Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer

Darcy Model and Brinkman-Extended Darcy Model

Mikhail A. Sheremet, Tatyana A. Trifonova

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Transient natural convection in a vertical cylinder partially filled with a porous media with heat-conducting solid walls of finite thickness in conditions of convective heat exchange with an environment has been studied numerically. The Darcy and Brinkman-extended Darcy models with Boussinesq approximation have been used to solve the flow and heat transfer in the porous region. The Oberbeck-Boussinesq equations have been used to describe the flow and heat transfer in the pure fluid region. The Beavers-Joseph empirical boundary condition is considered at the fluid-porous layer interface with the Darcy model. In the case of the Brinkman-extended Darcy model, the two regions are coupled by equating the velocity and stress components at the interface. The governing equations formulated in terms of the dimensionless stream function, vorticity, and temperature have been solved using the finite difference method. The main objective was to investigate the influence of the Darcy number 10-5 ≤Da ≤ 10-3, porous layer height ratio 0 ≤ d/L ≤ 1, thermal conductivity ratio 1 ≤ k1,3 ≤ 20, and dimensionless time 0 ≤ τ ≤ 1000 on the fluid flow and heat transfer on the basis of the Darcy and non-Darcy models. Comprehensive analysis of an effect of these key parameters on the Nusselt number at the bottom wall, average temperature in the cylindrical cavity, and maximum absolute value of the stream function has been conducted.

Original languageEnglish
Pages (from-to)437-463
Number of pages27
JournalTransport in Porous Media
Volume101
Issue number3
DOIs
Publication statusPublished - 1 Feb 2014

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Natural convection
Heat transfer
Fluids
Nusselt number
Vorticity
Finite difference method
Porous materials
Flow of fluids
Thermal conductivity
Boundary conditions
Temperature
Hot Temperature

Keywords

  • Boussinesq approximation
  • Brinkman-extended Darcy model
  • Conjugate natural convection
  • Darcy model
  • Stream function-vorticity formulation

ASJC Scopus subject areas

  • Catalysis
  • Chemical Engineering(all)

Cite this

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title = "Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer: Darcy Model and Brinkman-Extended Darcy Model",
abstract = "Transient natural convection in a vertical cylinder partially filled with a porous media with heat-conducting solid walls of finite thickness in conditions of convective heat exchange with an environment has been studied numerically. The Darcy and Brinkman-extended Darcy models with Boussinesq approximation have been used to solve the flow and heat transfer in the porous region. The Oberbeck-Boussinesq equations have been used to describe the flow and heat transfer in the pure fluid region. The Beavers-Joseph empirical boundary condition is considered at the fluid-porous layer interface with the Darcy model. In the case of the Brinkman-extended Darcy model, the two regions are coupled by equating the velocity and stress components at the interface. The governing equations formulated in terms of the dimensionless stream function, vorticity, and temperature have been solved using the finite difference method. The main objective was to investigate the influence of the Darcy number 10-5 ≤Da ≤ 10-3, porous layer height ratio 0 ≤ d/L ≤ 1, thermal conductivity ratio 1 ≤ k1,3 ≤ 20, and dimensionless time 0 ≤ τ ≤ 1000 on the fluid flow and heat transfer on the basis of the Darcy and non-Darcy models. Comprehensive analysis of an effect of these key parameters on the Nusselt number at the bottom wall, average temperature in the cylindrical cavity, and maximum absolute value of the stream function has been conducted.",
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AB - Transient natural convection in a vertical cylinder partially filled with a porous media with heat-conducting solid walls of finite thickness in conditions of convective heat exchange with an environment has been studied numerically. The Darcy and Brinkman-extended Darcy models with Boussinesq approximation have been used to solve the flow and heat transfer in the porous region. The Oberbeck-Boussinesq equations have been used to describe the flow and heat transfer in the pure fluid region. The Beavers-Joseph empirical boundary condition is considered at the fluid-porous layer interface with the Darcy model. In the case of the Brinkman-extended Darcy model, the two regions are coupled by equating the velocity and stress components at the interface. The governing equations formulated in terms of the dimensionless stream function, vorticity, and temperature have been solved using the finite difference method. The main objective was to investigate the influence of the Darcy number 10-5 ≤Da ≤ 10-3, porous layer height ratio 0 ≤ d/L ≤ 1, thermal conductivity ratio 1 ≤ k1,3 ≤ 20, and dimensionless time 0 ≤ τ ≤ 1000 on the fluid flow and heat transfer on the basis of the Darcy and non-Darcy models. Comprehensive analysis of an effect of these key parameters on the Nusselt number at the bottom wall, average temperature in the cylindrical cavity, and maximum absolute value of the stream function has been conducted.

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