The main objective of this study is to investigate the fluid flow and the heat transfer characteristics of nanofluids using multi-phase thermal LBM and to realize theenhancement of heat transfer characteristics considered in the Brownian motion. In multi-phase, fluid component($H_2O$) is driven by Boussinesq approximation, and nanoparticles component by the external force gravity and buoyancy. The effect of Brownian motion as a random movement is modified to the internal velocity of nanoparticles(Cu). Simultaneously, the particles of both the phases assume the local equilibrium temperature after each collision. It has been observed that when simulating $H_2O$-Cu nanoparticles, the heat transfer is the highest, at the particle volume fraction 0.5% of the particle diameter 10 nm. The average Nusselt number is increased approximately by 33% at the particle volume fraction 0.5% of the particle diameter 10 nm when compared with pure water.