Final steady flow near a stagnation point on a vertical surface in a porous medium

Keith Merrill, Matthew Beauchesne, Joseph Peter Previte, Joseph E. Paullet, Patrick Weidman

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

This paper investigates the large time (final state flow) solutions for unsteady mixed convection boundary layer flow near a stagnation point on a vertical surface embedded in a Darcian fluid-saturated porous medium. Through numerical computations Nazar et al. [R. Nazar, N. Amin, I. Pop, Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium, Int. J. Heat Mass Transfer 47 (2004) 2681-2688] concluded that for values of the mixed convection parameter λ > -1, the governing boundary value problem (BVP) had a unique solution. If λc ≈ -1.4175 < λ ≤ -1 two solutions were reported, and if λ < λc then no solutions were found. The purpose of this note is to provide further mathematical and numerical analysis of this problem. We prove existence of a solution to the governing BVP for all λ > -1. We also present numerical evidence that a second solution exists for λ > -1, thus giving dual solutions for all λ > λc. It is also proven that if λ < -2.9136 no solution to the BVP exists. Finally, a stability analysis is performed to show that solutions on the upper branch are linearly stable while those on the lower branch are linearly unstable.

Original languageEnglish (US)
Pages (from-to)4681-4686
Number of pages6
JournalInternational Journal of Heat and Mass Transfer
Volume49
Issue number23-24
DOIs
StatePublished - Nov 1 2006

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stagnation point
steady flow
Steady flow
Mixed convection
Porous materials
convection
boundary layer flow
Boundary layer flow
boundary value problems
Boundary value problems
Convergence of numerical methods
mass transfer
Mass transfer
heat
Fluids
fluids

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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title = "Final steady flow near a stagnation point on a vertical surface in a porous medium",
abstract = "This paper investigates the large time (final state flow) solutions for unsteady mixed convection boundary layer flow near a stagnation point on a vertical surface embedded in a Darcian fluid-saturated porous medium. Through numerical computations Nazar et al. [R. Nazar, N. Amin, I. Pop, Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium, Int. J. Heat Mass Transfer 47 (2004) 2681-2688] concluded that for values of the mixed convection parameter λ > -1, the governing boundary value problem (BVP) had a unique solution. If λc ≈ -1.4175 < λ ≤ -1 two solutions were reported, and if λ < λc then no solutions were found. The purpose of this note is to provide further mathematical and numerical analysis of this problem. We prove existence of a solution to the governing BVP for all λ > -1. We also present numerical evidence that a second solution exists for λ > -1, thus giving dual solutions for all λ > λc. It is also proven that if λ < -2.9136 no solution to the BVP exists. Finally, a stability analysis is performed to show that solutions on the upper branch are linearly stable while those on the lower branch are linearly unstable.",
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Final steady flow near a stagnation point on a vertical surface in a porous medium. / Merrill, Keith; Beauchesne, Matthew; Previte, Joseph Peter; Paullet, Joseph E.; Weidman, Patrick.

In: International Journal of Heat and Mass Transfer, Vol. 49, No. 23-24, 01.11.2006, p. 4681-4686.

Research output: Contribution to journalArticle

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