Onset of Three-Dimensional Thermal Convection in an Inclined Rectangular Cavity

Onset of three-dimensional thermal convection of a fluid in an inclined rectangular or cubic cavity is investigated under the assumptions that all the walls are rigid and of perfect thermal conductance, and that the cavity is exposed to a vertically linear temperature profile. The critical Rayleigh number R-c, at which a motionless state becomes unstable, is calculated numerically using a Galerkin spectral method with a divergence-free set of basis functions satisfying all boundary conditions. It is found for a cubic cavity that its inclination can cause the decrease in R,. Moreover, for a rectangular cavity, the exchange of the most unstable mode associated with the variation in inclination angles is observed.