Two-Dimensional Thermal Convection in a Parallelogram-Shaped Cavity with Inclined Sidewalls

Abstract

The effect of inclination of sidewalls on two-dimensional thermal convection of a fluid in a parallelogram-shaped cavity is investigated under the assumption that all walls are rigid, with perfect thermal conductance and with a vertically linear temperature profile connecting the temperatures on the horizontal top and bottom walls. The critical Rayleigh number R c , at which a motionless state becomes unstable, is calculated numerically for several values of inclination angle φ of sidewalls from the vertical direction and aspect ratio A . As φ increases from 0, the increase in R c and the exchange of most unstable eigenmode are observed for all A satisfying 0.3≤ A ≤3. Moreover, we find numerically that two steady convection states bifurcating from the motionless state at R c become unstable at different Rayleigh numbers for non-zero φ. Furthermore, the stability of the motionless state in an inclined fluid layer of infinite length is examined along with its relevance to stability in a parallelogram-shaped...