Flow Model Research Articles

Eco-Friendly 3D-Printed Concrete Using Steel Slag Aggregate: Buildability, Printability and Mechanical Properties

Utilizing steel slag aggregate (SA) as a substitute for river sand in 3D concrete printing (3DCP) has emerged as a new technique as natural resources become increasingly scarce. This study investigates the feasibility of using steel slag (SS) as fine aggregate for 3DCP. Ninety mixtures with varying steel slag aggregate-to-cement ratios (SA/C), water-to-cement ratios (W/C), and silica fume (SF) contents were designed to study the workability and compressive strength of the 3D-printed concrete. Additionally, the actual components were printed to evaluate the printability of these mixtures. The experimental results indicate that it is feasible to fully employ SA in concrete for 3D printing. Mixtures with slump values ranging from 40 to 80 mm and slump flow values varying from 190 to 210 mm are recommended for 3D printing. The optimal mix is determined to have SA/C and W/C ratios of 1.0 and 0.51, respectively, and an SF content of 10% by cement weight. A statistical approach was utilized to construct the prediction models for slump and slump flow. Moreover, to predict the plastic failure of the 3D-printed concrete structure, the modified prediction model with an SA roughness coefficient of 4 was found to fit well with the experimental data. This research provides new insights into using eco-friendly materials for 3D concrete printing.

Research on the efficiency analysis method of 9AT transmission planetary gear system based on power loss

As the core element of power transmission in Automatic Transmission (AT), the planetary gear system has advantages in the gear ratio range, load carrying capacity and transmission efficiency, and its transmission efficiency analysis is an important link in the design of automatic transmission.This paper proposes a method to analyze the transmission efficiency of planetary gear system of 9AT transmission considering power losses. Firstly, based on the hypergraph theory to establish the power transmission roadmap of each gear of the transmission (9AT) and the triangular hypergraph of the four-row planetary gear system, as well as the power flow model of the four-row planetary gear system without considering the power losses, and then the rotational speed, torque, and power change of each gear of the gear system are analyzed through the power spectrum. Secondly, a power flow model considering power losses and circulating power was established to analyze the influence law of different operating parameters (speed, torque, viscosity, gear meshing friction coefficient), and structural parameters (characteristic coefficients of each planetary row) on the transmission efficiency of the system. Finally, the equivalent planetary gear system transmission efficiency experimental bench considering losses is established to measure the transmission efficiency of the two-row planetary gear system at different speeds and torques, and the results of the experimental tests have the same trend with the theoretical calculations, which provides an analytical method to improve the transmission efficiency of the planetary gear system of the 9AT transmission.

Low carbon collaborative planning of integrated hydrogen-ammonia system and power distribution network

The conversion of renewable energy into chemical energy carriers, such as ammonia, enhances the accommodation of renewable energy for power distribution networks (PDN) and supports the decarbonization for ammonia production systems (APS). This paper addresses the integration of PDN with APS through a collaborative planning considering a carbon emission flow (CEF) model. A collaborative planning model with carbon emissions constraints is designed, and a sensitivity analysis is performed to evaluate the impact of varying renewable energy costs on the system. To further reduce carbon emissions from green ammonia production and stabilize renewable energy volatility, a nodal CEF model that incorporates energy storage systems (ESS), wind turbines (WT), and photovoltaics (PV) is proposed. The economic feasibility of the proposed model is verified via comprehensive experiments. Numerical results show that collaborative scheduling reduces both costs and carbon emissions in PDN and APS. Implementing a carbon tax encourages the transition from grey to blue ammonia production, while a decrease in renewable energy costs further promotes the shift from blue to green ammonia. Besides this, the analysis indicates that integrating long-term operation of WT and PV, together with low-cost renewable electricity and ESS, boosts the economic efficiency of the green ammonia production system.

