A new mechanism for buoyancy driven convection in pulsating viscous flows: A theoretical study

A new mechanism for the onset of thermal convection is proposed. This mechanism is the result of the interaction between a pulsating flow, viscous dissipation, and buoyancy within a channel. The study considers a Newtonian fluid moving inside an infinitely wide horizontal channel bounded by impermeable, rigid plates. The basic flow is characterized by a pulsating pressure gradient. Viscous dissipation acts as an internal heat source which produces a potentially unstable basic temperature gradient. The heat source has a vertical non uniform distribution inside the channel. This configuration is investigated with respect to the onset of buoyancy driven convection. The basic state fields are solved analytically by expanding them in series as functions of the pulsating frequency. In order to perform the linear stability analysis, an arbitrarily small perturbation is superimposed upon the basic state order zero solution. The normal mode method is employed and an ordinary differential eigenvalue problem is obtained. The perturbations were found to have zero angular frequency and thus the resonance phenomena between the basic flow and the perturbations can be neglected. The critical values of the governing parameter are obtained by solving the eigenvalue problem numerically. A growth rate analysis of the possibly unstable configurations relative to the most unstable mode is performed. The present study proves, theoretically, that a pulsating flow can undergo thermal convection. A future experimental study is suggested to validate the proposed instability mechanism.