Time-dependent analysis of the vortex instability in the thermal entrance region of an inclined parallel-plate channel

This paper applies a time-dependent three-dimensional linear stability theory to study the effect of inclination on the onset of vortex instability in the thermal entrance region of a parallel-plate channel. The normalized transient perturbation equations in the normal and streamwise directions are derived, and then solved together with the basic flow equations for a changing Rayleigh number to determine the neutral stability condition .