Some indications from instability results about the effectiveness of wall heating as a control option for channel flow

Abstract

This paper is a review of some of our recent work on the effect of wall heating on the stability of laminar flow in a channel. The summary of our results, some of them unexpected, is as follows. Viscosity stratification has very little effect on transient growth, whereas it results in linear mode stabilising or destabilising by an order of magnitude. It has hitherto been accepted that heat diffusivity does not affect stability. This is however true only for linear instability, transient growth is affected by an order of magnitude. Unusually, the growth is spanwise-independent and not in the form of streamwise vortices. It is also shown that flow is destabilised by secondary modes as the viscosity ratio increases. However, the viscosity ratio has no role in the selection of the pattern of ∧ vortices.