An Integral Method for Natural Convection of Van Der Waals Gases over a Vertical Plate

Abstract

This paper focuses on a study of natural convection in a van der Waals gas over a vertical heated plate. In this paper, for the first time, an approximate analytical solution of the problem was obtained using an integral method for momentum and energy equations. A novel simplified form of the van der Waals equation for real gases enabled estimating the effects of the dimensionless van der Waals parameters on the normalized heat transfer coefficients and Nusselt numbers in an analytical form. Trends in the variation of the Nusselt number depending on the nature of the interaction between gas molecules and the wall were analyzed. The results of computations for a van der Waals gas were compared with the results for an ideal gas.

Numerical Heat Transfer and Fluid Flow: A Review of Contributions to the Special Issue

“…Recent interest in the liquefaction of natural gas, which occupies only 1/600 of its volume, is due to the fact that it is easier and more economical to transport and store [18][19][20]. Some researchers stressed that 'the development of small-scale energy in the coming years is expected to be associated with the widespread use of liquefied natural gas, which is recognized as one of the most promising types of energy carriers' [21]. By taking into account the real thermophysical properties of the gas, Avramenko et al [21] analysed the method for solving steady-state natural convection of van Der Waals gas near a vertical heated plate.…”

“…Some researchers stressed that 'the development of small-scale energy in the coming years is expected to be associated with the widespread use of liquefied natural gas, which is recognized as one of the most promising types of energy carriers' [21]. By taking into account the real thermophysical properties of the gas, Avramenko et al [21] analysed the method for solving steady-state natural convection of van Der Waals gas near a vertical heated plate. The authors proposed a novel simplified form of equations in analytical form for real gases, enabling the estimation of the effects of the dimensionless van der Waals parameters on the normalized heat transfer coefficient and Nusselt number.…”

“…Using the integral method for the momentum and energy equations, they obtained an approximate analytical solution. The authors demonstrated changes in heat transfer intensity, which are due to effects that are considered by the van der Waals equation of state, but not by the ideal gas equation [21].…”