STABILITY OF CONVECTION FLOW IN A HORIZONTAL FLUID LAYER HEATED BY UNIFORM HEAT FLUXES

摘要

A study is made of linear stability of free convection flow in a horizontal cavity, heated from the four walls by a constant uniform heat flux. Fully developed base flow solutions are derived, for which the linear stability analysis predicts the critical conditions for the development of three-dimensional perturbations. Instabilities are always oscillating, generated by buoyancy or shear, depending on the Prandtl number. The most stable disturbances are the transverse across the base flow. Two-dimensional disturbances parallel to the base flow are the most unstable at small Pr, but oblique three-dimensional perturbations become the most unstable for Pr > 4.2. Critical conditions are determined for Rayleigh number and wavenumber vector in terms of Prandtl number.