Instabilities of boundary layers along a tilt plate dissipating uniform heat flux

The stabilities of natural convection boundary layers along a tilt uniform-heat-flux plate were studied theoretically and numerically. For some Prandtl numbers, three-dimensional instability may have two critical modes, whose critical frequencies are close to the internal wave frequency and the value of two-dimensional T-S (Tolmien-Schlichting) wave, respectively. Specially, at proper tilt angles the three-dimensional wave mode is more unstable than the two-dimensional T-S wave. This result that seems contradict with the Squire Theorem is caused by the additional buoyancy terms in the governing equations. Direct numerical simulations confirmed the critical properties of the three-dimensional waves. Since hydrodynamic instability always exists at the first stage of turbulence transition process, current results may provide theoretical basis for optimal design of fins with high heat transfer efficiency.EI0112397-24022