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

**A. A. Avramenko 1, I. V. Shevchuk 2,\*, Yu. Yu. Kovetskaya <sup>1</sup> and N. P. Dmitrenko <sup>1</sup>**


**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.

**Keywords:** natural convection; van der Waals gas; analytical solution

**Citation:** Avramenko, A.A.; Shevchuk, I.V.; Kovetskaya, Y..Y..; Dmitrenko, N.P. An Integral Method for Natural Convection of Van Der Waals Gases over a Vertical Plate. *Energies* **2021**, *14*, 4537. https:// doi.org/10.3390/en14154537

Academic Editor: Artur Bartosik

Received: 23 June 2021 Accepted: 24 July 2021 Published: 27 July 2021

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