**6. Conclusions**

The study has dealt with the problem of the steady-state natural convection of a van der Waals gas near a vertical heated plate. The problem was solved analytically based on an integral method. The novel solution was obtained for the first time using a novel, simplified form of the van der Waals equation of state proposed in our work [28]. To the authors' knowledge, such a solution has not yet been published in the literature.

The effects of the dimensionless Wa*<sup>a</sup>* and Wa*<sup>b</sup>* numbers on the normalized Nusselt number in the real gas compared to the ideal gas were estimated. The analysis of the calculation results showed that, with an increase in the Wa*<sup>a</sup>* number (which characterizes the additional pressure in the real gas), the normalized Nusselt number increases. This is due to an increase in the lifting force and velocity in the boundary layer. The effect of additional volume, which manifests itself in an increase in the Wa*<sup>b</sup>* number, causes a deterioration in the conditions for interaction between gas molecules and the wall. This is accompanied by a decrease in the Archimedes force and flow rate in the boundary layer, which leads to a weakening of heat transfer when compared with an ideal gas.

It was therefore shown that the change in the heat transfer intensity is due to effects that are considered by the van der Waals equation of state, but not by the ideal gas equation.

**Author Contributions:** Analytical investigation, A.A.A.; conceptualization, A.A.A. and I.V.S.; methodology, A.A.A. and I.V.S.; validation and formal analysis, A.A.A., I.V.S., and N.P.D.; writing—original draft preparation, review and editing, A.A.A., I.V.S., and Y.Y.K.; writing of the final manuscript, A.A.A. and I.V.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research contributions of A.A.A. and Y.Y.K. were funded via the program of research grants of the NAS of the Ukraine "Support of priority for the state scientific research and scientific and technical (experimental) developments" 2020–2021. Project 1.7.1.892: "Development of scientific and technical fundamentals of heat of mass transfer intensification in porous media for materials of building designs and the thermal engineering equipment".

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