Normalizing flow regularization for photoacoustic tomography

Abstract Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally demanding and requires rapid scanning, often leading to incomplete measurements. Deep neural networks, known for their efficiency in handling big data, are anticipated to be adept at extracting underlying information from images sharing certain characteristics, such as specific types of natural or medical images. We introduce a \ac{NFR} method designed to reconstruct images from incomplete and noisy measurements. The method involves training a normalizing flow network to understand the statistical distribution of sample images by mapping them to Gaussian distributions. This well-trained network then acts as a regularization tool within a Bayesian inversion framework. Additionally, we explore the concept of adaptive regularization selection, providing theoretical proof of its admissibility. A significant challenge in three-dimensional image training is the extensive memory and computation requirements. We address this by training the normalizing flow model using only small-size images and applying a patch-based model for reconstructing larger images. Our approach is model-independent, allowing the reuse of a well-trained network as regularization for various imaging systems. Moreover, as a data-driven prior, \ac{NFR} effectively leverages the available dataset information, outperforming artificial priors. This advantage is demonstrated through numerical simulations of three-dimensional photoacoustic tomography under various conditions of sparsity, noise levels, and limited-view scenarios.

A Thermal Model for a Hybrid Gas Bearing System in Oil-Free Turbochargers

Abstract With little drag friction, gas bearings operate at high rotor speed and high temperature and thus enable long operating life along with material damping for mechanical energy dissipation. However, most computational tools for modeling gas bearings are not accessible to bearing manufacturers or potential end-users, and the models are restricted to specific geometries and operating conditions or are missing important features, thus limiting their utility. This paper presents the thermal energy transport in a hybrid gas bearing for oil-free turbochargers with integrated heat and fluid flow models to produce a comprehensive thermo-hydrodynamic analysis predictive tool, and to design and evaluate air-lubricated gas bearings by predictions and experiments. An efficient algorithm couples the solution of the Reynolds equations and the thermal energy transport equations in the film between the rotor and a pad of the hybrid gas bearing, and updates the temperature-dependent viscosity and film thicknesses during the iterative process. The test repeats and averaged for each rotor speed from 2 krpm to 22 krpm at intervals of 2 krpm, for supply pressure varying along 25 psi to 100 psi and predicted film temperature matches well with the measured one. The parameters of interest in this analysis include the gas supply condition, bearing configuration, and the gas properties at high altitudes and high rotation speeds. The parametric study results show the density and kinematic viscosity are the most dominant properties of the gas lubrication for the film temperature.

Impact of thermal conductivity of a Williamson’s nanofluid flow due to a stretching sheet

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate.

Numerical study of Casson dusty hybrid nanofluid flow with volume fraction over a Darcy–Forchheimer porous medium

AbstractThis study develops a mathematical model for dusty Casson hybrid nanofluid flow over a vertical stretching sheet, considering the influence of volume fractions for the dust particles and nanoparticles, magnetic field and Darcy–Forchheimer penetrating medium. The nanoparticles used are TC4 (Ti‐6Al‐4V) and Nichrome (80% Ni and 20% Cr), suspended in unused engine oil (EO). The governing partial differential equations are transformed into ordinary ones using suitable transforms. Solutions are obtained numerically via the Matlab built‐in program Bvp4c technique and represent graphically the velocity, temperature, and concentration profiles for both the fluid and dust phases. Additionally, tabular forms present wall shear stress and heat transfer rate variations under different parameter values. It is found that the enhancing volume fraction parameter helps to boost the magnitude of shear stress, heat, and mass diffusivity.

Sediment Transport Dynamics Modeling of Overland Flow on Gentle Slopes Based on Flume Experiments

ABSTRACTSoil erosion is a global environmental issue, and sediment transport capacity (Tc) is critical for developing soil erosion models. This study conducted flume drainage experiments at six flow discharges (0.15, 0.25, 0.35, 0.45, 0.55, and 0.65 L s−1) and eight slope gradients (1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, and 12.0°) to investigate how the Tc of gentle slopes in the northeastern hilly region of China and water erosion factors are related and to establish a Tc model of overland flow. The study demonstrated a power–law relationship between Tc, flow discharge, and slope gradient, as evidenced by a high coefficient of determination (R2; 0.94) and Nash–Sutcliffe efficiency (NSE; 0.92) values. Additionally, there was a positive correlation between Tc and average flow velocity, with R2 and NSE values of 0.86 and 0.84, respectively. Among the hydrodynamic parameters tested, the average flow velocity was determined to be the most effective Tc predictor, surpassing stream power (R2 > 0.7, NSE > 0.7), shear stress (R2 > 0.6, NSE > 0.6), and unit stream power (R2 < 0.5, NSE < 0.5). These findings lay the foundation for developing process‐based sediment transport models for gentle slopes in the northeastern hilly regions of China.

