Second-order Slip Boundary Condition Research Articles

Microchannel Gas Flow in the Multi-Flow Regime Based on the Lattice Boltzmann Method.

In this work, a lattice Boltzmann method (LBM) for studying microchannel gas flow is developed in the multi-flow regime. In the LBM, by comparing previous studies' results on effective viscosity in multi-flow regimes, the values of the rarefaction factor applicable to multi-flow regions were determined, and the relationship between relaxation time and Kn number with the rarefaction factor is given. The Kn number is introduced into the second-order slip boundary condition together with the combined bounce-back/specular-reflection (CBBSR) scheme to capture the gas flow in the multi-flow regime. Sensitivity analysis of the dimensionless flow rate to adjustable parameters using the Taguchi method was carried out, and the values of adjustable parameters were determined based on the results of the sensitivity analysis. The results show that the dimensionless flow rate is more sensitive to j than h. Numerical simulations of Poiseuille flow and pulsating flow in a microchannel with second-order slip boundary conditions are carried out to validate the method. The results show that the velocity profile and dimensionless flow rate simulated by the present numerical simulation method in this work are found in the multi-flow regime, and the phenomenon of annular velocity profile in the microchannel is reflected in the phases.

Numerical investigation on flow, heat and mass transfer performance of fractional Oldroyd-B hybrid nanofluid as a coolant for power battery

This paper introduced for the first time a viscoelastic hybrid nanofluid as the coolant for direct contact cooling power battery. The governing boundary layer equations were established by adopting fractional Oldroyd-B model and fractional Buongiorno’s model. Second-order velocity slip boundary conditions were also considered. Then the solutions were numerically acquired by finite difference coupled with L1 algorithm. Impact of main physical parameters on the flow, heat and mass transfer of the viscoelastic hybrid nanofluid on the cylindrical battery was graphically presented and detailly discussed. Outcomes show that the heat transfer is improved by both Brownian motion(Nb) and thermophoresis(Nt) to different degrees. When Nb grows from 0.05 to 0.1, the average Nusselt number increases by 2.2%, higher than 0.027% of Nt. The slip behavior only affects the velocity distribution near the individual cell and slightly enhances heat and mass transfer. The velocity relaxation fractional derivative contributes to convection, heat and mass transfer on the cell wall, while velocity retardation fractional derivative behaves just the opposite. The proposed viscoelastic hybrid nanofluid with appropriate volume fractions of nanoparticles enhances heat transfer on the cell wall and is strongly recommended as a candidate for power battery coolant.

Velocity-slip boundary conditions and shape factor effects on MHD hybrid nanofluid flow via converging/diverging channels

The most important objective of this research-work is to investigate the impacts of velocity-slip boundary conditions and shape factor of solid nanoparticles on the hydrodynamic behavior of the nonlinear problem of MHD Jeffery–Hamel hybrid nanofluid flow where the mixture H2O-C2H6O2 (50%-50%) was utilized as a base fluid. Using appropriate velocity transformations, the basic partial differential equations arising from mathematical modeling are transformed into non-linear ordinary differential equations. Afterwards, the determined nonlinear equation was numerically solved utilizing Runge-Kutta-Fehlberg 4th–5th order approach featuring shooting technique and analytically with the help of Duan–Rach Approach (DRA). The impact of active factors like Reynolds number, channel half-angle, Hartman number, base fluids nature, hybrid nanoparticles, velocity-slip boundary conditions, shape and Geometry of solid nanoparticles on hybrid nanofluid velocity and skin friction coefficient are visualized and investigated. The minimal local skin friction is found to be obtainable with the nanoparticles of Platelet form and second-order slip model where a reduction of 70% is gained compared to the local skin friction coefficient with spherical nanoparticles when the Hartmann number is higher. Results obtained also reveal that a higher reduction of 69% in local skin friction coefficient intensity is observed for both hybrid phase Al2O3-Cu and mixture base fluid H2O-C2H6O2 with second-order slip boundary condition model when Knudsen number Kn = 0,08. A comparison was made between the results obtained from this investigation in particular cases and the results obtained via the HAM-based Mathematica package for validation. Also, the obtained analytical DRA data are compared with numerical RKF45 data and the ones represented in the literature. The comparison revealed that the results match perfectly which justifies applicability, validity, and the higher exactness of the adopted Duan-Rach approach.

