On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces

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Abstract

Possible natural transport mechanisms in cubical and shallow cavities with different heating conditions (from below or from the side) are investigatedby means of numerical solution of the non-linear model equations and multiprocessor computations. Attention is focused on a variety of three-dimensional steady effects that can arise in such configurations in the case of low-Pr liquids (silicon melt) even for relatively small values of the temperature gradient due to localized boundary effects and/or true instabilities of the flow. Such aspects are still poorly known or completely ignored owing to the fact that most of the existing experiments focused on the subsequent onset of oscillatory flow, or on the case of transparent (Pr >> 1) liquids. The influence of bothbuoyancy and surface tension forces is considered. The role played by the geometrical constraints and degrees of freedom in determining the three-dimensional structure of the flow field is discussed. Some effort is devotedto elucidate the results within the framework of existing (state-of-the-art) theories and to illustrate the deviation of results pertaining to a real three-dimensional geometry with respect to earlier two-dimensional models.
LanguageEnglish
Pages1-19
Number of pages19
JournalFluid Dynamics and Materials Processing
Volume1
Issue number1
DOIs
Publication statusPublished - 2005

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Steady flow
Containers
Heating
Liquids
Silicon
Thermal gradients
Surface tension
Flow fields
Geometry
Experiments

Keywords

  • Marangoni flow
  • buoyancy convection
  • three-dimensional steady flows
  • non-linear models
  • numerical solutions

Cite this

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title = "On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces",
abstract = "Possible natural transport mechanisms in cubical and shallow cavities with different heating conditions (from below or from the side) are investigatedby means of numerical solution of the non-linear model equations and multiprocessor computations. Attention is focused on a variety of three-dimensional steady effects that can arise in such configurations in the case of low-Pr liquids (silicon melt) even for relatively small values of the temperature gradient due to localized boundary effects and/or true instabilities of the flow. Such aspects are still poorly known or completely ignored owing to the fact that most of the existing experiments focused on the subsequent onset of oscillatory flow, or on the case of transparent (Pr >> 1) liquids. The influence of bothbuoyancy and surface tension forces is considered. The role played by the geometrical constraints and degrees of freedom in determining the three-dimensional structure of the flow field is discussed. Some effort is devotedto elucidate the results within the framework of existing (state-of-the-art) theories and to illustrate the deviation of results pertaining to a real three-dimensional geometry with respect to earlier two-dimensional models.",
keywords = "Marangoni flow, buoyancy convection, three-dimensional steady flows, non-linear models, numerical solutions",
author = "Marcello Lappa",
year = "2005",
doi = "10.3970/fdmp.2005.001.001",
language = "English",
volume = "1",
pages = "1--19",
journal = "Fluid Dynamics and Materials Processing",
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TY - JOUR

T1 - On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces

AU - Lappa, Marcello

PY - 2005

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N2 - Possible natural transport mechanisms in cubical and shallow cavities with different heating conditions (from below or from the side) are investigatedby means of numerical solution of the non-linear model equations and multiprocessor computations. Attention is focused on a variety of three-dimensional steady effects that can arise in such configurations in the case of low-Pr liquids (silicon melt) even for relatively small values of the temperature gradient due to localized boundary effects and/or true instabilities of the flow. Such aspects are still poorly known or completely ignored owing to the fact that most of the existing experiments focused on the subsequent onset of oscillatory flow, or on the case of transparent (Pr >> 1) liquids. The influence of bothbuoyancy and surface tension forces is considered. The role played by the geometrical constraints and degrees of freedom in determining the three-dimensional structure of the flow field is discussed. Some effort is devotedto elucidate the results within the framework of existing (state-of-the-art) theories and to illustrate the deviation of results pertaining to a real three-dimensional geometry with respect to earlier two-dimensional models.

AB - Possible natural transport mechanisms in cubical and shallow cavities with different heating conditions (from below or from the side) are investigatedby means of numerical solution of the non-linear model equations and multiprocessor computations. Attention is focused on a variety of three-dimensional steady effects that can arise in such configurations in the case of low-Pr liquids (silicon melt) even for relatively small values of the temperature gradient due to localized boundary effects and/or true instabilities of the flow. Such aspects are still poorly known or completely ignored owing to the fact that most of the existing experiments focused on the subsequent onset of oscillatory flow, or on the case of transparent (Pr >> 1) liquids. The influence of bothbuoyancy and surface tension forces is considered. The role played by the geometrical constraints and degrees of freedom in determining the three-dimensional structure of the flow field is discussed. Some effort is devotedto elucidate the results within the framework of existing (state-of-the-art) theories and to illustrate the deviation of results pertaining to a real three-dimensional geometry with respect to earlier two-dimensional models.

KW - Marangoni flow

KW - buoyancy convection

KW - three-dimensional steady flows

KW - non-linear models

KW - numerical solutions

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DO - 10.3970/fdmp.2005.001.001

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SP - 1

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JO - Fluid Dynamics and Materials Processing

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JF - Fluid Dynamics and Materials Processing

SN - 1555-256X

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