scholarly journals Mathematical modeling of three-layer flows with evaporation based on exact solutions

2021 ◽  
Vol 2119 (1) ◽  
pp. 012049
Author(s):  
E V Laskovets
Keyword(s):  
Mathematical Modeling ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Silicone Oil ◽  
Longitudinal Velocity ◽  
Stationary Flow ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gas System

Abstract The stationary flow in the “liquid-liquid-gas” system in a horizontal channel with solid impermeable upper and lower walls is investigated. Mathematical modeling in each of the layers of the system is based on exact solutions of a special type of Navier-Stokes equations in the Boussinesq approximation. The processes of vapor evaporation or condensation at the liquid-gas interface are modeled using the boundary conditions of the problem. In the upper layer the thermal diffusion effect and the effect of diffusional thermal conductivity are taken into account. Examples of three-layer flows for the “silicone oil - water - air” system are given. The influence of the thermal regime at the boundaries of the system and the thickness of the upper layer on the longitudinal velocity and temperature distribution is considered.

scholarly journals Construction of Exact Solution Describing Three-layer Flows with Evaporation in a Horizontal Channel

2021 ◽  
pp. 57-68
Author(s):  
Ekaterina V. Rezanova
Keyword(s):  
Exact Solution ◽  
Gas Flow ◽  
Stokes Equations ◽  
Silicone Oil ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Layer System ◽  
Soret And Dufour Effects ◽  
Navier Stokes Equations ◽  
Liquid Evaporation

The paper considers the flow in a three-layer system "liquid–liquid–gas" in a horizontal chan- nel with solid impermeable walls.The evaporation process at the thermocapillary interface of the liquid and gas is taken into account. The Soret and Dufour effects are taken into account in the upper layer filled with a gas-vapor mixture. The system of Navier-Stokes equations in the Boussinesq approximation is used as a mathematical model. A temperature regime is set on the channel walls. Liquid evaporation is modeled using the conditions at the liquid-gas interface. Exact solution of a special type describing the flow in a three-layer system is constructed. The velocity profiles are presented on the example of the "silicone oil–water–air" system for various values of gas flow rate, longitudinal temperature gradients at the system boundaries, thicknesses of liquid and gas-vapor layers

scholarly journals Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Lyapunov Analysis ◽  
Velocity Difference ◽  
Navier Stokes Equations ◽  
Previous Hypothesis ◽  
Kolmogorov Theory

The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity differenceΔuris derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics ofΔurand adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.

On the Generalized Navier-Stokes Equations

2003 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Ahmed Salem
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hankel Transforms ◽  
Fourier Sine ◽  
Special Cases

In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.

Modeling Of The Alloying Substances Distribution In The Melt During Pulsed Induction Heating Of The Substrate

2017 ◽  
Vol 12 (2) ◽  
pp. 111-118
Author(s):  
Vladimir Popov
Keyword(s):  
Induction Heating ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Empirical Formulas ◽  
Metal Solidification ◽  
Navier Stokes Equations ◽  
High Frequency Electromagnetic Field ◽  
Melting And Solidification

Under study is the applicability of the high-frequency electromagnetic field impulse for metal heating and melting with a view to its subsequent alloying. The processes of heating, phase transition, heat and mass transfer in the molten metal, solidification of the melt are considered with the aid the proposed mathematical model. The substrate surface is covered with a layer of alloying substances. The distribution of the electromagnetic energy in the metal is described by empirical formulas. Melting and solidification of the metal is considered at the Stephan’s approximation. The flow in the liquid is described by the Navier – Stokes equations in the Boussinesq approximation. According to the results of numerical experiments, the flow structure in the melt and distribution of the alloying substances was evaluated versus the characteristics of induction heating

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