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Upper and Lower Bounds on Knudsen Flow Rates

1967; American Institute of Physics; Volume: 8; Issue: 3 Linguagem: Inglês

10.1063/1.1705225

1527-2427

William Strieder, Stephen Prager,

Quantum Electrodynamics and Casimir Effect

Reciprocal variational principles are used to formulate upper and lower bounds on the low-pressure (Knudsen) flow rate of a gas through a channel of arbitrary geometry. The upper bound is equivalent to one obtained earlier by DeMarcus, but we believe the lower bound to be new. Explicit calculations are given for a short parallel-plate channel. The variational principles discussed here may be applied to a wide range of problems involving linear inhomogeneous integral equations.