Analysis of supercritical free convection in Newtonian and couple stress fluids through EOS approach

Abstract

Supercritical natural convection of Newtonian and couple stress fluids about an isothermal cylinder employing the equation of state (EOS) model is addressed in the current numerical investigation. At first, a suitable equation for heat expansion rate based on Redlich–Kwong EOS (RK-EOS), Soave modification EOS (Soave-EOS), Peng-Robinson EOS (PR-EOS) and Virial EOS (Virial-EOS) is obtained under the supercritical region in terms of compressibility parameter, pressure and temperature. The evaluated heat expansion rate values based on these equations of state and local NuX have been validated with practical values and found that the RK-EOS is an appropriate EOS to predict the natural convection characteristics of supercritical fluid (nitrogen) when compared to other models. The governing couple stress liquid circulation equations over a vertical cylinder are computationally solved by employing the finite difference technique. The current numerical study shows that the steady-state and transient velocity fields of a supercritical Newtonian fluid are considerably higher than couple stress fluid and these velocity profiles increase with an increase in reduced pressure and decrease with an increase in reduced temperature. Further, the thermal field is suppressed with magnifying reduced pressure and enhanced with amplifying reduced temperature. Using the present study, it can be concluded that the RK-EOS is considered to be an appropriate EOS to govern the thermal parameters of supercritical Newtonian and couple stress fluids.