Abstarct: In this thesis, numerical simulation of heat transfer and flow analysis of two dimension incompressible nano-fluids are developed using the combination of finite volume and lattice Boltzmann method. The flow and energy distribution functions are disceretized baxsed on cell-cantered scheme. Also, the D2Q9 lattice is used in conjunction with unstructured quadrilateral volumes. To enhance stability, an upwind second order pressure and temperature biasing factors are used as flux correctors on each lattice for flow and energy fluxes, respectively. The fourth-order artificial dissipation terms are taken into account to damp out spurious oscillations. Also, additional lattices at the edge of each boundary cell are introduced, which allow a much better descxription of the actual geometrical shape. These factors with combination of fifth-order Runge-Kutta time marching scheme has improved the accuracy and convergence of the results significantly. In order to demonstrate the temperature field, the double distribution function model is used. The unknown energy distribution function at the boundary node is decomposed into equilibrium and non-equilibrium parts. Then, the non-equilibrium part is approximated with a first order extrapolation of the non-equilibrium part of populations at the neighboring domain cells. This treatment enhances the domain stability and let for a faster convergence. Due to performance of lattice Boltzmann method, it is possible to implement the main factors in enhancement of heat transfer properties such as gravity, drag force, buoyancy, Brownian forces and attraction and repulsion DLVO forces for simulation of nano-fluids. The resulting model has been verified against different fluid and nano-fluid problems at low and moderate Reynolds numbers. Comparing with previous lattice Boltzmann simulations, the proposed approach greatly enhances the computational stability, which demonstrates the robustness of the proposed scheme on two dimensional unsteady flows. The results also indicate that the nano-fluids with low dense nano-particles such have higher velocity than those with high dense. Furthermore, it was found that outside the recirculation zones, nano-particles having high thermal conductivity (such as Ag or Cu) have more enhancements on the Nusselt number. However, within recirculation zones, nano-particles having low thermal conductivity (such as TiO2) have better enhancement on heat transfer.