Dynamic in‐motion wireless charging systems: Modelling and coordinated hierarchical operation in distribution systems

AbstractThe high adoption of electric vehicles (EVs) and the rising need for charging power in recent years calls for advancing charging service infrastructures and assessing the readiness of the power system to cope with such infrastructures. This paper proposes a novel model for the integrated operation of dynamic wireless charging (DWC) and power distribution systems offering charging service to in‐motion EVs. The proposed model benefits from a hierarchical design, where DWC controllers capture the traffic flows of in‐motion EVs on different routes and translate them into estimations of charging power requests on power distribution system nodes. The charging power requests are then communicated with a central controller that monitors the distribution system operation by enforcing an optimal power flow model. This controller coordinates the operation of distributed energy resources to leverage charging power delivery to in‐motion EVs and mitigate stress on the distribution system operation. The proposed model is tested on a test distribution system connected to multiple DWC systems in Salt Lake City, and the findings demonstrate its efficiency in quantifying the traffic flow of in‐motion EVs and its translation to charging power requests while highlighting the role of distributed energy resources in alleviating stress on the distribution system operation.

Time‐periodic solutions to heated ferrofluid flow models

AbstractIn this work, we prove the existence of time‐periodic solutions to a model describing a ferrofluid flow heated from below. Navier–Stokes equations satisfied by the fluid velocity are coupled to the temperature equation and the magnetostatic equation satisfied by the magnetic potential. The magnetization is assumed to be parallel to the magnetic field and is given by a nonlinear magnetization law generalizing the Langevin law. The proof is based on a semi‐Galerkin approximation and regularization methods together with the fixed point method.

Laminar boundary layers in three‐dimensional MHD natural convective flow past a semi‐infinite vertical plate with variable sinusoidal suction

AbstractThe primary goal of this study is to investigate how the diffusion‐thermo and thermo‐diffusion affect a three‐dimensional hydromagnetic natural convective flow of a radiating fluid past a uniformly moving isothermal and isosolutal semi‐infinite vertical plate subjected to a sinusoidal suction velocity. The asymptotic series expansion method is adopted to solve the equations governing the flow model and to find the analytical solutions. The effect of variable suction on the flow and transport characteristics is mainly highlighted in the study. Both the diffusion‐thermo and thermo‐diffusion effects improve the fluid velocity.

Nonlinear flow modeling of electro hydrostatic pump unit based on Gauss Newton iterative method for high performance control

For the electric hydrostatic pump unit (EPU), which is a crucial component in the electro hydraulic servo pump control system (EHSPCS), nonlinear flow modelling is a key challenge to achieve high performance operation, especially in position control. For the nonlinear flow of EPUs, simple linearization combined with compensation has become a popular control method recently. However, the control performance is constrained by the reliance on deviation correction. This paper proposes utilizing the Gauss Newton iterative method to investigate the nonlinear flow modeling in the EPU, aiming to obtain the mapping relationship between the load flow and operating parameters in the EPU, thereby directly improving the control performance. A nonlinear flow model is built by utilizing the Gauss Newton iterative method based on test data obtained from various operating conditions, and the mapping relationship is presented accordingly. Experimental studies show that compared to well-established methods, this model exhibits high accuracy and practicality in improving the control performance, particularly in position control of the EPU.

