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

Результат исследований: Материалы для журналаСтатья

22 Цитирования (Scopus)

Выдержка

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.

Язык оригиналаАнглийский
Страницы (с-по)437-463
Число страниц27
ЖурналTransport in Porous Media
Том101
Номер выпуска3
DOI
СостояниеОпубликовано - 1 фев 2014

Отпечаток

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

ASJC Scopus subject areas

  • Catalysis
  • Chemical Engineering(all)

Цитировать

Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer : Darcy Model and Brinkman-Extended Darcy Model. / Sheremet, Mikhail A.; Trifonova, Tatyana A.

В: Transport in Porous Media, Том 101, № 3, 01.02.2014, стр. 437-463.

Результат исследований: Материалы для журналаСтатья

@article{624921358ca34ee282674dcbf2f3454e,
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.",
keywords = "Boussinesq approximation, Brinkman-extended Darcy model, Conjugate natural convection, Darcy model, Stream function-vorticity formulation",
author = "Sheremet, {Mikhail A.} and Trifonova, {Tatyana A.}",
year = "2014",
month = "2",
day = "1",
doi = "10.1007/s11242-013-0253-8",
language = "English",
volume = "101",
pages = "437--463",
journal = "Transport in Porous Media",
issn = "0169-3913",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer

T2 - Darcy Model and Brinkman-Extended Darcy Model

AU - Sheremet, Mikhail A.

AU - Trifonova, Tatyana A.

PY - 2014/2/1

Y1 - 2014/2/1

N2 - 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.

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.

KW - Boussinesq approximation

KW - Brinkman-extended Darcy model

KW - Conjugate natural convection

KW - Darcy model

KW - Stream function-vorticity formulation

UR - http://www.scopus.com/inward/record.url?scp=84893636514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893636514&partnerID=8YFLogxK

U2 - 10.1007/s11242-013-0253-8

DO - 10.1007/s11242-013-0253-8

M3 - Article

AN - SCOPUS:84893636514

VL - 101

SP - 437

EP - 463

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 3

ER -