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- Natural convection heat transfer in a square cavity induced by heated plate is investigated using the lattice Boltzmann method. A suitable forcing term is represented in the Boltzmann equation. With the representation, the Navier-Stokes equation can be derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Top and bottom of the cavity are adiabatic; the two vertical walls of the cavity have constant temperatures lower than the plate’s temperature. The flow is assumed to be two-dimensional. Air is chosen as a working fluid (Pr=0.71). The study is performed for different values of Grashof number ranging from 103 to 105 for different aspect ratios and position of heated plate. The effect of the position and aspect ratio of heated plate on heat transfer are discussed. With increase of the Grashof number, heat transfer rate is increased in both vertical and horizontal position of the plate. The obtained results of the lattice Boltzmann method are validated with those presented in the literature.

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In this paper the effects of the inlet fluid temperature on the electro-osmotic flow pattern in a two-dimensional microchannel with constant walls temperature is investigated with solving the governing equations by the Lattice Boltzmann method. The main objective of this research is to study the effects of temperature variations on the distribution of ions and consequently internal electric potential and velocity field. For make possible to use the Boltzmann ion distribution equation, cup mean temperature for every cross section of the microchannel is used. At the used Lattice Boltzmann method, LBGK model for modeling the Boltzmann collision function and the Zou-He boundary conditions method for velocity field has been used. Wang model for solving the Poisson-Boltzmann and He-Chen model for solving the energy equation has been used. The results show that, with increase the temperature difference between the inlet flow and the walls, the electro-osmotic flow rate increases. Also, observed that with decrease the external electric potential and the electric double layer thickness and increase the temperature difference at the inlet zone of the microchannel, a region with return flow is formed which can be used for controlling the internal flow pattern.

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In this paper, steady incompressible flow patterns inside two-dimensional triangle, trapezoidal, semi-circular and arc-square cavities with moving boundaries are studied via lattice Boltzmann method. The effects of geometry of the cavities on flow pattern are also discussed. The effects of Reynolds number on the flow patterns in triangular, semi-circular and arc-square cavities are studied. Also, for arc-square cavity, it can be observed that by changing the size of top and bottom walls which means a change in the size of cut arcs from the circular, different flow patterns are formed. The influences of the side angles at constant Reynolds number on the flow patterns in the trapezoidal cavities are investigated. It is found out that the vortex near the bottom wall of trapezoidal cavity breaks up into two smaller vortices as side angles increase. The obtained results of the lattice Boltzmann method and the presented boundary condition are compared with those presented in the literature. It can be seen that the lattice Boltzmann method is a suitable method for flow simulation in the mentioned cavities.

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Since the lattice Boltzmann method (LBM) originally carries out the simulations on the regular Cartesian lattices; curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved boundary problems is extrapolation of macroscopic properties at boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation in boundary condition potentially causes abrupt changes in particle distributions. Therefore, a new curved boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to other physical fields. The proposed treatment is tested against several well established problems. Numerical results show that the present treatment is of second-order accuracy, and has well-behaved stability characteristics.

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In this paper, natural convection heat transfer inside an enclosure which is partially filled with porous layer is reported using lattice Boltzmann method. Generalized equations in modeling flow in porous media have been employed which are coupled with the lattice Boltzmann formulation of the momentum and energy equations. The present study investigates the effect of position of porous layer on heat transfer rate for different dimensionless parameters, such as Rayleigh number, Darcy number and porosity of the porous layer. In addition, a modified Rayleigh number is presented as an effective parameter which affects the degree of penetration of the fluid into the porous layers. The obtained results showed that the heat transfer rate in the case of vertical layer is more than that of horizontal porous layers.

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Abstract- In this paper, two-dimensional natural convection heat transfer in semi ellipse cavities is investigated using lattice Boltzmann method. The Prandtl number is taken as 0.71 that corresponds to that of air. Heat transfer and flow pattern are predicted at various Rayleigh numbers ranging from 104 to 106 for different aspect ratios. By increasing of the aspect ratio, the heat transfer rate in the cavity is increased for low Rayleigh numbers, but it is decreased for high Rayleigh numbers. The obtained results of the lattice Boltzmann method are validated with those presented in the literature and show that the lattice Boltzmann method can simulate heat transfer and flow pattern in complex cavities. Analysis of heat transfer in a semi-ellipse cavity using second order boundary condition on curved surfaces is among the novelties of the present work.

