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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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Internal-force-driven flows in which the force acting on channel cross sections have a perfect uniform distribution create a fully developed velocity field even the axial distribution of these forces is non-uniform. In this situation, firstly the driving force with non-uniform axial distribution can be removed temporarily and then one can use an equivalent axial uniform body forcealternatively throughout the channel. In this case, although the distribution and the driving force change but the resulting velocity profiles remain unchanged. The main advantage of thisreplacement is thatthe solution of the equations in the 3-D geometries canbe converted to a 2-D solution using Poisson equationin the channel cross section. After determining the velocity distribution in the cross section, one caninverselycalculate the actual pressure distribution easily. This will be done by resuming the real axial force. One of the applications of this simplification is that the simulation of MHD channel flows can be carried out easily.Good agreement between the results of the new solution method and the results ofthe perfect solutions shows that the present method with enough accuracy can be used for prediction of velocity and pressure fields in microfluidic networks.Consequently the heavy costs of 3-D analysis are reduced considerably.

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Flow analysis in the microchannels has recently accelerated dramatically. In this paper, numerical investigation of Joule heating effects on the electroosmotic flow through a microchannel with the trapezoidal cross-section and constant wall temperature have been presented. The energy equation for the temperature distribution, Navier–Stokes equation for the velocity distribution and a Poisson equation for the electric potential distribution have been solved by using the finite-volume method in a system curvilinear coordinates. Thermophysical properties such as the dynamic viscosity and electric conductivity vary with temperature. Results show that by increasing the Joule number, the temperature, velocity and mass flow rate increase with constant EDL number. Without considering the Joule heating effects, the increments of EDL number causes in the mass flow rate to increase, but with considering the joule heating effects, the increasing of mass flow rate continues until EDL number 15 and after that the flow rate decreases. On the other hand, when the cross-section is reduced by the increasing aspect ratio, the joule number remains constant while the mean temperature decreases.

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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 the present paper,by performing a two-dimensional simulation,the heat transfer from a hot cylinder to a cold square enclosure has been studied parametrically and the consequent effect of changing in cylinder diameter has been investigated. The 2-D governing equations have been solved using the finite volume method and TDMA in an ADI procedure for different diameters of cylinder inside a square enclosure with a constant characteristic length for two different Rayleigh numbers of 104 and 105.Results showed that the patterns of streamlines, isotherms and the Nusselt number values depend strongly on the Rayleigh number and also ratio of cylinder diameter to characteristic length of enclosure (2R/H). In this case, the centers of vortices created around the cylinder appear in bottom half of enclosure in 2R/H=0.4 for Ra=104 and in 2R/H= 0.5 for Ra=105. Moreover, it is observed that increasing the Rayleigh number and 2R/H ratio, the heat transfer rate from the enclosure is also increased.For example,in 2R/H=0.5, by increasing the Rayleigh number from 104 to 105, the average Nusselt enhances about 30 percent of its initial value and in Ra=105, by changing the 2R/H ratio from 0.2 to 0.5, the average Nusselt climbs almost 35 percent of its initial value.

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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 paper the effect of electromagnetic field lengths to change simultaneously is simulated on the temperature distribution and flow velocity of a MHD micropump considering the lateral electromagnetic diffusive regions. The geometry of flow is a two-dimensional channel between two parallel plates and the flow is assumed to be incompressible, steady and laminar. In addition, thermophysical properties such as the dynamic viscosity and electric conductivity of fluid are considered to be the function of temperature. The governing equations of both flow and electromagnetic fields have been solved using the finite volume numerical method a comprehensive analytical solution including velocity, pressure and temperature filed distributions has been derived for an special case. The numerical results show that by changing the length of electromagnetic fields and considering the fluid (water) properties as a function of temperature, for flow in a 1000 mm2 cross-section channel, magnetic field intensity 0.025 Tesla and electric field strength 20 volt/mm, the flow rate reaches 250 mLit/s and the mean cup temperature from 25 0C at entrance reaches to 40 0C at the exit of channel. However for constant properties, the flow rate and the mean cup temperature reach 70 mLit/s and more than 60 0C respectively.

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In this paper, a new immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate heat transfer problems with constant heat flux boundary condition. In this method, the no-slip boundary condition is enforced via implicit velocity correction method and the constant heat flux boundary condition is implied considering the difference between the desired heat flux and the estimated one. The velocity correction represented as a forcing term is added to Boltzmann equation and for temperature correction, a heat source/sink term is introduced to energy equation. Elimination of sophisticated grid generation process, simplicity and effectiveness while keeping the accuracy, are the main advantages of the proposed method. Using the developed method, natural convection around a hot circular cylinder with constant heat flux in an enclosure with cold walls has been simulated at Rayleigh numbers of 103–106. Moreover, effects of diagonal position of cylinder on the flow and heat transfer patterns and local Nusselt number distribution on the surface of cylinder and walls of enclosure have been investigated. The obtained results show that the location of maximum local Nusset number is extremely depended on the diagonal position of the cylinder. According to the results of this simulation, it can be said that the present method is able to imply accurately the constant heat flux boundary condition.

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In this paper, the mixing efficiency in electroosmotic flow inside a micromixer is simulated numerically for different states of non-uniform wall Zeta potential. The geometry of flow is a two-dimensional channel between two parallel plates and the flow is assumed to be incompressible, steady and laminar. The governing equations, including a Laplace equation for the distribution of external electric potential, a Poisson equation for the distribution of electric double layer potential, the Nernst-Planck equation for the distribution of ions concentration, the species convection-diffusion equation, the modified Navier-Stokes equations for the fluid flow field, have been solved using the finite volume numerical method. In order to validate the numerical results, the analytical results of an ideal electroosmotic flow in where throughout the walls are charged is compared with the obtained numerical results. The numerical results show that, by linear-ascending, linear-descending and parabolic changes of the wall Zeta potential at the middle length of the microchannel, the mixing efficiency increases compared to a constant Zeta potential. For the cases of linear changing of Zeta potential, the mixing efficiency increases to 86% and for parabolic change of Zeta potential the mixing efficiency increases to 75%, while the Zeta potential is constant at middle length the maximum of mixing efficiency increases to 64%. In the case that only the upper wall at middle length is charged, the results show that a vortex region is created in the flow. This vortex region causes a maximum (100%) mixing efficiency.

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Polymer Electrolyte Membrane Fuel Cells (PEMFCs) has been widely used in recent decades due to operating at low temperature with high energy density. Water management is one of the main challenges for the development and commercialization of PEMFCs, which has a significant impact on their performance. The behavior of liquid water in the PEMFCs is very important. In this study a pore scale model is used to investigate liquid water transport in the gas diffusion layer (GDL) of PEMFCs. The GDL layer generated by randomly placing circular solid particles. The pseudo-potential lattice Boltzmann (LB) proposed by shan and chen is used to simulate two phase flow. The code was validated in three modes and is verified correctly then, the effect of three pore size particles, porosity coefficient and hydrophobicity of the GDL on the water transfer has been investigated. The results show that, over time, the amount of saturation in the GDL increases and ultimately reaches a constant value. In addition to by reducing the diameter of the particles, the amount of saturation and the number of breakthrough sites decreased, which increases the oxygen penetration.Also, the amount of local water saturation in the catalyst layer (CL) interface and the GDL tends toward one, indicating that oxygen molecules in these regions should be dissolved in water and then fed to the CL. In addition to, the amount of liquid water inside the porous layer decreases with increasing hydrophobicity

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