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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.
The paper focuses on the analytical analysis of the propagation of a normal shock wave in an adiabatic gas flow with nanoparticles. A modified Rankine–Hugoniot model was used for this purpose. A solution is obtained for the Rankine–Hugoniot conditions in a gas flow with different nanoparticle concentrations, which makes it possible to analyze the dynamics of variation of the parameters of this type of flow under a shock wave. The variation of velocity, pressure and entropy production of the adiabatic gas flow during a direct shock wave depending on the concentration of nanoparticles in the gas was depicted graphically. It was revealed that increasing the nanoparticle concentration to φ ~ 0.1 weakens the effect of the shock wave, and then, after passing the zone of minimum parameters, the intensity of the shock wave increases.
Hybrid nanofluids have caught the attention of scholars and investigators in the present technological period due to their improved thermophysical features and the desire to boost heat transfer rates compared to those of conventional fluids. The present paper is mainly concerned with heat transmission in cone-disk geometry in the presence of a magnetic field, activation energy, and non-uniform heat absorption/generation. In this work, the cone-disk (CD) apparatus is considered to have a rotating cone (RC) and a stretching disk, along with iron oxide and cobalt ferrite-based hybrid nanofluid. Appropriate similarity transformations are employed to change the physically modeled equations into ordinary differential equations (ODEs). Heat transfer rates at both surfaces are estimated by implementing a modified energy equation with non-uniform heat absorption/generation. The outcomes illustrated that the inclusion of such physical streamwise heat conduction variables in the energy equation has a significant impact on the well-known conclusions of heat transfer rates. To understand flow profile behavior, we have resorted to the RKF-45 method and the shooting method, which are illustrated using graphs. The findings provide conclusive evidence that wall stretching alters the flow, heat, and mass profile characteristics within the conical gap. The wall deformation caused by disk stretching was found to have a potential impact of modifying the centripetal/centrifugal flow characteristics of the disk, increasing the flow velocity and swirling angles. A rise in activation energy leads to an improved concentration field.
The main objective of this study is to explore the inventive conception of the magnetohydrodynamic flow of a hybrid nanofluid over-porous stretching/shrinking sheet with the effect of radiation and mass suction/injection. The hybrid nanofluid advances both the manufactured nanofluid of the current region and the base fluid. For the current investigation, hybrid nanofluids comprising two different kinds of nanoparticles, aluminium oxide and ferrofluid, contained in water as a base fluid, are considered. A collection of highly nonlinear partial differential equations is used to model the whole physical problem. These equations are then transformed into highly nonlinear ordinary differential equations using an appropriate similarity technique. The transformed differential equations are nonlinear, and thus it is difficult to analytically solve considering temperature increases. Then, the outcome is described in incomplete gamma function form. The considered physical parameters namely, magnetic field, Inverse Darcy number, velocity slip, suction/injection, temperature jump effects on velocity, temperature, skin friction and Nusselt number profiles are reviewed using plots. The results reveal that magnetic field, and Inverse Darcy number values increase as the momentum boundary layer decreases. Moreover, higher values of heat sources and thermal radiation enhance the thermal boundary layer. The present problem has various applications in manufacturing and technological devices such as cooling systems, condensers, microelectronics, digital cooling, car radiators, nuclear power stations, nano-drag shipments, automobile production, and tumour treatments.
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.