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In the present study, the motion and deformation of a red blood cell in the incompressible viscous flow is simulated using the lattice Boltzmann method combined with the immersed boundary method. The lattice Boltzmann method is used to solve the flow field, whereas the immersed boundary method is used to simulate the dynamics of the red blood cell. The red blood cell is considered as an elastic boundary immersed in the fluid domain. The main advantage of the lattice Boltzmann method is that it solves only an algebraic equation. In the immersed boundary method the fluid domain is descretized using a regular Eulerian grid, while the immersed boundary is represented in the Lagrangian coordinates. The Eulerian grid points would not necessarily coincide with the Lagrangian points. The fluid- immersed boundary interaction is modeled using an appropriate form of delta function. The effects of the no-slip condition are taken into account via a forcing term added to the Navier-Stokes Equations (here the lattice Boltzmann equation). In the present study, the tank-treading motion of a red blood cell in the viscous shear flow is simulated. The results are found to be in good agreement with the available experimental and numerical ones.

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Two-phase flow modeling has been the subject of many investigations. However, fewer studies are corresponded for two-phase flow within a porous medium, because of additional complications. In this paper, two-phase flow with the density and viscosity ratio of 1, within a porous medium is simulated by Shan and Chen model. Due to inherent limitations and weaknesses of this approach in an independent control of surface tension, investigation of parameters such as Reynolds number, Froude and Weber is not applicable. However, porous medium parameters such as Darcy number and contact angle could be studied by changing the porous medium and contact angle. Competition between opposing forces against the drop and the capillary effect because of increasing the number of particles in the porous media is described using the Darcy number. Also the effect of the contact angle between liquid-gas phases and the solid surface is evaluated on the droplet penetration inside the porous medium.

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In the present work a new lattice Boltzmann (LB) framework has been developed to study the electroosmotic flows in a 2-D flat microchannel. The governing equations are presented in the continuum model, while a set of equivalent equations in LB model is introduced and solved numerically. In particular, the Poisson and the Nernst–Planck (NP) equations are solved by two new lattice evolution methods. In the analysis of electroosmotic flows, when the convective effects are not negligible or the Electric Double Layers (EDLs) have overlap, the NP equations must be employed to determine the ionic distribution throughout the microchannel. The results of these new models have been validated by available analytical and numerical results. The new framework has also been used to examine the electroosmotic flows in single and parallel heterogeneous microchannels.

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In this study, the collision of two drops using Lattice Boltzmann numerical method in two-phase flow has been investigated. The simulation for incompressible fluid is based on the model represented by Lee. The prominent feature of this model is to simulate fluids with high density ratios. Thus, the model has easily been compared with experimental results and its validity has been investigated. Using this simulation, the variation of non-dimensional parameters such as Weber number, Reynolds number, Impact parameter, density ratio, kinematic viscosity ratio, diameter ratio and velocity ratio of two drops were studied. Considering the results, it was shown that the Reynolds number, density ratio and relative velocity ratio have no effect on separation or coalescence of drops collision; while the variation of Weber number, Impact Parameter and kinematic viscosity ratio results in separation or coalescence. Moreover, by increase in Weber number, Reynolds number or density ratio or decrease in kinematic viscosity, the number of oscillations and the time needed to reach equilibrium increases. Likewise, the amplitude of oscillation and the deformation of the drops increase when the Weber number, Reynolds number or density ratio rise or the kinematic viscosity lowers.

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In this paper, the immersed boundary-lattice Boltzmann method has been employed to simulate non-Newtonian flow around curve boundaries. The pressure base lattice Boltzmann equations have been used to solve the Eulerian domain to estimate proper pressure gradient in the Poiseuille flow. In addition Immersed boundary method (IBM) utilizes a discrete set of force density is also used to represent the effect of boundary on flow domain. In addition to simulate the real physical dominate problem and study the right effects of non-Newtonian fluid properties, scaling parameters have been introduced to notice the relationship between physical and lattice variables. At First, the capability of present method is examined for simulating the power-law fluid flow around a confined circular cylinder and the results show good agreement with previous study. In the following, the power-law fluid flow around elliptical cylinder in a channel is investigated for three aspect ratios eta=1,1.5,2 and for 5

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In present paper the Inamuro Model based on free energy approach of the Lattice Boltzmann Method (LBM) was used to simulate the motion of bubble and coalescence of two bubbles under buoyancy force. By combining the Tanaka and Inamuro models, three-dimensional model of Inamuro was used in two-dimension for decreasing the computational cost. Firstly it was ensured that the surface tension effect and Laplace low for two density ratio 50 and 1000 were properly implemented. Secondly in next step, effect of governing dimensionless numbers problem such as Etvos number and Morton number on Reynolds number and terminal shape of bubble were investigated. Different flow patterns in various dimensionless numbers were obtained and by changing the dimensionless number, terminal change of bubble’s shape was seen. Finally, motion of two bubbles and terminal shape of coalescence of two bubbles were studied in different dimensionless number, which shape of first bubble was same to single bubble, but it was seen that second bubble experienced various shapes due to its location in wake of first bubble and less difference pressure on two sides of this bubble.

