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Mechanical Engineering

Chebyshev collocation method

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Full-Text Articles in Engineering

The Onset Of Convection In Rarefied Gases, Md Asif Zobaer Sep 2017

The Onset Of Convection In Rarefied Gases, Md Asif Zobaer

Electronic Thesis and Dissertation Repository

The onset of convection in the Rayleigh-BĂ©nard 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 ...


Convection Due To Spatially Distributed Heating, Mohammad Zakir Hossain Nov 2011

Convection Due To Spatially Distributed Heating, Mohammad Zakir Hossain

Electronic Thesis and Dissertation Repository

Convection in an infinite horizontal slot subject to spatially distributed heating has been investigated for a wide range of Prandtl numbers. The primary flow response consists of convection in the form of rolls. When heating wave number alpha is sufficiently large the convection is found to be limited to a layer adjacent to lower wall and a uniform conductive layer emerges at upper section of the slot.

Conditions leading to the emergence of secondary convection have been identified using linear stability of the above primary convection. The secondary convection gives rise to longitudinal, or transverse, or oblique rolls; or to ...