A numerical investigation of transient natural convective heat transfer to isobutane in the supercritical region

Current research article investigates numerically the time-dependent laminar free convective supercritical fluid (SCF) flow past a vertical cylinder. Two new thermodynamic models for the SCF have been considered. Based on these proposed models, in SCF two new equations for thermal expansion coefficient is obtained on the basis of Redlich-Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). It is shown that the thermal expansion coefficient is a function of temperature, pressure and compressibility factor. The evaluated analytical values of volumetric thermal expansion coefficient using RK-EOS are closer to the experimental values which confirm the greater accuracy of proposed RK-EOS as compared to that of VW-EOS. The set of non-dimensional partial differential equations for the SCF flow over a vertical cylinder are obtained and they are time-dependent, highly non-linear and coupled. Therefore, these complex equations are solved using the computational techniques such as Crank-Nicolson implicit finite difference scheme. Numerical simulations are performed for a well-known chemical compound like isobutane in the region of its critical point. The results concerning the velocity, temperature, and average momentum and heat transport coefficient profiles across the boundary layer are shown graphically and discussed for various values of control parameters. From the obtained graphical data, it is clear that temperature plays a prominent role than the pressure under supercritical condition.