Periodic time-dependent behavior of a rarefied gas between two parallel planes caused by an oscillatory heating of one plane is numerically studied based on the linearized Boltzmann equation. Detailed numerical data of the energy transfer from the heated plane to the unheated plane and the forces of the gas acting on the boundaries are provided for a wide range of the gas rarefaction degree and the oscillation frequency. The flow is characterized by a coupling of heat conduction and sound waves caused by repetitive expansion and contraction of the gas. For a small gas rarefaction degree, the energy transfer is mainly conducted by sound waves, except for very low frequencies, and is strongly affected by the resonance of the waves. For a large gas rarefaction degree, the resonance effects become insignificant and the energy transferred to the unheated plane decreases nearly monotonically as the frequency increases. The force of the gas acting on the heated boundary shows a remarkable minimum with respect to the frequency even in the free molecular limit.
Numerical Analysis of the Time-Dependent Energy and Momentum Transfers in a Rarefied Gas Between Two Parallel Planes Based on the Linearized Boltzmann Equation
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Doi, T. (November 3, 2010). "Numerical Analysis of the Time-Dependent Energy and Momentum Transfers in a Rarefied Gas Between Two Parallel Planes Based on the Linearized Boltzmann Equation." ASME. J. Heat Transfer. February 2011; 133(2): 022404. https://doi.org/10.1115/1.4002441
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