Entropy generation in magnetohydrodynamic radiative non-Darcy slip flow of a Casson nanofluid with Hall effects and activation energy

The present research work examines the entropy generation in the magnetohydrodynamic second-order slip flow of Casson nanofluid surpassing a horizontal stretching sheet inside a non-Darcy porous medium under the dominance of Hall current and nonlinear thermal radiation. The present model is made more realistic by taking second-order velocity slip flow. The energy field is pursued by incorporating the consequences of distinctive viscous dissipation and Joule heating. The chemical reaction incited by activation energy is comprised in the current exploration. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with second-order velocity slip and convective boundary conditions. A compatible similarity transformation comprised is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via the spectral quasi-linearization method. The present article deals with an in-depth exploration of the characteristics of diagnostic flow parameters against the-flow field and other efficient physical quantities with the help of distinctive graphs and tables. As per the regression analysis, the maximum relative error for the reduced Nusselt number ranging from .000090231% to .00015936% is less than that of the other physical quantities. Magnetic force, thermophoresis, and Brownian motion assist in lessening the heat transport rate, but it gets enriched under the Hall current effects. For the increasing Casson parameter, fluid movement tends to rise near the sheet’s surface and gets decelerated afterwards. The intense Hall current accelerates the Casson fluid’s motion. But the velocity components in xandz-directions become abated across the flow region due to increasing the first-order velocity slip parameter. Besides, the enhancement in the magnitude of the second-order velocity slip parameter undermines the velocity components in xandz-directions.

A modified lattice Boltzmann model for microcylindrical Couette gas flows

We develop an axisymmetric lattice Boltzmann (LB) model to simulate microcylindrical Couette gas flows (MCGF) in the slip regime and transition regime, respectively. A kinetic boundary scheme in the cylindrical coordinate system is proposed to fulfill the second-order slip boundary condition at the cylindrical wall. To consider the effect of the Knudsen layers for transition flows, local effective Knudsen numbers are introduced into the kinetic boundary scheme and relaxation time. Numerical tests are executed to acquire the velocity distributions of the time-independent and time-dependent MCGF. Comparisons with the analytical solution and direct Monte Carlo data are also implemented. The simulation results demonstrate that the developed LB model can successfully acquire the velocity distribution of the MCGF with an intermediate Knudsen number in the transition regime.

Numerical study of squeezing flow past a Riga plate with activation energy and chemical reactions: effects of convective and second-order slip boundary conditions

Background: The study of electric and magnetic characteristics, known as electro-magneto-hydrodynamic, has significant industrial, biological, and engineering applications. Plasma, electrolytes, saltwater, and liquid metals are some examples of electro-magneto fluids. The applications of squeezing flow are getting the intention of engineers and scientists due to its extensive usage in various fields, namely, food processing, industrial processing, biomechanics, mechanical and chemical engineering, etc. By considering such advantages in mind, the electromagneto-hydrodynamic squeezing flow through a Riga plate under the effect of connective and slips boundary conditions is examined in this study. Numerical Technique: The local numerical simulations have been done with help of the Shooting method based on the Secant iterative scheme. Results: The profiles of velocity, temperature, and concentration are plotted and discussed numerically under the effects of emerging parameters. The physical quantities, namely, wall shear rate, heat transfer rate, and Sherwood number are also discussed. It is found that the slip parameters decline in the velocity and concentration fields. The radiation parameter, Biot number, and Prandtl number accelerate the temperature of the fluid. The local Nusselt number enhances via the Prandtl number and radiation parameter.

