Convective Roll Instabilities of Vertical Throughflow with Viscous Dissipation in a Horizontal Porous Layer

Abstract

The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution due to the forced convection effect and to the viscous dissipation effect. A linear stability analysis of the basic solution is carried out in order to determine the conditions for the onset of convective rolls. The critical values of the wave number and of the Darcy-Rayleigh number are determined numerically by the fourth-order Runge-Kutta method. It is shown that, although generally weak, the effect of viscous dissipation yields an increase of the critical value of the Darcy-Rayleigh number for downward throughflow and a decrease in the case of upward throughflow. Finally, the limiting case of a vanishing boundary temperature difference is discussed.

Onset of Darcy-Brinkman convection with a uniform internal heat source and vertical throughflow

“…From Table 2, the comparison between Barletta et al [31] and the present linear stability theory results (Q = 0 and Da = 0) demonstrate excellent agreement. Fig.…”

“…When Q = 0 and Da = 0, the present problem can be reduced to the study of in Barletta et al [31]. From Table 2, the comparison between Barletta et al [31] and the present linear stability theory results (Q = 0 and Da = 0) demonstrate excellent agreement.…”

“…The e ect of vertical through ow of a non-newtonian power-law uid on the onset of convection in a horizontal uid saturated porous layer was examined in Barletta and Storesletten [30]. In the absence of Brinkman term, the present problem is similar to the problem considered in Barletta et al [31], in which viscous dissipation is considered as an internal heat source just as uniform internal heat source considered in this manuscript.…”

Viscous dissipation and thermoconvective instabilities in a horizontal porous channel heated from below

“…The Prats problem has been revisited by including both the contributions of viscous dissipation and pressure work in the local energy balance [18]. The case of a basic vertical throughflow with viscous dissipation has been considered [19], thus extending the analysis carried out by Homsy and Sherwood [20]. All these investigations confirmed that the effect of viscous dissipation may be the sole cause of the convective instabilities.…”

“…Quite recently, the effects of viscous dissipation have been investigated as the possible cause of convective instabilities in porous media [14][15][16][17][18][19]. In these papers, a fluid saturated porous layer with an infinite horizontal width and a finite thickness is considered.…”