Buoyant flow and instability in a vertical cylindrical porous slab with permeable boundaries

• Published in: International journal of heat and mass transfer Vol. 157; p. 119956
• Main Authors: Barletta, A., Celli, M., Rees, D.A.S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.2020; Elsevier BV
• Subjects: Aspect ratio; Boundaries; Conduction heating; Convection; Cylindrical slab; Dynamic stability; Eigenvalues; Flow instability; Flow stability; Flow velocity; Neutral stability curves; Permeability; Permeable boundary; Porous medium; Rayleigh number; Stability analysis; Temperature gradients; Velocity distribution; Cylindrical slab; Permeable boundary; Flow instability; Rayleigh number; Convection; Porous medium
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2020.119956

•We study stationary and parallel buoyant flow in a vertical annular porous passage.•The vertical cylindrical boundaries are considered both isothermal and permeable.•Transition to convective instability is due to the basic radial temperature gradient.•The linear dynamics of the perturbed flow is formulated as an eigenvalue problem.•The system becomes more an more unstable as the aspect ratio increases. The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid reservoirs. There exists a stationary parallel velocity field with a zero flow rate and pure conduction heat transfer. Its linear stability is analysed with normal mode perturbations of the pressure and temperature fields. The transition to convective instability is caused by the basic horizontal temperature gradient. Hence, its nature differs from that of the usual Rayleigh–Bénard instability. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem, solved numerically. Its solution provides the neutral stability curve at each fixed aspect ratio between the external radius and the internal radius. The critical Rayleigh number triggering the instability is evaluated for different aspect ratios. It is shown that the system becomes more an more unstable as the aspect ratio increases, with the critical Rayleigh number dropping to zero when the aspect ratio tends to infinity.