Comparative study of hybrid and nanofluid flows over an exponentially stretched curved surface with modified Fourier law and dust particles

Hybrid nanofluids are the prospective liquids that possess improved heat transfer enactment and thermophysical characteristics than conventional heat transfer fluids (water, oil, ethylene glycol) and single-particle nanoparticle immersed nanofluids. Here, a comparison of the hybrid nanofluid comprising copper, copper oxide nanosized particles with ethylene glycol (Cu-CuO/C2H6O2) as the customary liquid, with nanofluid copper-ethylene glycol (Cu/C2H6O2) is made. The flow of hybrid nanofluid is considered over an absorbent curved sheet which is stretched exponentially with dust particles with modified Fourier law. The modeled problem is assisted by the melting heat and second-order slip boundary conditions. The system of equations is coped numerically after applying the boundary layer theory to the system of governing equations. It is witnessed that dust phase and temperature are augmented for escalating estimations of the curvature parameter. It is also perceived that an escalation in the thermal relaxation and concentration parameter values results in a lowering temperature of the fluid. Furthermore, it is remarked that fluid velocity is enhanced for large disk curvature. The hybrid nanofluid in case of heat transfer comparison is far ahead of the nanofluid. The acquired outcomes are also endorsed by making a comparison with a published study. An outstanding agreement is attained.

Dual Solutions of EMHD Nanofluid at Stretching Sheet with Mixed Convection Slip Boundary Condition

In this paper stagnation boundary layer flow of nanofluid with mixed convection heat and mass transfer with Electrical Magneto Hydrodynamic (EMHD) effects over a second-order momentum slip boundary condition have been mathematically analysed. The governing equations are transformed by similarity variable and the problem becomes coupled third-order nonlinear coupled differential equations. We use fourth-order Runge Kuta method and shooting technique to find the solution. The effect of second-order momentum slip condition with linear thermal slip condition has determined. Variation of all nano energy conversion parameters depends on different factors has shown graphically. Some of the parameters possesses dual solution at different values of second-order velocity slip parameter (β1&β2).

Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Because of its mesoscopic nature and distinctive computing features, lattice Boltzmann method (LBM) is shown as a promising tool to simulate microscale gas flows. However, studies on the microtube flows are rare, and some fundamental problems for LBM to such flows still remain unsolved. In this work, three widely used kinetic boundary schemes, i.e., combined bounce-back and specular-reflection scheme, combined Maxwell-diffusion and specular-reflection scheme, and combined Maxwell-diffusion and bounce-back scheme, for the axisymmetric lattice Boltzmann equation (LBE) with multi-relaxation-time (MRT) are investigated. The discrete effects of the three boundary schemes in the axisymmetric MRT-LBE are observed by analyzing the micro-scale Hagen-Poiseuille flow, and the strategies of adjusting the parameters in the boundary schemes are put forward to implement the no-slip boundary condition and the second-order slip boundary condition. Some numerical tests are implemented to validate the proposed correction strategies for kinetic boundary schemes. Our analysis also shows that the kinetic boundary schemes of the axisymmetric Bhatnagar-Gross-Krook (BGK) LBE cannot realize the no-slip boundary condition and are also inapplicable to microscale gas flows with even some moderate Knudsen numbers (). Therefore, the axisymmetric MRT-LBE is superior to the axisymmetric BGK-LBE in realizing both the no-slip and slip boundary conditions.

A Novel Approach To Predict Gas Flow in Entire Knudsen Number Regime through Nanochannels with Various Geometries

Summary Various unified gas flow (UGF) and apparent permeability models have been proposed to characterize the complex gas transport mechanisms in shale formations. However, such models are typically expressed as combinations of multiple gas flow mechanisms so that they cannot predict gas velocity profile. In this study, we develop a novel approach to predict the gas velocity profile in the entire Knudsen number (Kn) regime for circular and noncircular (i.e., square, rectangular, triangular and elliptical) nanochannels and investigate the effects of cross-sectional geometry on gas transport in nanochannels. To this end, a new UGF model is proposed to describe the gas flow behaviors in the entire Kn regime, considering the effects of gas slippage, bulk diffusion, Knudsen diffusion, surface diffusion, and cross-sectional geometry of flow channel. In addition, the boundary condition of the semianalytical second-order slip model applicable to various cross-sectional geometries is modified by adjusting the slip coefficients through the comparison between the proposed UGF model and the Navier-Stokes (N-S) equation with second-order slip boundary condition. As a result, the velocity profile of free gas in the entire Kn regime for the nanochannel with a specific cross section can be determined by solving the second-order slip model with adjusted slip coefficients via the finite element method. The results indicate that the geometry of the cross section has a significant influence on the mass flow rate and gas velocity profile in nanochannels. The predicted mass flow rates for the nanochannels with identical hydraulic diameter decrease with the cross-sectional geometry in the sequence as ellipse > equilateral triangle > rectangle > square > circle. However, the ranking of velocity profiles for such nanochannels, which is governed by the cross-sectional geometry, also varies with Kn. These findings indicate that the developed approach can predict the synergetic gas transport (i.e., gas slippage, bulk diffusion, Knudsen diffusion, and surface diffusion) and gas velocity profile in nanochannels with different cross-sectional geometries for a wide range of Kn, which gives insight into the characterization of gas flow behaviors in nanoporous shale.

