# A numerical study of natural convection properties of supercritical water (H_{2}O) using Redlich–Kwong equation of state

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## 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 (\( \beta \)) 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 \( \beta \) values. The calculated values of \( \beta \) 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 \( {\text{H}}_{2} {\text{O}} \) 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.

## Keywords

Supercritical water Crank-Nicolson scheme RK-EOS PR-EOS virial-EOS VW-EOS correlation## Notes

### Acknowledgements

The first author Hussain Basha would like to thank Maulana Azad National Fellowship programme, University Grants Commission, Government of India, Ministry of Minority Affairs, MANF (F1-17.1/2017-18/MANF-2017-18-KAR-81943) for the Grant of research fellowship and to the Central University of Karnataka for providing the research facilities. NSV Narayanan thanks DST-SERB for the partial financial support through the research Grant (EMR/2016/000236). The authors wish to express their gratitude to the reviewers who highlighted important areas for improvement in this article. Their suggestions have served specifically to enhance the clarity and depth of the interpretation in the manuscript.

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