scholarly journals On the Nusselt Solution of a Nonisothermal Two-Fluid Inclined Film Flow

2009 ◽  
Vol 2009 ◽  
pp. 1-8
Author(s):  
Jürgen Socolowsky
Keyword(s):  
Film Flow ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Stationary Problem ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Free Boundary Value Problems ◽  
Two Fluid

Nonisothermal viscous two-fluid flows occur in numerous kinds of coating devices. The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In the present paper we are concerned with a particular problem of coupled heat and mass transfer. Marangoni convection is incorporated, too. The solvability of a corresponding stationary problem is discussed. The obtained results generalize previous results for a similar isothermal problem.

ON THE EXISTENCE AND UNIQUENESS OF TWO‐FLUID CHANNEL FLOWS

2005 ◽  
Vol 9 (1) ◽  
pp. 67-78 ◽  
Author(s):  
J. Socolowsky
Keyword(s):  
Stokes Equations ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Density Ratios ◽  
Steady State Solutions ◽  
Two Fluid

iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique. Dvieju, tekančiu kanale, klampiu skysčiu srauto uždavinys iškyla taikant ivairias skirtingu rušiu paviršiu padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačiu kraštiniu uždaviniu su laisvu paviršiumi Navje-Stokso lygtims. Straipsnyje nagrinejamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo sroves parametru kaip ir nuo klampumo ir tankio santykio stacionarus sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.

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 ON NONISOTHERMAL TWO‐FLUID CHANNEL FLOWS

2007 ◽  
Vol 12 (1) ◽  
pp. 143-156
Author(s):  
Jajanek Sokolowsky
Keyword(s):  
Thermocapillary Convection ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Stationary Problems ◽  
Two Fluid

Two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations or their modifications. In this paper we are concerned with the so‐called Boussinesq‐approximation of the coupled heat‐ and mass transfer. Thermocapillary convection is included. The solvability of two related stationary problems is discussed. The solution techniques of both problems are quite different. The obtained results generalize previous results for similar isothermal problems.

scholarly journals Thermo-solutal convection with Soret effect

2021 ◽  
Author(s):  
Md. Abdur Rahman
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Soret Effect ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Solutal Convection ◽  
Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

scholarly journals Thermo-solutal convection with Soret effect

2021 ◽  
Author(s):  
Md. Abdur Rahman
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Soret Effect ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Solutal Convection ◽  
Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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