Thermodynamic analysis of natural convection supercritical water flow past a stretching sheet using an equation of state approach

Abstract

The present numerical study examines the free convection heat transfer characteristics of supercritical water flow past a stretching sheet. A suitable equation for the thermal expansion coefficient in a supercritical fluid region is derived based on the equation of state (EOS) approach in terms of compressibility factor, pressure, and temperature. In the present study, the Redlich–Kwong equation of state (RK-EOS) is used to calculate the thermal expansion coefficient in the supercritical region. The values of the thermal expansion coefficient calculated through RK-EOS lies close to the NIST data values when compared to the other equations of state like the Van der Waals equation of state and ideal gas EOS. Also, the behaviour of Nusselt number is studied to characterize the heat transfer characteristics of supercritical water. However, the equations governing the supercritical fluid flow past a stretching sheet are coupled and nonlinear in nature. Hence, the Runge–Kutta fourth-order integration scheme with shooting technique is used to solve these equations. Numerical computations are performed for supercritical water under the influence of various control parameters. Similarity solutions are obtained in terms of flow profiles in the supercritical fluid region. The present study reports that the normal velocity profile decreases and the temperature field increases for increasing values of reduced pressure and reduced temperature. Also, the axial velocity profile shows the dual behaviour for increasing values of unsteady parameter, reduced temperature, and reduced pressure in the supercritical boundary layer region. Furthermore, the component of the normal velocity profile decays for increasing values of the unsteady parameter in the supercritical fluid region. The calculated values of the thermal expansion coefficient using RK-EOS lies in the proximity of NIST data values when compared to Van der Waals and ideal gas equations of state. Also, the local skin-friction coefficient decreases for increasing values of reduced pressure and reduced temperature. Furthermore, the magnitude of local heat transfer rate increases with increasing values of unsteady parameter. The RK-EOS is the suitable EOS approach for predicting the free convection properties of water in a supercritical region.