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Analytical solutions of the Navier–Stokes equation based on a locally fully-developed flow assumption with various gas slip models are presented and comparisons for velocity profile, flow rate, friction factor, and pressure distribution are performed. The effect of the second-order coefficient in the slip boundary condition becomes significant as the Knudsen number increases. Most slip models are limited to slip regime or marginally transition regime and break down around Kn = 0.1 while Sreekanth's model, followed by Mitsuya's model, gives a good agreement with the linearized Boltzmann solutions from slip regime up to Kn = 2 for flow rate and friction factor predictions. These two models should be of great use for slip flow analysis in micro-electro-mechanical systems (MEMS) and, in particular, in situations where the flow rate and flow resistance are of interest.

Isothermal gas flow in microtubes with a sudden expansion or contraction is studied numerically by lattice Boltzmann method. An axisymmetric D2Q9 model is used to simulate gas slip flow in micro-circular pipes. With the boundary condition combined specular and bounce-back schemes, the computed results are in excellent agreement with analytical solution for straight microtube. For the gas flow in the expanded or constricted tubes, we carried out simulations of several Knudsen numbers with inlet/outlet pressure ratio 3. It is found the pressure drop in each section can be predicted well by the theory of straight tubes. For smaller Knudsen number, flow separation in the expanded tube is observed. While for large Knudsen number, there is no vortex at corner and the streamlines are attached to boundary. In the constricted tube, the vortex at corner is very weak. These results are consistent with some experimental conclusions.

The problem of a steady boundary layer MHD slip flow over a stretching sheet in a water-based nanofluid containing different type of nanoparticles: Cu, Al₂O₃ and Ag has been investigated. An external strong magnetic field is applied perpendicular to the plate and the Hall effect is taken into consideration. The surface of the stretching sheet is assumed to move with a linear velocity and subject to power-law variation of the surface temperature. The governing partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by a Runge–Kutta–Fehlberg method with shooting technique. Effects of the physical parameters on the primary velocity, the secondary velocity and the temperature as well as on the wall shear stress and the rate of heat transfer have been presented graphically and discussed in detail. Investigated results indicate that the nanoparticle volume fraction and the slip parameter produce opposite effects on the skin friction coefficients of the primary and secondary flow. Also, the nanoparticle volume fraction and the types of nanoparticles demonstrate a more pronounced influence on the secondary flow than that on the primary flow and temperature distribution.

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

This research deals with an analysis of the Hall current effect on the mixed convective magneto-micropolar fluid flow over a permeable stretching/shrinking sheet. Impact of the Newtonian heating parameter is analyzed in the slip flow regime. The nonlinear equations of the fluid flow are derived with the help of a similarity transform and its solutions are obtained by Optimal Homotopy Analysis Method (OHAM). For limiting cases, obtained results are in excellent agreement with the available exact and numerical results in the literature. The graphical and tabular representations of the obtained results show significant effects of the physical parameters on the magneto-micropolar fluid flow and heat transfer characteristics. In particular, it is observed that, as the sheet stretches, a change in the Hall current parameter yields a higher horizontal velocity component for the lower value of the magnetic field parameter; while it produces a higher and shorter transverse velocity profile at high intensity of the magnetic field. In Magnetohydrodynamics (MHD) generators, Hall effects are an important consideration to analyze the heat transfer phenomenon with high temperature conducting fluids.

The objective of current communication is to study heat transfer phenomenon for slip flow of viscous fluid due to wavy channel with general cosine function boundaries and fixed amplitude. The walls along with slip boundary constraints are kept at different temperatures. The flow is incompressible and Newtonian with AIS as a predicting material being used to check the fluids and thermal properties. The Navier–Stokes expressions with 2D flow regime subject to heat transfer due to convection are used to develop the simulations. A parametric theoretical assumptions analysis is performed for specified range of Reynolds number (100–1000) with upper and lower surface vibration periods of 1 to 6. The results are displayed with graphs, surface and contours plots and first, ever a novel work was done to represent the percentage change in velocity magnitude and local Nusselt number as surface plots and contours, respectively. The results are authentic due to mesh independent study and verification with the experimental correlation. A periodic flow at the lower wall was deducted. The maximum and average rotation rates attain a linear relationship with Reynolds number and their correlation was found. The simulations show the strict relationship of Reynolds number and the geometry of the channel with shear rate. The pressure gradient in $y$-direction was found minimum in trough and maximum in the crest region. It has been observed that the boundary friction is reduced due to periodic variation of walls surface.

