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

• Published in: Transport in porous media Vol. 81; no. 3; pp. 461 - 477
• Main Authors: Barletta, Antonio, Rossi di Schio, Eugenia, Storesletten, Leiv
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-02-2010; Springer; Springer Nature B.V
• Subjects: Boundaries; Civil Engineering; Classical and Continuum Physics; Conduction heating; Conductive heat transfer; Dissipation; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Forced convection; Geotechnical Engineering & Applied Earth Sciences; Horizontal; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mathematical analysis; Mathematical models; Pollution, environment geology; Rayleigh number; Rolls; Runge-Kutta method; Sedimentary rocks; Stability analysis; Stress concentration; Temperature; Temperature distribution; Temperature gradients; Velocity distribution; Throughflow; Linear stability; Darcy’s law; Convective rolls; Porous medium; waves; coordinates; transport; velocity; convection; solution; instability; temperature; Darcy's law; porous media; methodology; stability
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-009-9417-y

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.