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An Analytical Investigation of Natural Convection of a Van Der Waals Gas over a Vertical Plate
(2021)

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

The paper focuses on a study of turbulence decay in flow with streamwise gradient. For the first time, an analytical solution of this problem was obtained based on the k‐ε model of turbulence in one‐dimensional (1D) approximation, as well as on the symmetry properties of the system of differential equations. Lie group technique enabled reducing the problem to a linear differential equation. The analytical solution enabled parametric studies, which are computationally cheap in comparison to CFD based simulations. The lattice Boltzmann method (LBM) in two‐dimensional approximation (2D) was used to validate the analytical results. Large eddy simulation (LES) Smagorinsky approach was used to close the LBM model. Computations revealed that the rate of turbulence decay is significantly different for the cases of positive and negative streamwise pressure gradient. The further comparisons showed that the analytical solution underpredicts the predictions by the numerical methodology, which can be attributed to the simplified problem statement used to derive the closed‐form analytical solution. Comparisons of calculations with experiments revealed that the theoretical models used in the study underpredict the measurements for flows with a positive pressure gradient. Hence it can be concluded that the LBM technique combined with the LES Smagorinsky model requires the further modification.

The paper focused on an analytical analysis of the main features of heat transfer in incompressible steady-state flow in a microconfusor with account for the second-order slip boundary conditions. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. As a result, novel solutions were obtained for the velocity and temperature profiles, as well as for the friction coefficient and the Nusselt number. These solutions demonstrated that an increase in the Knudsen number leads to a decrease in the Nusselt number. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics. It was also revealed that flow slippage effects on heat transfer weaken with an increase in the Prandtl number.

The paper presents results of the modelling of heat transfer at film boiling of a liquid in a porous medium on a vertical heated wall bordering with the porous medium. Such processes are observed at cooling of high-temperature surfaces of heat pipes, microstructural radiators etc. Heating conditions at the wall were the constant wall temperature or heat flux. The outer boundary of the vapor film was in contact with moving or stationary liquid inside the porous medium. An analytical solution was obtained for the problem of fluid flow and heat transfer using the porous medium model in the Darcy–Brinkman and Darcy–Brinkman–Forchheimer approximation. It was shown that heat transfer at film boiling in a porous medium was less intensive than in the absence of a porous medium (free fluid flow) and further decreased with the decreasing permeability of the porous medium. Significant differences were observed in frames of both models: 20% for small Darcy numbers at Da < 2 for the Darcy–Brinkman model, and 80% for the Darcy–Brinkman–Forchheimer model. In the Darcy–Brinkman model, depending on the interaction conditions at the vapor–liquid interface (no mechanical interaction or stationary fluid), a sharp decrease in heat transfer was observed for the Darcy numbers lower than five. The analytical predictions of heat transfer coefficients qualitatively agreed with the data of Cheng and Verma (Int J Heat Mass Transf 24:1151–1160, 1981) though demonstrated lower values of heat transfer coefficients for the conditions of the constant wall temperature and constant wall heat flux.

Solving problems of detonation control is associated with obtaining detailed information about the gas dynamics accompanying the detonation process. This paper focuses on the dynamics of real gas flow through a plane detonation wave. The influence of real gas parameters on the Chapman–Jouguet detonation process has been studied. The process is described using the Rankine–Hugoniot system of equations. To model the thermodynamic properties of a real gas, the van der Waals equation of state is used. Equations are obtained to determine the ratio of speeds and pressures during the passage of a wave. The influence of van der Waals parameters on changes in the parameters of the detonation process was elucidated. An increase in parameter A slows down the increase in pressure in the detonation wave, and an increase in parameter B enhances it. Differences in the speed of combustion products for ideal and real gases are shown. For an ideal gas, combustion products flow from the detonation front at a critical (sonic) speed. For a van der Waals gas, the speed of combustion products may be greater than the critical one. Moreover, both factors, additional pressure (A) and additional volume (B), lead to acceleration of combustion products. Effects of heat release on the process parameters were elucidated.

The focus of this paper was Jouguet detonation in an ideal gas flow in a magnetic field. A modified Hugoniot detonation equation has been obtained, taking into account the influence of the magnetic field on the detonation process and the parameters of the detonation wave. It was shown that, under the influence of a magnetic field, combustion products move away from the detonation front at supersonic speed. As the magnetic field strength increases, the speed of the detonation products also increases. A dependence has been obtained that allows us to evaluate the influence of heat release on detonation parameters.

Abstract
The paper represents an analysis of convective instability in a vertical cylindrical porous microchannel performed using the Galerkin method. The dependence of the critical Rayleigh number on the Darcy, Knudsen, and Prandtl numbers, as well as on the ratio of the thermal conductivities of the fluid and the wall, was obtained. It was shown that a decrease in permeability of the porous medium (in other words, increase in its porosity) causes an increase in flow stability. This effect is substantially nonlinear. Under the condition Da > 0.1, the effect of the porosity on the critical Rayleigh number practically vanishes. Strengthening of the slippage effects leads to an increase in the instability of the entire system. The slippage effect on the critical Rayleigh number is nonlinear. The level of nonlinearity depends on the Prandtl number. With an increase in the Prandtl number, the effect of slippage on the onset of convection weakens. With an increase in the ratio of the thermal conductivities of the fluid and the wall, the influence of the Prandtl number decreases. At high values of the Prandtl numbers (Pr > 10), its influence practically vanishes.