An Analytical Investigation of Natural Convection of a Van Der Waals Gas over a Vertical Plate

Andriy A. Avramenko,Margarita M. Kovetskaya,Igor V. Shevchuk

doi:10.3390/fluids6030121

Andriy A. Avramenko, Margarita M. Kovetskaya + Show 1 more

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https://doi.org/10.3390/fluids6030121

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Abstract

The study focused on a theoretical study of natural convection in a van der Waals gas near a vertical plate. A novel simplified form of the van der Waals equation derived in the study enabled analytical modeling of fluid flow and heat transfer. Analytical solutions were obtained for the velocity and temperature profiles, as well as the Nusselt numbers. It was revealed that nonlinear effects considered by the van der Waals equation of state contribute to acceleration or deceleration of the flow. This caused respective enhancement or deterioration of heat transfer. Results for a van der Waals gas were compared with respective computations using an ideal gas model. Limits of the applicability of the simplified van der Waals equations were pinpointed.

Highlights

For most engineering applications of gases, the ideal gas model can be used with quite high accuracy
Our objective is to look into the effects of the van der Waals equation of state on the modeling of natural convection and compare it with the case where natural convection is simulated using the ideal-gas equation of state
A novel simplified form of the van der Waals equation derived here enabled an analytical solution of the fluid flow and heat transfer problem

Summary

Introduction

For most engineering applications of gases, the ideal gas model can be used with quite high accuracy. Applications that require using real-gas models are processes near the condensation point of gases, critical points, at very high pressures, etc. Hydrogen fuel tanks [1] or ethylene polymerization reactors [2] operate at high system pressure levels. Effects occur that cannot be described by an ideal gas model. Gas density and the tank volume for the compressed gas cannot be estimated with sufficient accuracy. Tank filling can be simplified to a throttling valve where the Joule–Thomson effect occurs, which describes an adiabatic isenthalpic throttling accompanied with a drastic reduction of pressure and temperature [1]. Water vapor in steam power plants and refrigerant vapor in refrigerators cannot be treated as ideal gases [3]

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