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- W1971114019 abstract "Onsager’s classic treatment of axisymmetric, stationary flow in a rapidly rotating centrifuge is based on the theorem of minimum entropy production. For the case of end-driven flows, this approach yields a sixth-order, self-adjoint equation (the “pancake” equation) for a master potential, χ, whose second-order radial derivative is equivalent to axial mass flow. This formulation allows for a straightforward application of mass flow conditions on the axial boundaries, and χ provides a theoretical foundation for describing axial mass-driven flow in a centrifuge. Alternatively, several authors have described axisymmetric flow in a centrifuge by a sixth-order partial differential equation for temperature. So far, however, there has been no established theoretical connection between Onsager’s minimum principle and the thermal problem. This topic is considered in this paper and the corresponding derivation also results in a self-adjoint problem, in this case in terms of a temperature potential, Φ. Moreover, it may be shown that the corresponding variational form of the thermal problem is equivalent to the original Onsager entropy integral. The resulting Euler equation in the temperature potential Φ gives rise to a radial operator, M6, which, in terms of the composition of fundamental third-order operators (i.e., M6=L3L3* where L3 is the radial shear operator and L3* is the radial heat flux operator), is the commutation of the original “pancake” operator, L6 (i.e., L6=L3*L3). Furthermore, based on this relationship, M6 and L6 are shown to be isospectral except for the point 0, which is an eigenvalue of M6 but not of L6." @default.
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- W1971114019 date "2002-09-05" @default.
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- W1971114019 title "A new variational approach to gas flow in a rotating system" @default.
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- W1971114019 doi "https://doi.org/10.1063/1.1504451" @default.
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