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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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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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The aim of this paper was to study the thermophoresis effect on the deposition of nano-particles from diesel engine exhaust after the dilution tunnel using a computational modeling approach. Dilution tunnel was used in order to dilute the exhaust gas to the extend that was suitable for the measurement systems. The Lagrangian particle tracking method was used to model the dispersion and deposition of nano-particles. For the range of studied particle diameters (from 5 to 500 nm), the Brownian, thermophoresis, gravity and Saffman Lift forces are considered. After verifying the code, the importance of different forces was evaluated. Due to the temperature gradient between the exhaust gas and the pipe walls, particular attention was given to include the thermophoresis force in addition to the other forces acting on nano-particles. The results showed that for the range of nano-particle diameters studied, the Brownian force was the dominant force for particle deposition. Furthermore, the thermophoresis force was important even for relatively low temperature gradient and cannot be ignorable especially for larger particles. The maximum thermophoresis effect occurred for 100 nm particles. The gravity had negligible effects on nano-particle deposition and can be ignorable for particles with diameter less than 500 nm. The Saffman lift also had negligible effects and its effect was noticeable only for the deposition of 500 nm particles. The results of this paper could provide an understanding of two-phase flow emission from diesel engines especially after the dilution tunnel.