Mixed convection boundary-layer flow in a porous medium filled with water close to its maximum density

S. C. Ling, Roslinda Mohd. Nazar, I. Pop, J. H. Merkin

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

Original languageEnglish
Pages (from-to)139-151
Number of pages13
JournalTransport in Porous Media
Volume76
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

Mixed convection
Boundary layer flow
Porous materials
Water
Temperature

Keywords

  • Boundary-layer flow
  • Dual solutions
  • Mixed convection
  • Porous medium

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Catalysis

Cite this

Mixed convection boundary-layer flow in a porous medium filled with water close to its maximum density. / Ling, S. C.; Mohd. Nazar, Roslinda; Pop, I.; Merkin, J. H.

In: Transport in Porous Media, Vol. 76, No. 1, 2009, p. 139-151.

Research output: Contribution to journalArticle

@article{9675b4a7190d49b2826e7dc9f6258c9c,
title = "Mixed convection boundary-layer flow in a porous medium filled with water close to its maximum density",
abstract = "The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.",
keywords = "Boundary-layer flow, Dual solutions, Mixed convection, Porous medium",
author = "Ling, {S. C.} and {Mohd. Nazar}, Roslinda and I. Pop and Merkin, {J. H.}",
year = "2009",
doi = "10.1007/s11242-008-9240-x",
language = "English",
volume = "76",
pages = "139--151",
journal = "Transport in Porous Media",
issn = "0169-3913",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - Mixed convection boundary-layer flow in a porous medium filled with water close to its maximum density

AU - Ling, S. C.

AU - Mohd. Nazar, Roslinda

AU - Pop, I.

AU - Merkin, J. H.

PY - 2009

Y1 - 2009

N2 - The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

AB - The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

KW - Boundary-layer flow

KW - Dual solutions

KW - Mixed convection

KW - Porous medium

UR - http://www.scopus.com/inward/record.url?scp=59149091132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59149091132&partnerID=8YFLogxK

U2 - 10.1007/s11242-008-9240-x

DO - 10.1007/s11242-008-9240-x

M3 - Article

AN - SCOPUS:59149091132

VL - 76

SP - 139

EP - 151

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 1

ER -