fluids Article Convective to Absolute Instability Transition in a Horizontal Porous Channel with Open Upper Boundary Antonio Barletta * and Michele Celli Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy;
[email protected] * Correspondence:
[email protected]; Tel.: +39-051-209-3287 Academic Editor: Mehrdad Massoudi Received: 28 April 2017; Accepted: 10 June 2017; Published: 14 June 2017 Abstract: A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations. Keywords: porous medium; Rayleigh number; absolute instability 1. Introduction Cellular convection patterns may develop in an underlying horizontal flow under appropriate thermal boundary conditions. The classic setup for the thermal instability of a horizontal fluid flow is heating from below, and the well-known type of instability is Rayleigh-Bénard [1]. Such a situation can happen in a channel fluid flow or in the filtration of a fluid within a porous channel. Both cases are widely documented in the literature [1,2].