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

Ibrahim F. S.

Mechanics and Mechanical Engineering

2009

Vol. 13, nr 2

55-67

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.

Ibrahim F. S., Omer Gh. M.

Mechanics and Mechanical Engineering

2001

Vol. 5, nr 2

155-168

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.