During this study, the pressure drop and heat transfer coefficient of nanofluids in microchannel heat sink with trapezoidal duct are numerically investigated. The nanofluids based water created by Al2O3 particles in three different volume fractions of 0%, 0.15% and 0.26% are used to analyze their effects on heat transfer and the pressure drop. Under the laminar, steady-state flow conditions, the finite volume method is used to solve the governing equations of heat transfer and momentum. In this investigation, Temperature difference in inlet and outlet of one duct with micro Dimensionless is constant. So, this parameter controlled with heat flux from the bottom microchannel. By changing the heat flux Analysis shows that the nanofluids enhance heat transfer while the Reynolds number and the volume fractions are increasing and it makes to increasing thermal conductivity with lower heat flux in more volume fraction of nanoparticles in the base fluid (water). Pressure drop is remarkable in this study. Too, correlated equations were obtained for Nusselt number and friction factor, and its accuracies were acceptable.