Variable permeability effect on vortex instability of a horizontal natural convection flow in a saturated porous medium with variable wall temperature

Abstract

A linear stability theory is used to analyze the vortex instability of free convection boundary layer flow in a saturated porous medium adjacent to a horizontal surface 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 temperature profiles as well as local Nusselt number for the base flow are presented for the uniform permeability UP and variable permeability VP cases. The critical Rayleigh numbers and the associated wave numbers are obtained for both UP and VP cases. 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.

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

“…For the case μ * = 1, Equations (11)- (13) and (18)- (20) reduce to the two-dimensional base flow equations for constant viscosity evaluated at the ambient temperature of Aldoss et al [2] and for n = 0, ξ n = 0 to the same problem of pure free convection for isothermal surface of Jang and Leu [16]. It is interesting to note that, the parameter ξ n is a measure of the forced flow effect on free convection.…”

“…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].…”

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

“…The effect of VP on vortex instability of a horizontal mixed and free convection flow in a saturated porous medium was studied by Jang and Cheng [9], Hassanien et al [10,11]. For an inclined surface, the buoyancy force causing motion having a component in both the tangential and normal directions.…”