The significance of research on the specifications of the supercritical fluids becomes more evident with respect to the increase of their application in different food, chemical, polymer, oil, and gas industries. One of the major specification, is the coefficient of thermal expansion (β) where the ideal gas model was used in most of the processes in which this component is applied; the weakness of this model is that it is unable to make an accurate prediction of this parameter within the range of critical point. For this reason, in this study to determine the coefficient of thermal expansion, Redlich–Kwong equation of state is used and a new relation as a function of temperature, pressure, and compressibility is obtained. Comparing behavior of the curves obtained from this relation with experimental data, exhibits a favorable consistency. Moreover, natural convection heat transfer of the supercritical fluid in a vertical channel at constant temperature walls conditions were considered numerically. The governing equations were solved using the finite-volume method (FVM) and based on the SIMPLE Algorithm. After validation with the earlier studies. Then, the flow and heat transfer characteristics based on the obtained coefficient of thermal expansion were compared with the ideal gas assumptions. Finally, the trend of change in heat transfer coefficient away from the critical point was studied.