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1

Effect of thermal dispersion on free convection in a fluid saturated porous medium

Abbas I. A., El-Amin M. F.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 3

615-632

EN

The present article considers a numerical study of the thermal dispersion effect on the non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. The Forchheimer extension is considered in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and dispersion thermal diffusivity due to mechanical dispersion. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton-Raphson iteration. The finite element implementations are prepared by using the Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours and profiles as well as heat transfer rate in terms of the Nusselt number, which are shown on graphs, have been presented.

2

Thermal dispersion effects on non-Darcy axisymmetric free convection in a porous medium saturated with a non-Newtonian fluid

El-Amin M. F.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 1

77-86

EN

A boundary layer analysis is presented to study the effects of thermal dispersion of a non-Newtonian fluid on non-Darcy axisymmetric free convection over a horizontal surface embedded in a porous medium. The Ostwald-de-Waele power-law model is used to characterize the non-Newtonian fluid behavior. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. Similarity solutions are obtained when the surface temperature varies as the square root of the radial distance (i.e., the prescribed temperature PT) or when heat flux is constant (i.e., the prescribed heat flux PHF). The effects of the dispersion and non-Darcy parameters as well as the power-law index n on the velocity, temperature, the Nusselt number and the boundary layer thickness are shown on graphs. The numerical values of the rate of heat transfer through the boundary layer in terms of the Nusselt number are entered in a table.

3

MHD effects on a power-law fluid past a vertical plate embedded in a porous medium with variable surface heat flux

El-Amin M. F., Mohammadien A. A.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 1

117-131

EN

The present study is devoted to investigating the influences of magnetic field on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained with a prescribed variable surface heat flux. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Excess surface temperature has been presented for different values of the power-law index n, magnetic parameter Mn* and the exponent 'lambda'.

4

Thermal dispersion effects on non-Darcy axisymmetric free convection in a saturated porous medium with lateral mass transfer

Mansour M. A., El-Amin M. F.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 4

727-737

EN

An analysis is presented to study the effects of thermal dispersion and lateral mass flux on non-Darcy axisymmetric free convection on permeable horizontal surfaces in a fluid saturated porous medium. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. Similarity solutions are obtained when the surface temperature varies as the square root of the radial distance or when heat flux is constant. The effects of the dispersion, lateral mass flux and non-Darcy parameters on the velocity and temperature are shown on graphs. The numerical values of the rate of heat transfer as well as the total energy convected through the boundary layer are entered in tables.