Tsunami propagation and flooding maps: An application for the Island of Lampedusa, Sicily Channel, Italy

AbstractThe Mediterranean coastlines are densely populated zones which host key socio‐economic and commercial activities. For this reason, coastal areas are vulnerable sites in case of natural disasters as tsunamis that can strike coasts causing widespread damage to the population and facilities. For these reasons, several studies were performed over the last decade to study the impact of tsunami waves on the coasts. This research assessed the inundation risk due to a tsunami wave which can hit the southeastern coast of Lampedusa Island. The coastal low‐lying geomorphological setting of the southeastern part of the island led to significant socio‐economic growth, but Lampedusa falls within the Mediterranean Sea, a high‐tsunamigenic area, therefore, the need to investigate tsunami propagation and coastal flooding of this sensitive site emerged. For this scope, a calculation chain model was implemented incorporating three steps: the DELFT‐3D software for earthquake effects modelling, MIKE 21 Flow Model FM for nearshore propagation and HEC‐RAS for onshore tsunami inundation modelling. The simulations illustrate the impact of three tsunami scenarios with different magnitudes (Mw 8.5, 7.5, 6.5) generated by hypothetical earthquakes in the Hellenic Arc. In the Mw 8.5 magnitude scenario, significant flooding occurs in the harbour region, with maximum water depths reaching approximately 3.5 m. The maximum water velocity in this scenario reaches about 15 m/s in the eastern portion, adjacent to cliffs impacted by the tsunami wave. In contrast, the Mw 7.5 magnitude scenario demonstrates reduced flooded areas, with the cliffs containing the waves and preventing further flooding. Water depths and velocities in the Mw 7.5 scenario remain minimal. Changes in both propagation and flooding are not significant between scenarios Mw 7.5 and Mw 6.5. This methodology can be employed for more accurate tsunami wave simulations not only in the Mediterranean region but also in various case studies.

A qualitative analysis of the artificial neural network model and numerical solution for the nanofluid flow through an exponentially stretched surface

This article aims to analyze the two-dimensional (2D) nanofluid (Ag/C2H6O2) flow past an exponentially stretched sheet. The magnetic field impact, heat source/sink, and convection in the thermal profile are taken into account. The complexity of the problem is reduced by introducing a dimensionless group of functions. The reduced model is transformed into a system of first-order ordinary differential equations (ODEs). This system is further analyzed with the artificial neural network (ANN), which is trained using the Levenberg–Marquardt algorithm. The whole dataset is sub divided into three parts: training (70%), validation (15%), and testing (15%). The impact of nonlinear heat source/sink parameter, magnetic parameter, volume fraction of nanoparticles, and Prandtl number is displayed through graphs. The heat source, volume fraction, and the Prandtl number cause an increase in the thermal profile with its larger values. The magnetic parameter causes a decline in both the thermal and momentum boundary layers with its higher values. The analysis shows that the thermal energy profile is enhanced with the larger values of the volume fraction of silver nanoparticles and heat source. For each case study, the residual error (RE), regression line, and validation of the results are presented. The performance of the proposed methodology is numerically tabulated for the nanoparticle volume fraction shown in Table 3, where the minimum absolute error (AE) is 5.3373e−11 at ϕ=0.05. Based on this, we recommend ϕ=0.05 for better performance. The AEs for the ANN and bvp4c are computed for the state variables in Tables for the magnetic parameter M=5,10, and 15. These tables show the overall performance of the ANN and further validate the present study. We have also validated the results of the ANN through the mean squared error graphically, where the accuracy of the proposed methodology is proven.

Least-squares pressure recovery in reduced order methods for incompressible flows

In this work, we introduce a method to recover the reduced pressure for Reduced Order Models (ROMs) of incompressible flows. The pressure is obtained as the least-squares minimum of the residual of the reduced velocity with respect to a dual norm. We prove that this procedure provides a unique solution whenever the full-order pair of velocity-pressure spaces is inf-sup stable. We also prove that the proposed method is equivalent to solving the reduced mixed problem with reduced velocity basis enriched with the supremizers of the reduced pressure gradients. Optimal error estimates for the reduced pressure are obtained for general incompressible flow equations and specifically, for the transient Navier-Stokes equations. We also perform some numerical tests for the flow past a cylinder and the lid-driven cavity flow which confirm the theoretical expectations, and show an improved convergence with respect to other pressure recovery methods.

