Non-Oberbeck–Boussinesq effects on the convective stability in a transient natural convection boundary layer for water

Abstract

The non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer are investigated using the linearised disturbance equation for water flows up to a temperature difference of $\Delta T=40$ K at two ambient temperatures, $T_{\infty }=293$ K and $T_{\infty }=333$ K. Results reveal that the instability of the natural convection boundary layer in water is completely driven by buoyancy. The neutral stability curves are shown to be sensitive to the choice of reference temperature — when evaluated at the film temperature $T_f$, the flow is stabilised by heating at small Grashof number near the critical point; but is destabilised at higher Grashof number. An increased ambient temperature is also shown to have a stabilising effect on the flow. For the buoyancy-driven instability, we propose a reference temperature for the purpose of generalising the neutral stability curves at different $\Delta T$ and $T_{\infty }$ values.