The effect of density variation caused by temperature difference of cooling air and a free disk on the heat transfer of the disk was simulated numerically.The difference of heat transfer between compressible and incompressible cooling air was compared by the local Nusselt number of the free disk.The following conclusions can be drawn on a comparative basis: the relative difference of the local Nusselt number is dominantly controlled by dimensionless local temperature difference

regardless of the influence of the distribution curve exponent of surplus temperature

dimensionless maximal temperature difference and rotating Reynolds number.A correlation formula of relative difference of local Nusselt number and dimensionless local temperature difference was presented by fitting numerical data.