# Interdisciplinary Applied Mathematics

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A=(257r d2n)_1.    (1.5)

For example, for air at standard conditions, A « 6.5 x 10-8 m.

TABLE 1.1. Thermophysical properties of typical gases used in microdomain applications at atmospheric conditions (298 K and 1 atm).

 Gas Density Dynamic Thermal Conductivity [W/(m K)] Thermal Specific Mean [kg/m3] Viscosity Diffusivity Heat Free [kg/ (m s)] [m2/s] [J/(kg K)] Path [in] Air 1.293 1.85E-5 0.0261 2.01E-5 1004.5 6.111E-8 n2 1.251 1.80E-5 0.0260 2.00E-5 1038.3 6.044E-8 О 1.965 1.50E-5 0.0166 1.00E-5 845.7 4.019E-8 о to 02 1.429 2.07E-5 0.0267 2.04E-5 916.9 6.503E-8 He 0.179 1.99E-5 0.150 1.60E-4 5233.5 17.651E-8 Ar 1.783 2.29E-5 0.0177 1.93E-5 515.0 6.441E-8

The gas molecules are traveling with speeds proportional to the speed of sound. The mean-square molecular speed of gas molecules is given in (Vincenti and Kruger, 1977):

c = — = V 3 RT,    (1-6)

V P

where R is the specific gas constant. For air under standard conditions this corresponds to    486    m/s.    This    value    is    about    three to five    orders    of

magnitude greater than the typical average speed in microscale gas flows.

With regard to the time scales of intermolecular collisions, we can obtain an    average value    by    taking    the    ratio    of    the    mean free    path    to the

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