Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: Non-Darcian model

O. M. Haddad; M. A. Al-Nimr; A. N. Al-Khateeb

doi:10.1016/j.ijheatmasstransfer.2003.09.033

Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: Non-Darcian model

O. M. Haddad, M. A. Al-Nimr, A. N. Al-Khateeb

Aerospace Engineering

Jordan Univ. of Sci./Technology

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Brinkman term (no-slip condition) to cover the flow. It is found that there are four dimensionless parameters controlling the local thermal equilibrium assumption: the volumetric Biot number (Bi_v), the modified Rayleigh number (Ra_m), the modified Darcy number (Da) and the ratio of effective to dynamic viscosity (λ). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.

Original language	British English
Pages (from-to)	2037-2042
Number of pages	6
Journal	International Journal of Heat and Mass Transfer
Volume	47
Issue number	8-9
DOIs	https://doi.org/10.1016/j.ijheatmasstransfer.2003.09.033
State	Published - Apr 2004

Keywords

Laminar flow
Natural convection
Non-Darcian
Porous media
Two phase

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10.1016/j.ijheatmasstransfer.2003.09.033

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title = "Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: Non-Darcian model",

abstract = "The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Brinkman term (no-slip condition) to cover the flow. It is found that there are four dimensionless parameters controlling the local thermal equilibrium assumption: the volumetric Biot number (Biv), the modified Rayleigh number (Ram), the modified Darcy number (Da) and the ratio of effective to dynamic viscosity (λ). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.",

keywords = "Laminar flow, Natural convection, Non-Darcian, Porous media, Two phase",

author = "Haddad, \{O. M.\} and Al-Nimr, \{M. A.\} and Al-Khateeb, \{A. N.\}",

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T1 - Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium

T2 - Non-Darcian model

AU - Haddad, O. M.

AU - Al-Nimr, M. A.

AU - Al-Khateeb, A. N.

PY - 2004/4

Y1 - 2004/4

N2 - The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Brinkman term (no-slip condition) to cover the flow. It is found that there are four dimensionless parameters controlling the local thermal equilibrium assumption: the volumetric Biot number (Biv), the modified Rayleigh number (Ram), the modified Darcy number (Da) and the ratio of effective to dynamic viscosity (λ). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.

AB - The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Brinkman term (no-slip condition) to cover the flow. It is found that there are four dimensionless parameters controlling the local thermal equilibrium assumption: the volumetric Biot number (Biv), the modified Rayleigh number (Ram), the modified Darcy number (Da) and the ratio of effective to dynamic viscosity (λ). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.

KW - Laminar flow

KW - Natural convection

KW - Non-Darcian

KW - Porous media

KW - Two phase

UR - https://www.scopus.com/pages/publications/1642439295

U2 - 10.1016/j.ijheatmasstransfer.2003.09.033

DO - 10.1016/j.ijheatmasstransfer.2003.09.033

M3 - Article

AN - SCOPUS:1642439295

SN - 0017-9310

VL - 47

SP - 2037

EP - 2042

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

IS - 8-9

ER -

Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: Non-Darcian model

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