A basic model of unconventional gas microscale flow based on the lattice Boltzmann method

A new method for selecting dimensionless relaxation time in the lattice Boltzmann model was proposed based on similarity criterion and gas true physical parameters. At the same time, the dimensionless relaxation time was modified by considering the influence of the boundary Knudsen layer. On this basis, the second-order slip boundary condition of the wall was considered, and the key parameters in the corresponding combined bounce-back/specular-reflection boundary condition were deduced to build a new model of unconventional gas microscale flow simulation based on the lattice Boltzmann method suitable for high temperatures and high pressures. The simulation results of methane gas flow driven by body force in infinite micro-channels and flow driven by inlet-outlet pressure differential in long straight channels were compared with the numerical and analytical solutions in the literature to verify the accuracy of the model, and the dimensionless relaxation time modification was formally optimized. The results show that the new model can effectively characterize the slippage effect, compression effect, gas density and the effect of boundary Knudsen layer in the micro-scale flow of unconventional natural gas. The new model can achieve a more comprehensive characterization of the real gas flow conditions and can be used as a basic model for the simulation of unconventional gas flow on the micro-nano scale.

Numerical Study of Nanoparticle Deposition in a Gaseous Microchannel under the Influence of Various Forces

Nanoparticle deposition in microchannel devices inducing contaminant clogging is a serious barrier to the application of micro-electro-mechanical systems (MEMS). For micro-scale gas flow fields with a high Knudsen number (Kn) in the microchannel, gas rarefaction and velocity slip cannot be ignored. Furthermore, the mechanism of nanoparticle transport and deposition in the microchannel is extremely complex. In this study, the compressible gas model and a second-order slip boundary condition have been applied to the Burnett equations to solve the flow field issue in a microchannel. Drag, Brownian, and thermophoretic forces are concerned in the motion equations of particles. A series of numerical simulations for various particle sizes, flow rates, and temperature gradients have been performed. Some important features such as reasons, efficiencies, and locations of particle deposition have been explored. The results indicate that the particle deposition efficiency varies more or less under the actions of forces such as Brownian force, thermophoretic force, and drag force. Nevertheless, different forces lead to different particle motions and deposition processes. Brownian or thermophoretic force causes particles to move closer to the wall or further away from it. The drag force influence of slip boundary conditions and gas rarefaction changes the particles’ residential time in the channel. In order to find a way to decrease particle deposition on the microchannel surface, the deposition locations of different sizes of particles have been analyzed in detail under the action of thermophoretic force.

Heat transfer and hydrodynamics of slip confusor flow under second-order boundary conditions

The paper focused on an analytical analysis of the main features of heat transfer in incompressible steady-state flow in a microconfusor with account for the second-order slip boundary conditions. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. As a result, novel solutions were obtained for the velocity and temperature profiles, as well as for the friction coefficient and the Nusselt number. These solutions demonstrated that an increase in the Knudsen number leads to a decrease in the Nusselt number. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics. It was also revealed that flow slippage effects on heat transfer weaken with an increase in the Prandtl number.

Numerical Modelling of Microchannel Gas Flows in the Transition Flow Regime Using the Cascaded Lattice Boltzmann Method.