Flow and heat transfer insights into a chemically reactive micropolar Williamson ternary hybrid nanofluid with cross-diffusion theory

Abstract The need for efficient nanotechnology has led to unexpected developments. Conserving continuous thermal propagation is essential in many industrial and thermal systems because it improves the efficiency of thermal engineering engines and machinery. Therefore, a promising platform to increase thermal power energy is the hybridization of magnetic nanoparticles in a heat-supporting, non-Newtonian fluid. In light of the above applications, a mathematical model is established to analyze the variable fluid features of the thermally radiative and chemically reactive flow of a micropolar Williamson ternary hybrid nanofluid with electromagnetohydrodynamic and electroosmosis forces on a porous stretching surface. Stratification boundary conditions and variable fluid properties were used to analyze the thermal and solutal behavior of the fluid flow. Furthermore, to measure the disorder of the flow system, entropy generation was considered by the impact of Joule heating and viscous dissipation. To develop the numerical scheme BVP4C in MATLAB, we first converted the mathematical flow model into two ordinary differential equations using a suitable transformation. The graphical and numerical results were determined against several parameters of a ternary hybrid nanofluid ( MWCNT , A l 2 O 3 , SiC ) ({\rm{MWCNT}},\hspace{0.25em}{\rm{A}}{{\rm{l}}}_{2}{{\rm{O}}}_{3},\hspace{0.25em}{\rm{SiC}}) and unary nanofluid ( A l 2 O 3 ) ({\rm{A}}{{\rm{l}}}_{2}{{\rm{O}}}_{3}) . The results indicate that the heat transfer rate is more prominent in the ternary hybrid nanofluid than in the unary nanofluid because the addition of nanofluids to the base fluid is used to improve the heat transport rate. It can be seen from the figures that a greater estimation of the magnetic and electric field parameters improves the fluid velocity because, for low values of M ≤ 1 M\le 1 , the aiding force is dominant compared to the retarding force, which results in an improvement in the velocity profile. Furthermore, the entropy generation rate increases for higher values of the Brinkman number and temperature ratio parameter because more heat is produced due to the greater values of Br {\rm{Br}} .

Simulation of Discovering Market Opportunities Using AI Methods

Due to the strong turbulence that exists in the business environment, the view is sometimes articulated that the time horizon of decisions is no longer a hallmark of strategic management. Opposing views argue that a turbulent environment changes the trajectory of reaching future objectives determined by strategic decisions. Such trajectories require the company to be agile, which is manifested by seizing opportunities. Opportunities arise because the environment is volatile. An example of market opportunity is the unsatisfied demand for products. Buyers are driven by different motives when choosing between products that are alternative to them. From the producer's point of view, the purchase is therefore random. As a consequence, the alignment of the offered product portfolio with the actual purchasing decisions of customers is undetermined. In this article, we address the problem of determining the product portfolio structure expected by customers, i.e. one that is consistent with their future purchasing decisions. We hypothesise that this problem can be represented by a model of flows between alternative resources. Problems of this type are solved using Markov Chain Monte Carlo (MCMC) methods. In order to discover the expected demand (opportunity), we simulated the flow model we developed using the Metropolis-Hastings algorithm, which is a special case of the MCMC method used in AI. Due to operating on numerical data, such simulations fall under quantitative research. In the article, we present a model of customer flows between alternative products and then the simulation result, which is the expected value of these flows (stationary point). We convert this value into the structure of the product portfolio using a model of customer purchasing decisions that we have developed. The obtained results confirm the effectiveness of our method and have significant practical value, especially for SMEs. It also enables the assessment of the company's product strategy based on real sales data. The application of our methodology is limited to discovering opportunities in situations where purchasing decisions are influenced by variable environmental factors, causing irregular purchases by individual customers. It is useful, for example, in discovering opportunities in markets such as Household Articles, Furniture, Vehicles, Equipment Repairs, Construction, and many others.

Combination of two-fluid model and delayed equilibrium model for the critical flow in a slit

