On the correctness of a phenomenological model of equilibrium phase transitions in a deformable elastic medium

1992 ◽  
Vol 3 (2) ◽  
pp. 181-191
Author(s):  
A. M. Meirmanov ◽  
N. V. Shemetov
Keyword(s):  
Mathematical Model ◽  
Continuous Medium ◽  
Equilibrium Phase ◽  
Elastic Solid ◽  
Complementary Energy ◽  
Structure Of Solutions ◽  
Two Phase ◽  
Pure Phase ◽  
The Mathematical Model ◽  
Uniqueness Of A Solution

In this paper we investigate the mathematical model of the equilibrium of a finite volume in ℝn (n = 1,2, 3) of a two-phase continuous medium, under the assumption that each pure phase is an isotropic elastic solid. The main results in this paper are:(i) the existence and uniqueness of a solution of this mathematical model;(ii) a discussion of the stress-strain law associated with the free energy of this two-phase continuous medium, which is multiple-valued due to the non-smoothness of the Gibbs potential (complementary energy);(iii) a description of the structure of solutions in plane strain.

scholarly journals Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Ahmed M. Saad ◽  
Amgad Salama ◽  
Shuyu Sun
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Porous Media ◽  
Magnetic Nanoparticles ◽  
Additional Term ◽  
Flow In Porous Media ◽  
Phase System ◽  
Two Phase ◽  
The Mathematical Model ◽  
Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

Mathematical Modeling of Impingement of an Air Jet in a Liquid Bath

2010 ◽  
Vol 1276 ◽  
Author(s):  
J. Solórzano-López ◽  
R. Zenit ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Free Surface ◽  
Gas Flow ◽  
Two Phase ◽  
Arc Furnaces ◽  
Air Jet ◽  
Image Velocimetry ◽  
Oxygen Gas ◽  
The Mathematical Model

AbstractPhysical and mathematical modeling of jet-bath interactions in electric arc furnaces represent valuable tools to obtain a better fundamental understanding of oxygen gas injection into the furnace. In this work, a 3D mathematical model is developed based on the two phase approach called Volume of Fluid (VOF), which is able to predict free surface deformations and it is coded in the commercial fluid dynamics software FLUENTTM. Validation of the mathematical model is achieved by measurements on a transparent water physical model. Measurements of free surface depressions through a high velocity camera and velocity patterns are recorded through a Particle Image Velocimetry (PIV) Technique. Flow patterns and depression geometry are identified and characterized as function of process parameters like distance from nozzle to bath, gas flow rate and impingement angle of the gas jet into the bath. A reasonable agreement is found between simulated and experimental results.

Regularity of Dust Distributing in Fully Mechanized Caving Face and Negative Pressure Spray Dust-Settling Technology

2012 ◽  
Vol 246-247 ◽  
pp. 624-628 ◽  
Author(s):  
Wen Nie ◽  
Wei Min Cheng
Keyword(s):  
Mathematical Model ◽  
Negative Pressure ◽  
Lagrangian Model ◽  
Dust Particles ◽  
Phase Flow ◽  
Dust Pollution ◽  
Two Phase ◽  
Fluent Software ◽  
The Mathematical Model ◽  
Hydraulic Supports

The mathematical model of solving two-phase flow of gas and dust particles was built by established the k-ε equation. Moreover, by basing on Eulerian-Lagrangian model and using FLUENT software, the diffusion rule of dust pollution in full-mechanized caving face was confirmed. Based on negative pressure spray dust-settling mechanism, negative pressure spray technology was developed between hydraulic supports, in drawing opening position and shearer, and it was determined by the optimal spray pressure for 4 MPa. After negative pressure spray technology was applied in fully mechanized caving face, the dust concentration was down significantly.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
pp. 09
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

scholarly journals Modelling and thermodynamic analysis of ejector flow for application at design and off design operating conditions in an ejector air conditioner

2021 ◽  
Vol 12 (3) ◽  
pp. 3455-3467
Author(s):  
Anoop Kumar. M Et.al
Keyword(s):  
Mathematical Model ◽  
Heat Input ◽  
Flow Analysis ◽  
Cooling Capacity ◽  
Two Phase ◽  
Entrainment Ratio ◽  
Air Conditioning System ◽  
The Mathematical Model ◽  
Minimum Quality