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips’ impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both $e_1$ and $\epsilon$ parameters.

A three-dimensional compressible numerical model of micro-channel is established with consideration of the effect of velocity slip near walls. Meanwhile the gas viscosity is modified based on the Knudsen number using Veijola's model. The model is proved to be credible by comparing with analytical data. A new non-dimensional parameter relative slip length L_s/D_h is found to be very useful for describing friction characteristic for compressible flow with slip in micro-scale. The correlation for fRe with this new non-dimensional parameter L_s/D_h is suggested.

This work focused on slip flow over a non-Newtonian nanofluid fluid flow past a stretching sheet with particles–liquid suspension. The convective boundary condition is taken into account. Similarity transformations are utilized to reduce the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Runge–Kutta–Fehlberg scheme is used to get the numerical solution. Important parameters are analyzed through graphs and skin friction coefficient. Nusselt numbers are presented in tables. Investigation reveals that slip parameter decreases the velocity field and Biot number increases the temperature field.

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

An imbibition process of water into a matrix is required to investigate the influences of large-volume fracturing fluids on gas production of unconventional formations. Slip flow has been recognized by recent studies as a major mechanism of fluid transport in nanotubes. For nanopores in shale, a slip boundary is nonnegligible in the imbibition process. In this study, we established an analytic equation of spontaneous imbibition considering slip effects in capillaries. A spontaneous imbibition model that couples the analytic equation considering the slip effect was constructed based on fractal theory. We then used a model for various conditions, such as slip boundary, pore structure, and fractal dimension of pore tortuosity, to capture the imbibition characteristics considering the slip effect. A dynamic contact angle was integrated into the modeling. Results of our study verify that the slip boundary influences water imbibition significantly. The imbibition speed is significantly improved when slip length reaches the equivalent diameter of a tube. Therefore, disregarding the slip effect will underestimate the imbibition speed in shale samples.

An analysis is performed to study the unsteady hydromagnetic heat and mass transfer of blood in a time-dependent porous narrow blood vessel over a permeable inclined stretching surface under slip conditions. The unsteadiness in the flow, temperature and concentration fields is caused by the time dependence of the stretching velocity, surface temperature and the surface concentration. Thermal radiation, chemical reaction, velocity slip, thermal slip and concentration slips are considered. Similarity transformations are used to convert the governing time-dependent non-linear boundary layer equations for momentum, heat equation and species equations into a system of ordinary differential equations. The resulting non-linear coupled differential equations are solved numerically by using fourth order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number has been studied and numerical results are presented graphically and in tabular form. Comparisons with previously published work are performed and the results are found to be in excellent agreement.

An investigation of the magnetohydrodynamics (MHD) boundary layer slip flow over a vertical stretching sheet in nanofluid with non-uniform heat generation/absorbtion in the presence of a uniform transverse magnetic field has been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the surface of the sheet. The results show that there are significant effects of various pertinent parameters on velocity and temperature profiles.

The field of nanofluidics research has spanned over the past decade with a variety of promising applications. We investigate the “laminar boundary layer flow” of a Newtonian nanofluid past a moving extendable/contractable horizontal plate with surface velocity and thermal slip effects. The passively controlled nanofluid model (PCM) is considered. Such models are physically more realistic as compared to the “actively controlled models” (ACM). Using Lie symmetry group method, the governing equations are reduced by a set of highly coupled nonlinear ODE’s with thermo-solutal coupled boundary conditions. The reduced equations are solved numerically by a generalized collocation method. The influences of the emerging parameters on the local skin friction factor and the local Nusselt number are depicted numerically. The skin friction is decreased as the thermophoresis and buoyancy ratio parameters are decreased. The heat transfer rates reduce with thermophoresis and buoyancy ratio parameters. Velocity slip also leads to a rise in wall temperature gradient. This study is relevant to near-wall flows in nanofluid fuel cells, nano-materials processing, etc.