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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

Combined heat and mass transfer on non-Darcy natural convection in a fluid saturated porous medium with thermophoresis

El-Hakiem M. A., El-Kabeir S. M., Rashad A. M.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 1

9-18

EN

The present investigation deals with the combined heat and mass transfer with the effects of thermal dispersion, radiation on non-Darcy natural convection in a fluid saturated porous medium with thermophoresis. The goveming equations, reduced to local similarity boundary layer equations using suitable transformations are obtained. Forchheimer extension is considered in the fIow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat fIux in the energy equation. For the fluids having the Lewis number Le=l.O, 10.0, numerical values of the local Stanton number are presented in a tabular form for different values of the thermophoretic parameter [...], thermal dispersion and thermal radiation for the two cases of Darcy and non-Darcy porous medium. The concentration distributions are show n graphically for various values of the thermophoretic parameter, thermal dispersion and thermal radiation.

3

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.

4

The effect of thermal dispersion on hydromagnetic flow and heat transfer past a continuously moving porous boundary with temperature dependent viscosity

Bishay S. S., Seddeek M. A., Mohamdien Gh. F.

Mechanics and Mechanical Engineering

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2002

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Vol. 6, nr 1

43-49

EN

The effects of thermal dispersion and magnetic field on the flow and heat transfer past a continuously moving porous plate in a stationary fluid has been analyzed. The fluid viscosity is assumed to vary as an inverse linear function of temperature. By means of the similarity solutions, deviation of the velocity and temperature fields as well as the skin friction and heat transfer results from their constant values are determined numerically by using the shooting method. The effects of thermal dispersion, variable viscosity, magnetic field, and suction (or injection) parameters on the velocity and temperature profiles have been studied.

5

Forced convection in heterogeneous porous media: the effect of thermal dispersion

Kuznetsov A. V.

International Journal of Applied Mechanics and Engineering

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2002

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Vol. 7, no 2

565-590

EN

This paper presents a new analytical solution to a problem of forced convection in a heterogeneous channel filled with two different layers of isotropic porous media. The Brinkman-Forchheimer-extended Darcy equation is utilized to describe the fluid flow in the porous layers, and the effect of transverse thermal dispersion is accounted for in the energy equations. Three momentum boundary layers are identified in the channel: a boundary layer at the solid wall and two boundary layers at the interface between the porous media. The dependence of the Nusselt number on the Darcy numbers, Forchheimer coefficients, and particle Reynolds numbers in different parts of the channel is investigated. This study demonstrates that thermal dispersion has a strong effect on the Nusselt number in the channel for large particle Reynolds numbers.

6

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.