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

TL;DR

This paper investigates the stability of viscous buoyant flows in a horizontal channel with adiabatic walls, focusing on the onset of thermal instability under high Prandtl number conditions through numerical analysis.

Contribution

It provides a numerical stability analysis of buoyant flows in a horizontal channel, emphasizing the effects of viscous heating and dual flow solutions in a high Prandtl number regime.

Findings

Identification of neutral stability curves for the flow

Determination of critical parameters for instability onset

Analysis of viscous dissipation effects on flow stability

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 of 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 focussed 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.