A new thermodynamic computational model has been proposed for the current study, which deals with the free convective supercritical Casson fluid flow past a vertical cylinder. In this model, pressure, temperature and compressibility factor are the critical parameters to govern the thermal expansion coefficient. The present model is based on the Redlich–Kwong equation of state. Comparisons with experimental results and determined values of thermal expansion coefficient for the choice of chemical compound (isobutene) from the present study show great similarity. The chemical compound isobutane has many industrial applications. For instance, in geothermal power plant, supercritical isobutane is employed as a working fluid, it is used in the deactivated (USY alkylation) catalyst regeneration, it is used in heat pumps and many other industrial processes. Furthermore, isobutane finds extensive application as a propellant in foam products and aerosol cans, as a refrigerate gas in freezers and refrigerators, as a feedstock in industries of petrochemical importance, for standardisation of gas mixtures and emission monitoring, etc. In addition, the Casson fluid flow model can be used to study the blood flow rheology, slurry flows, etc. The numerical scheme such as Crank–Nicolson type is demonstrated to simplify the governing nonlinear coupled partial differential equations. The transient results of flow-field variables, coefficients of heat and momentum transport for a Casson fluid under supercritical condition for various values of reduced pressure and reduced temperature are computed and discussed through graphs.