Abstract. In this study we have numerically investigated the mixed convection heat transfer over an isothermal vertical plate into a supercritical fluid. First, an equation for the thermal expansion coefficient was derived as a function of the temperature, the pressure, the Redlich-kwong constants and the compressibility factor. The trend of the curves obtained with this equation and with values from tables of thermodynamic properties was similar and they diverge at critical point. These features confirmed the validity of equation obtained in this work. Then, the governing systems of partial differential equations are solved numerically using the finite difference method. The local Nusselt number was then calculated and plotted as a function of the local Rayleigh number. It was observed that the curves corresponding to supercritical conditions are notably above of the line corresponding to the classic correlation, which means that the heat transfer considerably increases in the critical region. A parametric study is also performed in order to illustrate the influence of the Richardson number which is known as the mixed convection parameter on the velocity and temperature profiles. It is observed that Buoyancy forces can enhance the surface heat transfer rate when they assist the forced convection, and vice versa

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