scholarly journals Cosmological Models with Two Fluids. II. Conformal and Conformally Flat Metrics

1972 ◽  
Vol 25 (1) ◽  
pp. 83 ◽  
Author(s):  
CBG McIntosh ◽  
JM Foyster
Keyword(s):  
Cosmological Models ◽  
Conformally Flat ◽  
Elementary Functions ◽  
Two Fluids ◽  
Usual Form ◽  
Walker Metric ◽  
Similar Solutions ◽  
Conformally Flat Metrics ◽  
Two Fluid

Similar solutions to those in Part I are given for two-fluid cosmological models when the Robertson?Walker metric in its usual form is replaced by "conformal" and "conformally flat" forms. In these cases the solutions can be written in terms of elementary functions when (3v1?2)/(3v2?2) = 1?m?1, m = 1,2,3,... The relation of these solutions to one-fluid solutions with k = � 1 is also discussed.

scholarly journals Cosmological Models with Two Fluids. I. Robertson?Walker Metric

1972 ◽  
Vol 25 (1) ◽  
pp. 75 ◽  
Author(s):  
CBG McIntosh
Keyword(s):  
Equation Of State ◽  
Cosmological Constant ◽  
Cosmological Models ◽  
Fluid Models ◽  
Elementary Functions ◽  
Anisotropic Models ◽  
Two Fluids ◽  
All Solutions ◽  
Walker Metric ◽  
Two Fluid

Exact solutions in terms of elementary functions are given for flat, homogeneous and isotropic, relativistic cosmological models which contain two fluids, each with an equation of state of the form where p is the pressure, ? is the density, is a constant, and For other forms of v1/v2, the relevant solution is given in terms of a hypergeometric function. The cases when one of the v?s is equal to 2/3 or 2 are analogous to models with a Robertson?Walker metric with k = � 1 and to anisotropic models of the type discussed by Jacobs respectively. All solutions for the two-fluid models can be written in terms of elementary functions when v1 = 0, which is analogous to a cosmological constant. The fact that all two-fluid solutions with v1 = 2/3 which can be written in terms of elementary functions are given means that all such one-fluid solutions with k = � 1 are given.

Transit cosmological models in FRW universe under the two-fluid scenario

2019 ◽  
Vol 16 (01) ◽  
pp. 1950007 ◽  
Author(s):  
Pryanka Garg ◽  
Rashid Zia ◽  
Anirudh Pradhan
Keyword(s):  
Cosmological Models ◽  
Observational Cosmology ◽  
Accelerating Universe ◽  
Frw Universe ◽  
Two Fluids ◽  
Slowing Down ◽  
Two Fluid Scenario ◽  
The Universe ◽  
Two Fluid ◽  
Friedmann Robertson Walker

This paper is an attempt to revisit the Friedmann–Robertson–Walker (FRW) cosmological models under the new scenario of observational cosmology, which has established that the current universe is expanding with an increasing rate, in contrast to the earlier belief that the rate of expansion is constant or slowing down. This paper represents a model which encompasses both, earlier decelerating and the current accelerating universe, passing through a transition phase. The universe is assumed to be filled with two fluids, barotropic and dark energy. We have considered two cases; first, when these fluids are assumed to be non-interacting and second, when they interact with each other. Some physical, kinematic and geometric properties of the model are also discussed along with the acceptability and stability of the solution. The results found are very compatible with the established results as well as recent observations.

scholarly journals Topology design of two-fluid heat exchange

2020 ◽  
Author(s):  
Hiroki Kobayashi ◽  
Kentaro Yaji ◽  
Shintaro Yamasaki ◽  
Kikuo Fujita
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Heat Transfer Rate ◽  
Design Variable ◽  
Pressure Loss ◽  
Transfer Rate ◽  
Maximum Heat ◽  
Variable Field ◽  
Two Fluids ◽  
Two Fluid

