Supercritical fluid has been widely applied in many industrial applications.The traditional Reynolds-averaged Navier-Stokes (RANS) equations are directly applied for turbulent flow and heat transfer of the supercritical fluid,ignoring turbulent effect of the thermal physical properties due to the intense nonlinearity.This paper deduces a set of Reynolds-averaged Navier-Stokes equations for supercritical fluid (SCF-RANS equations) to depict turbulent flow and heat transfer of the supercritical fluid taking all the physical parameters as variables.The SCF-RANS equations include many new correlation terms due to fluctuation of the thermal physical properties.Model methods for the new correlation term have been discussed for closing the SCF-RANS equations.Some of them have relatively mature models,while others are completely new and need profound physical theoretical analysis for proposing reasonable models.This paper provides referable information for these new correlations as far as authors know.The SCF-RANS equations not only provide the formulation special for flow and heat transfer of the supercritical fluid,but also represent the most sophisticate form of the RANS equations,for every involved physical property has been considered as variable without any simplification.