Viscous heating and instability of the adiabatic buoyant flows in a horizontal channel

Author:

Barletta A.1ORCID,Celli M.1ORCID,Rees D. A. S.2ORCID

Affiliation:

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

2. Department of Mechanical Engineering, University of Bath 2 , Bath BA2 7AY, United Kingdom

Abstract

The stability of buoyant flows occurring in the mixed convection regime for a viscous fluid in a horizontal plane-parallel channel with adiabatic walls is investigated. The basic flow features a parallel velocity field under stationary state conditions. There exists a duality of flows, for every prescribed value of the mass flow rate across the channel cross-section, caused by the combined actions of viscous dissipation and the buoyancy force. As pointed out in a previous study, only the primary branch of the dual solutions is compatible with the Oberbeck–Boussinesq approximation. Thus, the stability analysis will be focused on the stability of such flows. The onset of the thermal instability with small-amplitude perturbations of the basic flow is investigated by assuming a very large Prandtl number, which is equivalent to a creeping flow regime. The neutral stability curves and the critical parametric conditions for the onset of instability are determined numerically.

Funder

Ministero dell'Istruzione, dell'Università e della Ricerca

Publisher

AIP Publishing

Subject

Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering

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