Natural convection on a vertical plate with variable heat flux in supercritical fluids

The present article investigates laminar free convection with uniform or non-uniform prescribed surface heat flux over a vertical flat plate in supercritical fluid, numerically. A new equation for thermal expansion coefficient in a supercritical fluid is derived based on Redlich–Kwong equation of state as a function of pressure, temperature and the compressibility factor. Calculated values of thermal expansion coefficient have been compared with the experimental results which show better accuracy in comparison with van der Waals ones. The governing systems of partial differential equations were solved numerically using the finite difference method. The local Nusselt number was calculated and plotted as a function of the local Rayleigh number. Using supercritical fluids in constant heat flux free convection, decrease wall temperature in comparison with under critical fluids. It was observed that positive and negative slopes of surface heat flux distribution increases and decreases the heat transfer coefficient, respectively.

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► Natural convection of supercritical fluids was studied, numerically.
► In contrast with other works, thermal expansion coefficient was variable in our work.
► Thermodynamic model has been developed to represent thermal expansion coefficient.
► Using supercritical fluid in constant heat flux, decreases wall temperature.
► Results show improvement of heat transfer in linearly increasing heat flux.