The classical Gill's stability problem for stationary and parallel buoyant flow in a vertical porous slab with impermeable and isothermal boundaries kept at different temperatures is reconsidered from a different perspective. A three-layer slab is studied instead of a homogeneous slab as in Gill's problem. The three layers have a symmetric configuration where the two external layers have a high thermal conductivity, while the core layer has a much lower conductivity. A simplified model is set up where the thermal conductivity ratio between the external layers and the internal core is assumed as infinite. It is shown that a flow instability in the sandwiched porous slab may arise with a sufficiently large Rayleigh number. It is also demonstrated that this instability coincides with that predicted in a previous analysis for a homogeneous porous layer with permeable boundaries, by considering the limiting case where the permeability of the external layers is much larger than that of the core layer.

Antonio Barletta, Michele Celli, Stefano Lazzari, Pedro V. Brandão (2022). Gill's problem in a sandwiched porous slab. JOURNAL OF FLUID MECHANICS, 952, 1-20 [10.1017/jfm.2022.919].

Gill's problem in a sandwiched porous slab

Antonio Barletta
;
Michele Celli;
2022

Abstract

The classical Gill's stability problem for stationary and parallel buoyant flow in a vertical porous slab with impermeable and isothermal boundaries kept at different temperatures is reconsidered from a different perspective. A three-layer slab is studied instead of a homogeneous slab as in Gill's problem. The three layers have a symmetric configuration where the two external layers have a high thermal conductivity, while the core layer has a much lower conductivity. A simplified model is set up where the thermal conductivity ratio between the external layers and the internal core is assumed as infinite. It is shown that a flow instability in the sandwiched porous slab may arise with a sufficiently large Rayleigh number. It is also demonstrated that this instability coincides with that predicted in a previous analysis for a homogeneous porous layer with permeable boundaries, by considering the limiting case where the permeability of the external layers is much larger than that of the core layer.
2022
Antonio Barletta, Michele Celli, Stefano Lazzari, Pedro V. Brandão (2022). Gill's problem in a sandwiched porous slab. JOURNAL OF FLUID MECHANICS, 952, 1-20 [10.1017/jfm.2022.919].
Antonio Barletta; Michele Celli; Stefano Lazzari; Pedro V. Brandão
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/917223
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