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Three dimensional linear stability analysis for onset of natural convection flow in a cubic cavity is performed by using the spectral element method. The cubic cavity is placed horizontally and is heated from the bottom surface and cooled from the upper one. The lateral boundaries are assumed to be rigid and in a thermally medium state between conducting and insulating which can be established by introducing Biot number. The fluid is in a motionless state if the Rayleigh number is small. On the other hand, natural convection occurs if the Rayleigh number exceed a critical value. The critical Rayleigh numbers for the onset of the natural convection are evaluated numerically for various Biot numbers by constituting eigenvalue problem using linear stability theory. In addition, the velocity and temperature field at the critical state are obtained and discussed.

Stability of Natural Convection in a Cubic Cavity by Spectral Element Method