Basic natural convection in a vertical porous layer differentially heated from its sidewalls subject to lack of local thermal equilibrium

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Abstract

A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.

Original languageEnglish (US)
Pages (from-to)2387-2396
Number of pages10
JournalInternational Journal of Heat and Mass Transfer
Volume54
Issue number11-12
DOIs
StatePublished - May 2011

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Natural convection
free convection
Heat flux
heat flux
Fluids
fluids
Temperature
temperature
Heating
heating
temperature profiles
derivation
Hot Temperature
symmetry

Keywords

  • Heat flux
  • Lack of local thermal equilibrium (LaLotheq)
  • Local thermal non-equilibrium (LTNE)
  • Natural convection
  • Porous media

ASJC Scopus subject areas

  • Mechanical Engineering
  • Condensed Matter Physics
  • Fluid Flow and Transfer Processes

Cite this

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title = "Basic natural convection in a vertical porous layer differentially heated from its sidewalls subject to lack of local thermal equilibrium",
abstract = "A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.",
keywords = "Heat flux, Lack of local thermal equilibrium (LaLotheq), Local thermal non-equilibrium (LTNE), Natural convection, Porous media",
author = "Peter Vadasz",
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AU - Vadasz, Peter

PY - 2011/5

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N2 - A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.

AB - A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.

KW - Heat flux

KW - Lack of local thermal equilibrium (LaLotheq)

KW - Local thermal non-equilibrium (LTNE)

KW - Natural convection

KW - Porous media

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