Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions

31st UIT (Italian Union of Thermo-fluid-dynamics) Heat Transfer Conference 2013

Celli, Michele^1 ; Barletta, Antonio^1 ; Storesletten, Leiv^2

Department of Industrial Engineering, Alma Mater Studiorum Universitá di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy^1

Department of Mathematics, University of Agder, Postboks 422, 4604 Kristiansand, Norway^2

关键词: Darcy-Rayleigh number;    Dimensionless parameters;    Horizontal porous layers;    Isothermal boundary conditions;    Local thermal equilibrium;    Local thermal non-equilibrium;    Onset of instabilities;    Thermal conductivity ratio;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/501/1/012004/pdf
DOI  :  10.1088/1742-6596/501/1/012004

来源: IOP

【 摘 要 】

The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is adopted to detect the onset conditions of convective rolls. Beyond the Darcy-Rayleigh number, playing the role of order parameter for the transition to instability, the relevant dimensionless parameters are the inter-phase heat transfer parameter and the thermal conductivity ratio. The disturbance governing equations, formulated as an eigenvalue problem, are solved numerically by a shooting method. Results are reported for the neutral stability curves and for the critical values for the onset of instability.