Free Convection Boundary Layer Flow Past a Vertical Surface in a Porous Medium with Temperature-Dependent Properties

K. Vajravelu, K. V. Prasad, Robert A. van Gorder, Jinho Lee

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Numerical solutions for the free convection heat transfer in a viscous fluid at a permeable surface embedded in a saturated porous medium, in the presence of viscous dissipation with temperature-dependent variable fluid properties, are obtained. The governing equations for the problem are derived using the Darcy model and the Boussinesq approximation (with nonlinear density temperature variation in the buoyancy force term). The coupled non-linearities arising from the temperature-dependent density, viscosity, thermal conductivity, and viscous dissipation are included. The partial differential equations of the model are reduced to ordinary differential equations by a similarity transformation and the resulting coupled, nonlinear ordinary differential equations are solved numerically by a second order finite difference scheme for several sets of values of the parameters. Also, asymptotic results are obtained for large values of {pipe}f w {pipe}. Moreover, the numerical results for the velocity, the temperature, and the wall-temperature gradient are presented through graphs and tables, and are discussed. It is observed that by increasing the fluid variable viscosity parameter, one could reduce the velocity and thermal boundary layer thickness. However, quite the opposite is true with the non-linear density temperature variation parameter.

Original languageEnglish
Pages (from-to)977-992
Number of pages16
JournalTransport in Porous Media
Volume90
Issue number3
DOIs
Publication statusPublished - 2011 Dec 1

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Boundary layer flow
Natural convection
Porous materials
Ordinary differential equations
Fluids
Temperature
Pipe
Viscosity
Buoyancy
Density (specific gravity)
Thermal gradients
Partial differential equations
Thermal conductivity
Boundary layers
Heat transfer

All Science Journal Classification (ASJC) codes

  • Catalysis
  • Chemical Engineering(all)

Cite this

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abstract = "Numerical solutions for the free convection heat transfer in a viscous fluid at a permeable surface embedded in a saturated porous medium, in the presence of viscous dissipation with temperature-dependent variable fluid properties, are obtained. The governing equations for the problem are derived using the Darcy model and the Boussinesq approximation (with nonlinear density temperature variation in the buoyancy force term). The coupled non-linearities arising from the temperature-dependent density, viscosity, thermal conductivity, and viscous dissipation are included. The partial differential equations of the model are reduced to ordinary differential equations by a similarity transformation and the resulting coupled, nonlinear ordinary differential equations are solved numerically by a second order finite difference scheme for several sets of values of the parameters. Also, asymptotic results are obtained for large values of {pipe}f w {pipe}. Moreover, the numerical results for the velocity, the temperature, and the wall-temperature gradient are presented through graphs and tables, and are discussed. It is observed that by increasing the fluid variable viscosity parameter, one could reduce the velocity and thermal boundary layer thickness. However, quite the opposite is true with the non-linear density temperature variation parameter.",
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Free Convection Boundary Layer Flow Past a Vertical Surface in a Porous Medium with Temperature-Dependent Properties. / Vajravelu, K.; Prasad, K. V.; van Gorder, Robert A.; Lee, Jinho.

In: Transport in Porous Media, Vol. 90, No. 3, 01.12.2011, p. 977-992.

Research output: Contribution to journalArticle

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