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1

Variable Permeability Effect on Vortex Instability of Free Convection Flow Over Inclined Heated Surfaces in Porous Media

Ibrahim F. S.

Mechanics and Mechanical Engineering

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2009

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Vol. 13, nr 2

55-67

EN

A linear stability analysis is performed for the study of the onset of vortex instability in free convection flow over an inclined heated surface in a porous medium, where the wall temperature is a power function of the distance from the origin. The variation of permeability in the vicinity of the solid boundary is approximated by an exponential function. The variation rate itself depends slowly on the streamwise coordinate, such as to allow the problem to possess a set of solutions, invariant under a group of transformations. Velocity and temperaturę profiles as well as local Nusselt number for the base flow are presented for the uniform permeability UP and variable permeability VP cases. The resulting variable coefficient eigenvalue problem is solved numerically. The critical parameter Ra*xtan2 ø and the critical wave number k* are computed for different prescribed wall temperature distribution of the inclined surface for both UP and VP cases. It is found that the larger the inclination angle with respect to the vertical, the morę susceptible is the flow for the vortex mode of disturbances; and in the limit of zero inclination angle (i.e vertical heated plate) the flow is stable for this form of disturbances. Also, it is found that the variable permeability effect tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance.

2

Unsteady free convection flow in the stagnation-point region of a rotating sphere embedded in a porous medium

Hassanien I. A., Ibrahim F. S., Omer G. M.

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 2

89-98

EN

The problem of the unsteady free convection flow in a fluid saturated porous medium of a rotating sphere in the presence of a solid matrix exerting first and second resistance is studied. Numerical solutions are obtained for the cases of constant wall temperature (CWT) and constant heat flux (CHF). The non-linear coupled partial differential equations governing the flow have been solved numerically using finite difference. The effects of the first resistance parameter ξ, the buoyancy parameter λ, the Prandtl number Pr, the variation of the angular velocity with time (ε > 0) on the skin friction and heat transfer rate ue discussed, is shown the figures. It is found that the buoyancy force enhanced both the skin fraction and the heat transfer rate. The effect of the presence of the first resistance decreases the skin friction and the heat transfer rate.

3

Ibrahim F. S., Omer Gh. M.

Mechanics and Mechanical Engineering

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2001

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Vol. 5, nr 2

155-168

EN

The problem of mixed convection along non-isothermal vertical flat plate embedded in a porous medium with variable permeability is analyzed. Non-similar solutions are obtained for power- law variation of the surface heat flux in the form qw(x) = bxm. The entire mixed convection regime is covered by non-similarity parameter ζ = [1+Rax/Pe3/2x)1/3]-1, from pure forced convection ζ = 1 to pure free convection ζ = 0.0. A finite difference scheme was used to solve the system of transformed governing equations. Velocity and temperature profiles, and local Nusselt numbers are presented. It is found that as ζ decreases from 1 to 0, the thermal boundary thickness increases first and then decreases. But the local Nusselt number in the form Nux(Pe1/2x+Ra1/3x)-1 decreases first and then increases. The variation of permeability increases Nusselt number of all values of ζ.

4

Non-Darcian effect on mixed convection of non-Newtonian fluids along a vertical plate with variable heat flux in porous media

Ibrahim F. S.

Mechanics and Mechanical Engineering

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2001

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Vol. 5, nr 1

41-54

EN

A nonsimilar boundary layer analysis is presented for the problem of non-Darcian mixed convection in power-law type non-Newtonian fluids along a vertical plate embedded in a fluid-saturated porous media. The surface heat flux is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter ξ and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter ξ = Pe1/2x/(Pe1/2x+(Ra*x)1/(2n+1)) from pure forced convection (ξ, = 1) to pure free convection (ξ = 0). The present work examines the effects of non-Darcian flow phenomena and the variation of heat flux on mixed convection transport and demonstrates the variation in heat transfer prediction on different fluid types. It was found that the present problem depends on four parameters, namely the non-Darcian parameter Re , the mixed convection parameter ξ, the viscosity index n, and the heat flux expononant λ. The impact of these governing parameters on the surface heat transfer rate is discussed in great detail. Also represented velocity and temperature profiles are presented.

5

Influence of variable permeability on combined convection along a non-isothermal wedge in a saturated porous medium

Ibrahim F. S., Hassanien I. A.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 4

699-714

EN

Mixed convection along a vertical non-isothermal wedge embedded in a fluid - saturated porous media incorporating the variation of permeability and thermal conductivity is studied. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter 'ksi' and a pseudo-similarity variable 'eta' are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter 'ksi'=[1+(Rax/Pex)1/2]-1 from pure forced convection ('ksi'=1) to pure free convection ('ksi'=0). The problem is solved using nonsimilarity solution for the case of variable wall temperature. Velocity and temperature profiles as well as the local Nusselt number are presented. The wedge angle geometry parameter ranged from 0 to 1.