In this article, a lattice Boltzmann (LB) method for studying microchannel gas flows is developed in the framework of the cascaded collision operator. In the cascaded lattice Boltzmann (CLB) method, the Bosanquet-type effective viscosity is employed to capture the rarefaction effects, and the combined bounce-back/specular-reflection scheme together with the modified second-order slip boundary condition is adopted so as to match the Bosanquet-type effective viscosity. Numerical simulations of microchannel gas flow with periodic and pressure boundary conditions in the transition flow regime are carried out to validate the CLB method. The predicted results agree well with the analytical, numerical, and experimental data reported in the literature.

A dynamic apparent permeability model for shale microfractures: Coupling poromechanics, fluid dynamics, and sorption-induced strain

The widely distributed microfractures play an important role in shale gas production. However, limited studies focus on gas flow behavior in microfractures, and ignore the complex transport mechanisms, leading to a large error for gas permeability evaluation. In this work, a newly dynamic apparent permeability (AP) model, coupling poromechanics, sorption-induced strain, and gas slippage, has been proposed to effectively reveal the gas flow mechanisms through microfractures of shale. Specifically, a dynamic aperture is innovatively incorporated into the Navier-Stokes (N–S) equation using the second-order slip boundary condition to calculate the gas velocity and volume flux in single microfracture. Based on that, the gas transport model for microfracture networks considering the distributions of aperture and tortuosity is derived using the fractal theory. The newly developed model is verified well with experimental data and network simulation. Results indicate that the gas conductance highly depends on the structure of microfracture networks (i.e., the maximum aperture and fractal dimensions). There are three different AP evolutions under various boundary conditions (i.e., constant confining pressure (Pc), constant pore pressure (Pp), and constant effective stress (σeff)) resulting from the coupling transport mechanisms. The AP presents a similar shape of “V” at reservoir conditions (i.e., constant Pc ), indicating the “negative contribution” of poromechanics at an early stage, and the “positive contribution” for both gas slippage and sorption-induced strain at the late stage should be underlined during gas production. Moreover, the “negative factor” of poromechanics is positively correlated with fracture compressibility coefficient but negatively associated with Biot's coefficient at high pressures (>15 [MPa]). Increasing gas desorption capacity, fracture spacing, and internal swelling coefficient can enhance the “positive factor” of sorption-induced strain at low pressures (<15 [MPa]). This work provides a theoretical guidance to develop shale gas effectively.

A new model for the transport of gaseous hydrocarbon in shale nanopores coupling real gas effect, adsorption, and multiphase pore fluid occupancies

A new gaseous hydrocarbon transport model, considering pore geometry, multiphase pore fluid occupancy, and porous deformation, has been developed to characterize the real gas flow in both nanoscale organic and inorganic porous media. To do so, Navier-Stokes equations were solved with modified second-order slip boundary conditions in nanocapillaries of organic matter (OM) and nanoslits of inorganic matrix (iOM). Due to gas adsorption, both surface diffusion and bulk gas flow affect the apparent gas permeability (AGP) of OM. Particularly, the Langmuir-slip model is used for the calculation of boundary velocity of bulk gas. In contrast, gas flow in a single nanoslit of iOM accounts for the impact of adsorbed water film with a certain thickness quantified by Li's model [15]. Additionally, porous deformation and real gas effect are included in both models of OM and iOM. As such, a unified AGP model of shale matrix is formulated based on the total organic carbon (TOC) content including contributions of both OM and iOM. Results show that, under depressurization condition, the AGP of OM/iOM with a large pore size distribution (PSD) presents a similar shape of “V”, while the AGP of iOM with a small PSD increases monotonously. The total flow capacity of OM is contributed by competitive mechanisms of surface diffusion, induced- and pure- bulk gas flow under various PSDs and pressure. For gas flow capacity in iOM with a small PSD, it can be weakened by adsorbed water film but compensated by nanoscale effect considerably at low pressures. Moreover, a higher relative humidity (RH) leads to a thicker water film resulting in a lower gas conductance. The AGP of shale matrix can be reduced or enhanced by the TOC content when accounting for gas adsorption and adsorbed water film. Besides, the real gas effect enhances flow capacity significantly in small pores with a high pressure. The proposed model provides a comprehensive understanding of the gas flow mechanism in shale nanopores under reservoir conditions.