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Emulsion consists of drops of one liquid dispersed into another immiscible liquid, is a novel technique for producing monodisperse droplets. The aim of this research is using the Lattice Boltzmann Method (LBM) to simulate two-phase flows in micro-channels to access the emulsification process. To this approach, The Index-Function Model proposed by He, is used to simulate drop formation in emulsification process in a co-flowing micro-channel with a complex geometry and three inlets. The simulation is performed to investigate the mechanism of drop generation due to dripping and jetting modes and the mode between them. Index function model, which is a new reliable model to evaluate two-phase flows, is applied to track the motion and deformation of the interface between the two immiscible fluids. Accuracy of our results is examined by two well-known basic analytical models including Relaxation of a rectangular drop and coalescence of two static droplets. Our results indicate good agreements with analytical data. The dimensionless numbers such as Capillary and Velocity ratio were used. The Capillary number is one of the most important dimensionless numbers in determination of fluid flow characteristics in micro-channels. The simulations reproduce dripping, widening jetting and narrowing jetting simultaneously in a coflowing microchannel in agreement with the experimental ones. This indicates that index function LBM model has a good accuracy and high stability to simulate this kind of flow.

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In the present Paper, solution methods for simulating compressible flows and shock wave simulation by using Lattice Boltzmann Method(LBM) and simulation of shock wave in the bubble with a moving boundary is evaluated. The standard LBM is found to be incapable of predicting compressible flows and confront instabilities in high Mach number flows. But with some efforts that has been made in recent years, new models for stable solutions of the compressible equations are established. Modified Lax–Wendroff finite difference scheme that has stabale solutions has been used for discretizing Lattice Boltzmann equation. In this study models based on the compressible Euler and compressible multispeed Navier-Stokes to simulate compressible lattice Boltzmann method have been used. The dynamics of compressible bubble busing Rayleigh-Plesset equation have been obtained. Simulation of shock wave in the bubble with other computational fluid dynamics methods has been carried out, However, due to the weakness of the Lattice Boltzmann method for compressible flow, no effort to study the physic of this phenomena has been done with this method. The purpose of this simulation is to achieve a distribution of thermodynamic properties through the radius while collapsing and eventually forming the Sonoluminescence phenomena that caused by the collision of shock waves in the center of the bubble to one other,with lattice boltzmann method.

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In this paper, natural convective heat transfer of nanofluids in a uniform magnetic field between the square cavity and inner cylinder, was simulated via Lattice Boltzmann Method. The inner cylinder in square shape, diamond, and circular has been examined. Square cavity walls and inner cylinder surfaces are at a constant cold and warm temperature, respectively. The flow, temperature, and magnetic field is calculated with solving flow, temperature, and magnetic distribution functions simultaneously. D2Q9 lattice arrangement for each distribution function is used. The results clearly show the behavior of fluid flow and heat transfer between the cavity and the cylinder. The results have been validated with available valid results showing relatively good agreement. The effects of Rayleigh number, Hartmann number, void fraction and type of nanoparticles on natural convective heat transfer are investigated. This study shows that for all three geometries used with the same void fraction, type of nanofluid, and Rayleigh number, natural convective heat transfer decreases with Hartmann number. Also, when Hartmann number was had fixed, natural convective heat transferwas increased with Rayleigh number. Thus, to select the right geometry for optimum natural convective heat transfer, our needs to pay special attention to Hartmann and Rayleigh numbers. In addition, viod fraction and type of nanofulid can affect heat transfer directly.

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In this paper, based on lattice-Boltzmann method (LBM), the steam condensation and growth of a droplet on the horizontal cold wall and falling down on vertical wall has been simulated. The Lee’s LBM model which is stable in the high density and viscosity ratios is used. This method is accompanied with solving the temperature equation and adding a phase change source term. The Lee model is based on Cahn-Hilliard theory which is assumed to be incompressible flow and therefore the velocities of the flow are divergence-free. when phase change occurs this condition will not be satisfied. A phase change source term is added on the interface of gas and liquid phase. Solution of temperature field in a passive scalar method of solving the flow field is separated and Boussinesq assumption would be influence the flow field of the temperature field. The density ratio of 25 is considered to be in this paper which is density ratio of steam and water. The model is extended to two dimensions (D2Q9) to simulate droplet condensation. The simulation results are compared in various grids. The effects of gravitational acceleration, equilibrium contact angle, the cold wall and also the mass conservation, have been investigated separately. Finally the stream field for the different time step has been analyzed.

