Characteristic time of instabilities threshold appearance in transient mixed convection

The objective of the present work is to study the evolution of the characteristic time of appearance of instabilities in opposing flows in transient mixed convection. The situation of a vertical pipe with convective exchange at the external surface is considered from a numerical viewpoint. A decrease in the characteristic time of appearance of the instabilities is observed with the increase in the Richardson number. Moreover, a stability diagram of the opposing flows in mixed convection using the Pe–Ri coordinates is proposed. This diagram underlines the critical Richardson number beyond which the flow is always unstable (Ric ≈ 1).