Mixed convection flow past a vertical plate: Stability analysis and its direct simulation

Stability of mixed convection flow past vertical flat plate have been investigated here using compound matrix method (CMM) to solve linearized equations arising out of a spatial analysis and by direct numerical simulation (DNS) using a Boussinesq approximation. CMM is applied to study spatial stability of mixed convection flow past a vertical plate. A double loop in the neutral curve is shown in the forced convection limit of opposing flows for the first time. To check this and other observations of the linear analysis, two-dimensional Navier–Stokes equations are also solved here with the buoyancy term represented by the Boussinesq approximation. This type of receptivity study, by direct simulation have been extended here for mixed convection flows. Also, we establish the presence of a spatio-temporally growing wave-front for this flow—that was shown to exist in Sengupta et al. [T.K. Sengupta, A.K. Rao, K. Venkatasubbaiah, Spatio-temporal growing wave-fronts in spatially stable boundary layers, Phys. Rev. Lett. 96 (224504) (2006) 1–4; T.K. Sengupta, A.K.Rao, K. Venkatasubbaiah, Spatio-temporal growth of disturbances in a boundary layer and energy based receptivity analysis, Phys. of Fluids 18 (094101) (2006) 1–9] for boundary layer developing over a horizontal flat plate in the absence of heat transfer.