A numerical study of confinement effects on the instability of the thermal boundary layer adjacent to a vertical heated plate

The instability and unsteady behaviour of the thermal boundary layer (TBL) developing along a vertical plate subject to a constant heat flux are investigated numerically. The emphasis is on the confinement effects. Three configurations are considered: a single (unconfined) heated plate, a one-wall heated channel, and a double-wall heated channel. For the single-plate case, a continuous wavelet analysis reveals spatial and temporal evolution of dominant frequencies in the TBL. A band of response frequencies is identified to characterise the spectral properties of the TBL. It is found that, in general, confinement tends to weaken TBL instability compared to the unconfined case, shifting spectral response toward lower frequencies and weakening vortical structures. However, among the confined cases, the stabilising effect varies non-monotonically with confinement ratio – the ratio of the TBL thickness over the channel width, while heat transfer characterised by the Nusselt number increases monotonically with the confinement ratio. It is also found that heating the opposing plate further exacerbates the confinement effect, particularly at high Rayleigh numbers. • Instability of uniformly heated thermal boundary layer is investigated numerically. • The dominant frequency of the boundary layer varies both spatially and temporally. • Confinement tends to stabilise thermal boundary layer relative to unconfined case. • The Nusselt number increases monotonically with increasing confinement ratio.