---

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.

---

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.