UC San Diego

Flow that develops over a semi-infinite horizontal plate has been studied over the past decades. In this particular case, a boundary-layer flow over a horizontal hot plate is chosen and its stability characteristics at a finite distance from the leading edge are analyzed. A critical value of the Grashof number Gr based on the local boundary-layer thickness is defined and used to analyze the resulting instability.

Due to the nature of the hot plate, the Boussinesq approximation used in previous linear stability analyses becomes less desirable since wall-to-ambient temperature differences are not close to unity. And as a result, a non-Boussinesq analysis is needed and presented here for two instability modes: vortex, i.e. Gortler-like streamwise vortices, and wave, i.e. spanwise traveling waves.

Numerical results are presented such as the neutral stability curve, and critical Grashof number for Prandtl numbers of 0.7 over a wide range of wall-to-ambient temperature ratios. It is found that as this ratio increases, the susceptibility of the flow to the vortex mode of instability decreases while the wave mode instability becomes more prominent. The present study provides an approach suitable for both the vortex and wave instability modes with different wall-to-ambient temperature ratio. The results for the two modes are compared with each other as well as to other available instability data.