Vortex instability of mixed convection boundary layer flow adjacent to a non‐isothermal inclined surface in a porous medium with variable permeability

Abstract

A linear stability theory is used to analyze the vortex instability of mixed convection boundary layer flow over an inclined heated surface in a porous medium with variable permeability. 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. The surface temperature is assumed to vary as a power function of the distance from the origin. In the main flow analysis, both the streamwise and normal component of the buoyancy force are retained in the momentum equations. The present formulation permits the angles of inclination ranging from 0 to close to 90 degrees from the horizontal. Local Nusselt number is presented for the uniform permeability (UP) and variable permeability (VP) cases. The critical Peclet numbers and the associated wave numbers are obtained for both the UP and VP cases. It is found that the VP effect tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance.

Effect of Variable Viscosity on Vortex Instability of Mixed Convection Boundary Layer Flow Adjacent to a Non-isothermal Horizontal Surface in a Porous Medium

“…This is primarily because of numerous applications of flow through porous media, such as material transfer associated with the storage of radioactive nuclear waste, separation processes in the chemical industry, filtration, transpiration cooling, transport processes in aquifers, and ground water pollution. The problem of the vortex mode of instability in mixed or natural convection over a horizontal or inclined heated plate in a saturated porous medium has recently received considerable attention (see e.g., [3,[5][6][7]9,10,12,13,20]). A comprehensive discussion and literature survey on this subject can be found in the recent book by Nield and Bejan [23].…”

Effect of variable viscosity on vortex instability of non-Darcy free convection boundary layer flow adjacent to a non-isothermal horizontal surface in a porous medium

“…The problems of the vortex mode of instability in free and mixed convection flows over horizontal and inclined heated surfaces in saturated porous media have received considerable attention (see [1][2][3][4][5][6][7][8][9][10][11]). The instability mechanism is due to the presence of a buoyancy force component in the direction normal to the surface.…”

“…The importance of the problems is due to a large number of technical applications, such as material transfer associated with the storage of radioactive nuclear waste, separation processes in the chemical industry, filtration, transpiration cooling, transport processes in aquifers, and ground water pollution. Some researchers considered Darcy model [1][2][3][4][5], others considered non-Darcy model [6][7][8][9][10][11]. A comprehensive literature survey on this subject can be found in the recent book by Nield and Bejan [12].…”