Heat Transfer in Porous Microchannels with Second-Order Slipping Boundary Conditions

The paper presents results of a study of forced convection in a vertical flat and circular microchannels incorporating porous medium under slip boundary conditions of the first and second orders. The problem was solved analytically and compared with numerical simulations based on the lattice Boltzmann method. Effects of porosity and slip velocity on velocity and temperature profiles were investigated. Behavior of the normalized Nusselt number as a function of the Knudsen and Prandtl numbers, as well as the parameter M characterizing porosity of the medium in the microchannel, was also elucidated. Computations indicated that a decrease in porosity (an increase in the parameter M) causes a decrease in the velocity and temperature jumps on the wall, which contributes to the increase in the Nusselt number. Considering the effect of the second-order slip boundary conditions leads to the decrease in the velocity jump on the wall, when the coefficient A2 (this coefficient considers the second-order slip boundary conditions) changes from negative to positive values. The heat transfer rate at high Prandtl numbers increases with the increasing Knudsen number, because of the improved thermal interaction of the flow with the channel wall. Given the second-order boundary conditions, the effect of parameter A2 was not observed at small Prandtl numbers (Pr ≤ 1). For A2 0 the normalized Nusselt number decreases in comparison with the case of A2 = 0 (the first-order boundary conditions). The results by the analytical solution and the lattice Boltzmann method are in a good agreement with each other for A2 ≥ 0, with the differences ≤ 1%. For A2 < 0, the differences between two models are more noticeable. For A2 ≥ 0, predictions by the analytical model lie higher than the numerical results, whereas for A2 < 0, numerical simulations exceed the analytical solution.

Lattice Boltzmann Simulation of Micro Gas Flows Over a Wide Range of Knudsen Numbers

To characterize the microflow over a larger range of Knudsen numbers, an improved kinetic equation considering the volume diffusion effect for nonideal gases was presented based on Klimontovich's kinetic equation and Enskog equation-based lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model. Then, with the modified effective viscosity and the second-order slip boundary condition, a series of numerical simulations of gas flows with different mean Knudsen numbers were carried out based on the proposed model. Compared with the solutions of Navier–Stokes equations, Navier–Stokes equations with different slip boundary conditions, bivelocity hydrodynetics, and experimental data, we found that the present model can be valid up to a Knudsen number of 30. It is also shown that the present model furnishes a better solution in the transitional flow regime (0.1 &lt; Kn &lt; 10). The results not only illustrate that the present model could offer a satisfactory solution to a wider range of mean Knudsen number, but also show the importance of the compressibility and surface-dominated effects in micro gas flows. The improved model provides a promising tool for handling the micro gas flows with complex geometries and boundaries.

Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

PurposeThe paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions.Design/methodology/approachThe paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other.FindingsThe analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions.Originality/valueThe novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

Rarefied transitional flow through diverging nano and microchannels: A TRT lattice Boltzmann study

Rarefied isothermal gaseous flow through long diverging micro and nanochannels is investigated in this paper using the two-relaxation-time (TRT) lattice Boltzmann method (LBM). The simulations are performed over a wide range of Knudsen number, pressure ratio, and divergence angle. The Bounce-Back Specular Reflection (BSR) slip boundary condition is applied and is connected to the second-order slip boundary condition coefficients by means of the antisymmetric relaxation time and the bounce-back portion parameter. The effects of the slip coefficients on the wall and centerline Mach numbers, as well as the mass flow rates, are investigated. The numerical results are validated with those of the direct simulation Monte Carlo (DSMC) reported in the literature. The results show that the local pressure distributions are almost independent of the slip coefficients with excellent agreements with DSMC over a wide range of the divergence angle. Our results demonstrate that there is a specific divergence angle at each pressure ratio where the local unbounded Knudsen and, as a result, Mach numbers remain constant along the channel. This observation is almost independent of the slip coefficients, and the underlying reason is that the pressure drop is compensated by an increase in the channel area.