shooting technique.

The influence of compositional variation of alloy nanoparticle, nanoparticle concentration, magnetic effect, slip parameters and Biot number are presented for various flow characteristics. Interesting results on skin friction and Nusselt number are obtained for different composition of aluminium and copper.

A novel result of the analysis reveals that impact of magnetic field near the boundary is suppressed by the slip effect.

This study aims to purpose the suitable location of slip boundary condition and microscale surface textures to enhance the tribological performance of the hydrodynamic journal bearings.

Mass conserving Elrod cavitation algorithm with considering slip boundary condition has been used for predicting the static performance characteristics (load carrying capacity, coefficient of friction and volumetric inflow rate) of finite cylindrical shape textured journal bearings.

It has been observed that the full textured bearing with slip boundary condition in between 0°–180° circumferential region gives a significant reduction in the lubricant rupture zone. However, the introduction of textures up to the interface of slip and the no-slip region is increasing the load-carrying capacity and reduces the shear stress. This reduction in shear stress with combined slip and surface textures is effective in increasing the volumetric inflow rate of the lubricant.

The combined effect of slip boundary condition and surface texturing is increasing the scope of liquid lubricants in hydrodynamic journal bearings and further contributing toward the development of small-scale rotating machines.

The study related to the use of mass conserving Elrod cavitation algorithm for finding the optimum location of slip and surface texture zones has been found rare in the literature. Previous studies show that the mass conserving Elrod cavitation algorithm gives realistic results for textured bearings and its findings show good agreement with the experimental observations.

The purpose of this paper is to investigate the effect of boundary slip on hydrodynamic performance of liquid film seal considering cavitation.

A mathematical model of liquid film seal with slip surface was established based on the Navier slip model and Jakobsson–Floberg–Olsson (JFO) boundary condition. Liquid film governing equation was discretized by the finite difference method and solved by the SOR relaxation iterative algorithm and the hydrodynamic performance parameters of liquid film seal were obtained considering boundary slip and cavitation.

The results indicate that the values of performance parameters are affected significantly by the slip length under the condition of high speed and low differential pressure.

The performances of liquid film seal are investigated considering slip surface and cavitation. The results presented in the study are expected to provide a theoretical basis to improve the design method of liquid film seal.

The purpose of this paper is to investigate the effect of slip position on the performance of liquid film seal.

A mathematical model of liquid film seal with slip/no-slip surface was established based on the Navier slip model and JFO boundary condition. Liquid film governing equation was discretized by the finite difference method and solved by the SOR relaxation iterative algorithm and the effects of slip position on sealing performance are discussed.

The results indicate that boundary slip plays an important role in the overall performance of a seal and a reasonable arrangement of slip position can improve the steady-state performance of liquid film seal.

Based on the mathematical model, the optimal parameters for liquid film seal with boundary slip at groove are obtained. The results presented in this study are expected to provide a theoretical basis to improve the design method of liquid film seal.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2020-0082/