Application of lattice Boltzmann method for simulation of nanofluid natural convection in a square cavity with a hot obstacle

In this paper natural convection of nanofluid around a hot obstacle simulates in a square cavity with east and west cool walls and an adiabatic wall in north and a hot wall in south by Lattice Boltzmann Method. Flow is quiet and non-compressible and nanofluid is water-Tio2. We use D2Q9 LBM for velocity and fluid temperature. The purpose of this study is investigation of heat transfer around a hot obstacle in a square cavity and the effect of Rayleigh number, obstacle dimension, volume fraction of nanofluid, cavity dimensions, surface ratio and various models of computing heat transfer conductivity coefficient and viscosity coefficient on Nusselt number. This investigat is done for the first time. The results show that, by increasing of Rayleigh number and volume fraction, average of Nusselt number will increase. The average of Nusselt number will increase when obstacle dimensions increase to 0.5L but it will decrease when the obstacle dimensions increase to 0.7L. Vortexes will create in 0.8L and it causes to increase of heat transfer. By reduplicating the obstacle width heat transfer is better than reduplicating the obstacle length. The average of Nusselt number increases by increasing of cavity’s length and it will decrease by increasing of cavity’s wide. All results are equal in Hamilton-crosser and Maxwell- Garnett model when the surface ratio is one. But heat transfer will increase by decreasing surface ratio. The average of Nusselt Number in Wang model is less than Nusselt Number in Brinkman model.