Transient Flow and Heat Transfer Characteristics of non-Newtonian Supercritical Third-Grade Fluid (CO2) past a Vertical Cylinder

Abstract

Abstract The present study deals with the time-dependent natural convective supercritical third-grade fluid flow past a vertical cylinder. A new thermodynamic model for the supercritical carbon di-oxide (CO2) has been derived. In this model the thermal expansion coefficient is characterized as a function of pressure, temperature and compressibility factor. This model uses the Redlich-Kwong equation of state (RK-EOS). The numerically calculated thermal expansion coefficient values of CO2 are validated with available experimental results. The governing non-linear coupled partial differential equations are solved by using Crank-Nicolson method. The obtained numerical data is described in terms of velocity, temperature, skin-friction and Nusselt number through the graphs and tables for the different set of physical parameters. It is observed that the unsteady velocity is an increasing function of reduced pressure and reduced temperature; whereas it is a decreasing function with respect to third-grade fluid parameter. The temperature field is enhanced near the critical point for the increasing values of third-grade fluid parameter. In supercritical fluid region for the increasing values of reduced pressure and reduced temperature, the skin-friction values are magnified against time. Also, the average heat transfer rate decreases for increasing values of third-grade fluid parameter.