In rarefied gases, mass and heat transport processes interfere with each other, leading to the mechano-caloric effect and thermo-osmotic effect, which are of interest to both theoretical study and practical applications. We employ the unified gas-kinetic scheme to investigate these cross coupling effects in gas flows in micro-channels. Our numerical simulations cover channels of planar surfaces...

The present paper deals with the two-dimensional numerical simulation of gaseous flow and heat transfer in planar microchannel and nanochannel with different wall temperatures in transitional regime 0.1≤Kn≤1 . An atomistic molecular simulation method is used known as thermal lattice-Boltzmann method. The results of simulation are presented in four cases corresponding to the Fourier flow, shear-...

* Present address: Applied Mathematics Department, Brookhaven National Laboratory, Upton, New York. • See, for instance, L. Landau and E. Lifshitz, Fluid Mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1959). scribed by the classical theory of Stokes and Kirchoff. • This theory is, of course, based on the Navier-Stokes equations. However, for high-frequency sound propagation in ...

Let K n denote the Cartesian product Kn Kn Kn, where Kn is the complete graph on n vertices. We show that the domination number of K n is ⌈

Knudsen compressors are devices without any moving parts that use the nanoscale phenomenon of thermal transpiration to pump or compress a gas. Thermal transpiration takes place when a gas is in contact with a solid boundary along which a temperature gradient exists. If the characteristic length scale is on the order of, or smaller than, the molecular mean free path, then the gas flows from cold...

Let the random variable Zn,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1, ..., n}. We show that V ar(Zn,kn ) = o((EZn,kn ) ) as n → ∞ if and only if kn = o(n 2 5 ). In particular then, the weak law of large numbers holds for Zn,kn if kn = o(n 2 5 ); that is, lim n→∞ Zn,kn EZn,kn = 1, in probability. We also ...

Let S(n, k) denote the Stirling number of the second kind, and let Kn be such that S(n,Kn − 1) < S(n,Kn) ≥ S(n,Kn + 1). Using a probabilistic argument, we show that, for all n ≥ 2, ⌊e⌋ − 2 ≤ Kn ≤ ⌊e ⌋+ 1, where ⌊x⌋ denotes the integer part of x, and w(n) denotes Lambert’s W function.