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In this paper, cavity flow is simulated numerically. Forced convection in different Reynolds numbers between 100 and 5000 is simulated. Different and complex thermal boundary conditions are applied and various parameters are calculated numerically. Up and down walls are in constant temperature and left and right walls are thermal insulation in the first thermal boundary condition. The Left and the down walls are in constant temperature and the temperature of the up and the right walls changes linearly in the second thermal boundary condition. For the third thermal boundary condition, the left and the down walls are in constant temperature and the temperature of the up and the right walls changes sinusoidally. For this purpose, a code is written in the FORTRAN software. Streamlines, isotherms, local and mean Nusselt number are obtained and shown in different figures and one table. Grid independence is surveyed and some obtained results are validated with other researchers' work. In these simulations, the Prandtl number is considered to be 0.71 because of the air's Prandtl number. For time discretization, a fifth-order Runge-Kutta is used and for convective fluxes, the averaging scheme with fourth-order damping term is used.

In this paper, forced, free, and mixed convections in incompressible flow were studied numerically. Nano-sized Al2O3, TiO2, MgO, and ZnO ceramics with water were considered as nano-fluids. Simulations were carried out for cavity flow with different boundary conditions and aspect ratios, as well as flow over stationary and rotating cylinders. The mean Nusselt number ( ̅̅̅̅ ) and friction factor for cavity flow and ̅̅̅̅ for flow over a cylinder were compared for different nano-fluids. A new code was developed in FORTRAN 95 for numerical simulations. A fifth-order Runge-Kutta method for time discretization and a characteristicbased scheme for convective terms were used in this code. The averaging scheme on the secondary cells is used to obtain viscous fluxes. Primary results are validated with other researcher's outputs. Results showed that MgO-water and ZnO-water had maximum and minimum heat transfer rates, respectively. Moreover, maximum and minimum shear stresses were recorded for the Al2O3-water and TiO2-water, respectively. Using nano-fluid increases the heat transfer rate between 15 and 37 percent depending on the Richardson number and selected nano-particles.

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