ИСТИНА

In [Maslov, V.P., Myasnikov, V.P., Danilov, V.G.], the filtration of a heated gas (thermal convection in a porous medium) was considered, and a "lock-in" effect of the flow was discovered: when the heat release rate exceeds a certain critical value, the gas does not flow through the medium, and its temperature increases infinitely. When a liquid flow is heated in a cylinder (at high pressures), a heat release crisis can also occur, which is similar to a smoothed effect of the "lock-in" type of thermal convection in a porous medium. If Poiseuille flow is established in the cylinder, the average velocity over the cross-section (flow rate) satisfies a law of motion of the Darcy's law type, that is, the liquid flow rate obeys the same equations of motion as the filtration velocity of a liquid (gas) in a porous medium. In [Maslov, V.P., Myasnikov, V.P., Danilov, V.G.], the thermal conductivity of the gas was neglected, and the flow in a vertical cylinder with its upper base open to the atmosphere was considered (the pressure is specified at the inlet and outlet of the cylinder). In addition, the ideal gas equation of state was investigated. In this work, this result is generalized to the case of the van der Waals equation of state. Another result is related to the formulation where all quantities are specified at the beginning of the pipe (which corresponds to flow in a pipe considered as part of a pipeline). In this case, the system is solved for any value of heat release, but as the heat release approaches critical values, the temperature begins to increase rapidly, which reflects the same "lock-in" effect in a smoothed manner. The dependence of the critical heat release on the flow parameters is investigated. A comparison of the obtained theoretical values with experimental data shows good agreement. The research is supported with the financial support of the Ministry of Science and Higher Education of the Russian Federation in the framework of a scientific project under agreement No. 075-15-2025-013 by St. Petersburg State University as part of the national project “Science and Universities” in 2025.