Electronic Thesis and Dissertation Repository


Master of Engineering Science


Mechanical and Materials Engineering


Dr. Roger E. Khayat


The onset of convection in the Rayleigh-Bénard problem for a monatomic rarefied gas at small Knudsen number has been investigated. Compressibility-induced density variations have been considered without imposing any restriction on the magnitude of temperature difference. A linear temporal stability analysis has been conducted for a compressible slip-flow model considering a Maxwellian gas and the dispersion relation is calculated using a Chebyshev collocation method. A neutral stability curve obtained in the Froude-Knudsen number plane marks transition to convection from a pure conduction state. The critical wave number observed for the onset of convection is in good agreement with the existing literature. A comparison of two molecular interaction models: hard-sphere and Maxwellian gas, a more realistic model, for predicting the boundaries of the convection domain has been presented here which is expected to be useful for future studies on related topics using more realistic gas models.