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In this paper 2D numerical model is used to study the effect of depth of airway surface liquid (ASL) on the muco-ciliary transport. An immersed boundary-lattice Boltzmann method is used to solve the momentum equation. In this study mucus is considered as the viscoelastic fluid an Oldroyd-B model is used as the constitutive equation of it. Immerse boundary method is used to study the propulsive effect of the cilia and also the effects of mucus– periciliary layer interface. Our results show that mean mucus velocity becomes maximized when the PCL depth is equal to the standard value of it i.e. 6 μm. By increasing or decreasing the depth of PCL or increasing the depth of mucus layer, mean mucus velocity reduces. Our study also shows that mucus viscosity ratio can play an important role on the muco-ciliary clearance. It means that by increasing the Newtonian part of mucus viscosity or by decreasing elastic contribution of the mucu, mean mucus velocity increases significantly. So reducing mucus velocity results from changing ASL depth can be completely modified by increasing the Newtonian part of mucus viscosity.

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In the current study, the motion and deformation of an elastic membrane in a two-dimensional channel with and without a groove is simulated using a combined lattice Boltzmann-immersed boundary method. The lattice Boltzmann method is used to solve the fluid flow equations and the immersed boundary method is used to incorporate the fluid-membrane interaction. The elastic membrane is considered as a flexible boundary immersed in the flow domain. In the immersed boundary method, the membrane is represented in the Lagrangian coordinates while the fluid domain is discretized on a uniform fixed Eulerian grid. The interaction between the fluid and the membrane is modeled using Dirac delta function. The effects of no-slip boundary condition are enforced by addition of a forcing term to the lattice Boltzmann equation. Depending on the flow rate, the initial location and stiffness of the elastic membrane, the size of the groove, the membrane only rotates inside the groove or the flow moves it out of the groove. The results are presented in terms of flow velocity and pressure fields and membrane configuration at different times. Comparison between the present results and the available numerical and experimental ones shows good agreement between them.

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The purpose of this paper is to investigate theLow-Density Lipoproteins (LDL) mass transfer in vessel walls using the Lattice Boltzmann Method (LBM). High Schmidt number of LDL leads to numerical instability of LBM.In order to solve this problem, LBM and finite volume method (FVM) are combined.In this hybrid method, the blood velocity field is solved by LBM using the single relaxation time, SRT, model and FVM has been used for LDL concentration equation. LBM is able to simulate flow and mass transfer for the Schmidt number, Sc, up to 3000 only if the time consuming multi relaxation time is used. However, the purposed hybrid method suggested in this article can be used to solve the problem for Sc as high as 107. Good agreement between our results obtained from the hybrid simulation and the available results in the literature and noticeable decrease in CPU time compared with when the LBM is used for both flow and mass transfer, indicates the ability of the hybrid method.Finally, the hybrid methodis used to simulate the mass transfer of LDL particles and investigate the effective factors for increasing the surface concentration, such as the size of LDL particles, wall suction velocity, wall shear stress, Newtonian and non-Newtonian fluids behavior and change of concentration boundary layer with various Schmidt number.

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Numerous models have been proposed to incorporate various equations of state (EOS) into the pseudo potential model. This paper presents an investigation of different EOS types based on the Gong and Cheng model in multiphase-single component flows by the lattice Boltzmann method. Primarily, it is conducted to investigate eight EOS’s classified in four categories; the Shan- Chen EOS, the cubic EOS, the non-cubic EOS, and the cubic and non-cubic combination EOS. The results show that each EOS type results in producing relatively similar spurious currents and has a maximum achievable density ratio. Although by choosing a proper beta parameter for every EOS the simulation errors decrease dramatically, our results show it is impossible to set a constant parameter for the non-cubic EOS. Therefore, a new equation is introduced to predict an efficient beta for the cubic and the Shan- Chen EOS’s. It is also found that the non-cubic, cubic, and non-cubic and cubic combination EOS’s have a wider temperature range and larger density ratios respectively. Hence, we determine a temperature dependent function for the beta parameter prediction instead of using a fixed value for the non-cubic EOS. The results are noticeably in better agreement with those of the Maxwell construction (theoretical results).