Abstract Heat exchangers are devices that typically transfer heat between two fluids. The performance of a heat exchanger such as heat transfer rate and pressure loss strongly depends on the flow regime in the heat transfer system. In this paper, we present a density-based topology optimization method for a two-fluid heat exchange system, which achieves a maximum heat transfer rate under fixed pressure loss. We propose a representation model accounting for three states, i.e., two fluids and a solid wall between the two fluids, by using a single design variable field. The key aspect of the proposed model is that mixing of the two fluids can be essentially prevented. This is because the solid constantly exists between the two fluids due to the use of the single design variable field. We demonstrate the effectiveness of the proposed method through three-dimensional numerical examples in which an optimized design is compared with a simple reference design, and the effects of design conditions (i.e., Reynolds number, Prandtl number, design domain size, and flow arrangements) are investigated.

scholarly journals Simulation of Free Surface Compressible Flows via a Two Fluid Model

2008 ◽  
Author(s):  
Fre´de´ric Dias ◽  
Denys Dutykh ◽  
Jean-Michel Ghidaglia
Keyword(s):  
Free Surface ◽  
Wave Breaking ◽  
Compressible Flows ◽  
Fluid Model ◽  
Three Dimensional ◽  
Two Fluids ◽  
Equation Of States ◽  
Two Fluid Model ◽  
Velocity Pressure ◽  
Two Fluid

The purpose of this communication is to discuss the simulation of a free surface compressible flow between two fluids, typically air and water. We use a two fluid model with the same velocity, pressure and temperature for both phases. In such a numerical model, the free surface becomes a thin three dimensional zone. The present method has at least three advantages: (i) the free-surface treatment is completely implicit; (ii) it can naturally handle wave breaking and other topological changes in the flow; (iii) one can easily vary the Equation of States (EOS) of each fluid (in principle, one can even consider tabulated EOS). Moreover, our model is unconditionally hyperbolic for reasonable EOS.

scholarly journals Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Ismahan Binshati ◽  
Harumi Hattori
Keyword(s):  
Asymptotic Behavior ◽  
Fourier Transform ◽  
Global Existence ◽  
Maxwell Equations ◽  
Decay Rates ◽  
Asymptotic Behavior Of Solutions ◽  
Two Fluids ◽  
The Fourier Transform ◽  
Rates Of Decay ◽  
Two Fluid

We study the global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler–Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical, and we also add friction between the two fluids. In addition, we discuss the rates of decay of Lp−Lq norms for a linear system. Moreover, we use the result for Lp−Lq estimates to prove the decay rates for the nonlinear systems.

scholarly journals On-wall and interior separation in a two-fluid boundary layer

2019 ◽  
Vol 119 (1) ◽  
pp. 1-21
Author(s):  
Sergei N. Timoshin ◽  
Pallu Thapa
Keyword(s):  
Boundary Layer ◽  
Pressure Variation ◽  
Flow Reversal ◽  
Reversed Flow ◽  
Two Fluids ◽  
Transverse Pressure ◽  
Fluid Boundary ◽  
Interior Flow ◽  
High Reynolds ◽  
Two Fluid

Abstract A two-fluid boundary layer is considered in the context of a high Reynolds number Poiseuille–Couette channel flow encountering an elongated shallow obstacle. The flow is laminar, steady and two-dimensional, with the boundary layer shown to have the pressure unknown in advance and a specified displacement (a condensed boundary layer). The focus is on the detail of the flow reversal triggered by the obstacle. The interface between the two fluids passes through the boundary layer which, in conjunction with the effects of gravity and distinct densities in the two fluids, leads to several possible topologies of the reversed flow, including a conventional on-wall separation, interior flow reversal above the interface, and several combinations of the two. The effect of upstream influence due to a transverse pressure variation under gravity is mentioned briefly.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

scholarly journals A Relativistic Algorithm with Isotropic Coordinates

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Ngubelanga ◽  
S. D. Maharaj
Keyword(s):  
Spherically Symmetric ◽  
Conformally Flat ◽  
Einstein Field Equations ◽  
Elementary Functions ◽  
Field Equations ◽  
Isotropic Coordinates ◽  
New Exact Solutions ◽  
Symmetric Spacetimes ◽  
Particular Solution ◽  
Conformally Flat Metric

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contain isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.

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