Effect of Conduction in Bottom Wall on Bénard Convection in a Porous Enclosure with Localized Heating and Lateral Cooling

A. Alhashash, H. Saleh, Ishak Hashim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length-0.2 ≤ H ≤ 0.9, the wall thickness-0.05 ≤ D ≤ 0.4, the thermal conductivity ratio-0.8 ≤ Kr ≤ 9.8, and the Biot number-0.1 ≤ Bi ≤ 1.1. It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.

Original languageEnglish
Pages (from-to)305-318
Number of pages14
JournalTransport in Porous Media
Volume96
Issue number2
DOIs
Publication statusPublished - Dec 2012

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Enclosures
Heat transfer
Cooling
Heating
Thermal conductivity
Finite difference method
Temperature
Convection
Hot Temperature

Keywords

  • Conjugate heat transfer
  • Darcy's law
  • Localized heating
  • Natural convection

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Catalysis

Cite this

Effect of Conduction in Bottom Wall on Bénard Convection in a Porous Enclosure with Localized Heating and Lateral Cooling. / Alhashash, A.; Saleh, H.; Hashim, Ishak.

In: Transport in Porous Media, Vol. 96, No. 2, 12.2012, p. 305-318.

Research output: Contribution to journalArticle

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AU - Saleh, H.

AU - Hashim, Ishak

PY - 2012/12

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N2 - Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length-0.2 ≤ H ≤ 0.9, the wall thickness-0.05 ≤ D ≤ 0.4, the thermal conductivity ratio-0.8 ≤ Kr ≤ 9.8, and the Biot number-0.1 ≤ Bi ≤ 1.1. It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.

AB - Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length-0.2 ≤ H ≤ 0.9, the wall thickness-0.05 ≤ D ≤ 0.4, the thermal conductivity ratio-0.8 ≤ Kr ≤ 9.8, and the Biot number-0.1 ≤ Bi ≤ 1.1. It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.

KW - Conjugate heat transfer

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