Accurately predicting the mass flux, pressure profile, and velocity profile of the critical flow in a slit is essential for analyzing the breaking process of the liquid phase and calculating the aerosol source term for leak-before-break (LBB) monitoring and Loss of Coolant Accident (LOCA) risk analysis. A new critical flow model combining Two-fluid Model (TFM) and Delayed Equilibrium Model (DEM) is built to get accurate profiles while avoiding the same phase velocity in DEM and the arbitrary critical flow criterion in TFM. The new model is verified using past experiments of the critical flow in a slit. It proves to be accurate in mass flux but not in critical pressure, with maximum relative errors of around 25% in mass flux and around 80% in critical pressure. The new model is optimized for higher accuracy in critical pressure. The empirical equation of saturated phase mass flow rate fraction gradient is optimized by conducting approximate pressure profile calculation and regression analysis. The maximum relative error decreases little while the ratio of critical pressure relative errors lying in the range of ±40% increases after optimization. In contrast, the difference in the average abstract relative error of pressure between original TFM-DEM and DEM is much larger, for the maximum relative error of mass flux and critical pressure are around 25% and 110%. The comparison between the original and optimized TFM-DEM proves that the new critical flow model is accurate in mass flux and can be optimized to raise pressure calculation accuracy. The comparison between the original TFM-DEM and DEM proves that the phase velocity difference is the major source of accuracy improvement in the pressure profile.

Numerical simulation of hydrate flow in gas-dominated undulating pipes considering nucleation and deposition behaviors

The distribution and deposition of hydrates in deep-water gas transportation pipelines are crucial for safety. Current simulations of hydrate flow based on the population balance model have predominantly focused on water-dominant systems and neglect the nucleation and deposition of hydrates. By establishing a model for a hydrate flow in a gas-dominant system that considers the uneven distribution of the liquid film on the wall, hydrate nucleation, gas–liquid mass transfer, particle adhesion and aggregation, and dynamic deposition, we achieved simulation of the entire process of hydrate formation, aggregation, breakage, and deposition. Simulations in undulating pipelines were carried out to investigate the effects of gas velocity, liquid injection, pressure, and pipeline structure on distribution patterns. The results showed increasing the gas velocity enhanced the dispersion of particles and increasing the pressure increased the rate of aggregation. The formation of blocky aggregates posed significant risk in the rear section of the lower-bend pipe.

Comparisons between full molecular dynamics simulation and Zhang's multiscale scheme for nanochannel flows.

In a very small surface separation, the fluid flow is actually multiscale consisting of both the molecular scale non-continuum adsorbed layer flow and the intermediate macroscopic continuum fluid flow. Classical simulation of this flow often takes over large computational source and is not affordable owing to using molecular dynamics simulation (MDS) to model the adsorbed layer flow, if the flow field size is on the engineering size scale such as of 0.01-10mm or even bigger like occurring in micro or macro hydrodynamic bearings. The present paper uses full MDS to validate Zhang's multiscale flow model, which yields the closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. Here, full MDS was carried out for the pressure-driven flow of methane in the nano slit pore made of silicon respectively with the channel heights 5.79nm, 11.57nm, and 17.36nm. According to the number density distribution, the flow areas were respectively discriminated as the adsorbed layer zone and the intermediate fluid zone. The values of the characteristic parameters for Zhang's multiscale scheme were extracted from full MDS and input to Zhang's multiscale flow equations respectively for calculating the flow velocity profile and the volume flow rates of the adsorbed layers and the intermediate fluid. It was found that for these three channel heights, the flow velocity profiles calculated from Zhang's model approximate those calculated from full MDS, while the total flow rates through the channel calculated from Zhang's model are close to those calculated from full MDS. The accuracy of Zhang's multiscale flow model is improved with the increase of the channel height. The recent modification of the optimized potential for liquid simulation (MOPLS) model was used to calculate the interaction force between two methane molecules. In order to calculate the interaction force between the wall atoms and the methane molecules accurately, our previous non-equilibrium multiscale MDS was used. The interaction forces between the methane molecule and the wall atom were obtained from the coupled potential function by the L-B mixing rule when the fluid molecules arrived at near wall. The methane molecule diameter was obtained from the radial distribution function by using equilibrium MDS under the same initial conditions. The local viscosities across the adsorbed layer were obtained from the local velocity profile by using the Poiseuille flow method. The motion equation of the methane molecule was solved by the leapfrog method. The temperature of the simulation system was checked by Bhadauria's method, i.e., the system temperature was rectified by the velocities in the y- and z-directions. The flow velocity distributions across the channel height and the volume flow rates through the channel were also calculated from Zhang's closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate fluid flow. The results respectively obtained from full MDS and Zhang's multiscale flow equations were then compared.