Ejector flow in an ejector air conditioning system using R245fa is analysed for entrainment ratio and potential refrigeration effect, at varying temperature and heat input conditions in  the generator ranging from 60C to 100C and 2kW to 5kW respectively. The effect of varying generator temperature in cooling capacity of the system when the vapour ejectoris operating at design evaporator and condenser temperatures of 10C and 35C respectively is investigated. The mathematical model of the vapour ejector with optimum area ratio is developed and validated. A critical entrainment ratio of 0.385 is obtained corresponding to generator temperature of 100C. When the generator temperature is varied from 60C to 100C, the cooling capacity range from 0.3kW at generator heat input of 2 kW to 1.78 kW at 5 kW heat input. Further, the operation of the system is analysed for off design operating condition corresponding to reduced heat input rate in the generator. In that case the state of primary refrigerant flow in ejector inlet will be two phase and a mathematical model for two-phase ejector flow is developed and validated. Ejector flow analysis revealed the minimum quality of flow at ejector inlet to maintain adequate backpressure for condensation to occur range from 0.72 at 60C to 0.22 at 100C. The corresponding refrigeration refrigeration effect produced is less than the respective designed operation value byits  12.2% to 8%. Further, analysis of the system shows that at least 7 kW heat input at 100C is required to produce 1 ton of cooling effect. Ejector flow in an ejector air conditioning system using R245fa is analysed for entrainment ratio and potential refrigeration effect, at varying temperature and heat input conditions in  the generator ranging from 60C to 100C and 2kW to 5kW respectively. The effect of varying generator temperature in cooling capacity of the system when the vapour ejectoris operating at design evaporator and condenser temperatures of 10C and 35C respectively is investigated. The mathematical model of the vapour ejector with optimum area ratio is developed and validated. A critical entrainment ratio of 0.385 is obtained corresponding to generator temperature of 100C. When the generator temperature is varied from 60C to 100C, the cooling capacity range from 0.3kW at generator heat input of 2 kW to 1.78 kW at 5 kW heat input. Further, the operation of the system is analysed for off design operating condition corresponding to reduced heat input rate in the generator. In that case the state of primary refrigerant flow in ejector inlet will be two phase and a mathematical model for two-phase ejector flow is developed and validated. Ejector flow analysis revealed the minimum quality of flow at ejector inlet to maintain adequate backpressure for condensation to occur range from 0.72 at 60C to 0.22 at 100C. The corresponding refrigeration refrigeration effect produced is less than the respective designed operation value byits  12.2% to 8%. Further, analysis of the system shows that at least 7 kW heat input at 100C is required to produce 1 ton of cooling effect.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

Modelling the Wear Process of Inhomogeneous Bodies

2005 ◽  
Author(s):  
I. G. Goryacheva
Keyword(s):  
Mathematical Model ◽  
Phase Composition ◽  
Contact Mechanics ◽  
Two Phase ◽  
Wear Process ◽  
Substrate Interface ◽  
Inhomogeneous Bodies ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Local Hardening

The approaches of contact mechanics are used to evaluate the evolution of the contact characteristics in wear process of inhomogeneous bodies (coated bodies, two-phase composition, bodies with inclusions, etc.). The mathematical model is formulated and used to study the kinetics of the wear process depending on the parameters of inhomogeneity such as size and density of inclusions, waviness at the coating-substrate interface, local hardening parameters, etc.

scholarly journals Numerical model of heat transfer in three phases of the poroelastic medium

2016 ◽  
Vol 38 (2) ◽  
pp. 53-59
Author(s):  
Anna Uciechowska-Grakowicz ◽  
Tomasz Strzelecki
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Solid Phase ◽  
Irreversible Thermodynamics ◽  
Pore Fluid ◽  
Gas Filtration ◽  
Two Phase ◽  
Phase Medium ◽  
Thermal Consolidation ◽  
The Mathematical Model

Abstract In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

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