Sådhanå (2019) 44:37 Ó Indian Academy of Sciences https://doi.org/10.1007/s12046-018-1035-3Sadhana(0123456789().,-volV)FT3](0123456789().,-volV) A numerical study of natural convection properties of supercritical water (H2O) using Redlich–Kwong equation of state HUSSAIN BASHA1, G JANARDHANA REDDY1,* and N S VENKATA NARAYANAN2 1 Department of Mathematics, Central University of Karnataka, Kalaburagi 585 367, India 2 Department of Chemistry, Central University of Karnataka, Kalaburagi 585 367, India e-mail:
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[email protected] MS received 8 January 2018; revised 2 November 2018; accepted 16 November 2018; published online 25 January 2019 Abstract. In this article, the Crank-Nicolson implicit finite difference method is utilized to obtain the numerical solutions of highly nonlinear coupled partial differential equations (PDEs) for the flow of supercritical fluid (SCF) over a vertical flat plate. Based on the equation of state (EOS) approach, suitable equations are derived to calculate the thermal expansion coefficient (b) values. Redlich–Kwong equation of state (RK-EOS), Peng-Robinson equation of state (PR-EOS), Van der Waals equation of state (VW-EOS) and Virial equation of state (Virial-EOS) are used in this study to evaluate b values. The calculated values of b based on RK-EOS is closer to the experimental values, which shows the greater accuracy of the RK-EOS over PR-EOS, VW-EOS and Virial-EOS models. Numerical simulations are performed for H2O in three regions namely subcritical, supercritical and near critical regions. The unsteady velocity, temperature, average heat and momentum transport coefficients for different values of reduced pressure and reduced temperature are discussed based on the numerical results and are shown graphically across the boundary layer.