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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.

Flow management using natural instabilities

Floryan J. M.

Archives of Mechanics

2006

Vol. 58, nr 6

575-596

Accidental introduction of a small disturbance into an unstable flow leads to a large change in the form of the motion, e.g., laminar-turbulent transition. We wish to explore this phenomenon in the design of flow management strategies. We want to modulate the flow using a small input of external energy in such a way that the flow evolves through a natural instability process to a new, more desirable form. This presentation is focused on the use of distributed surface roughness for such purposes.