Rarefied gases, conduction

The local value of Knudsen number determines the degree of rarefaction and the degree of validity of the continuum model in a particular flow. The different Knudsen number regimes depicted in Fig. 2 have been determined empirically and are therefore only approximate for a particular flow geometry. The pioneering experiments in rarefied gas dynamics were conducted by Knudsen in 1909 [24]. 

The investigations of Hertz were given a new impetus only a few decades later in the studies of Knudsen [20] and Langmuir [21]. The interest of Knudsen in vaporization was prompted by his studies of thermal conductivity and rarefied gas flow, as well as by the possibility of development of the effusion... 

Tunc and Bayazitoglu [3] have calculated for the T case the fully developed Nusselt numbers for microtubes through which a rarefied gas flows by taking into account the viscous dissipation but neglecting axial conduction in the fluid and the flow work. They defined the Brinkman number (Eq. 20) with ATref = Te — Tip and used in the slip boundary conditions (Eqs. 8 and 19) (x = = a., = a, = 1. The values of the Nusselt... 

For gas-filled granular beds, the thermal conductivity of the gas may be very low. Since gas phase heat conduction mainly occurs near the points of contact between adjacent solid particles, the distance for heat conduction over the gas phase may approach the mean free path of the gas molecules. This reduces the thermal conductivity of the gas further, since the whole system may become rarefied for evacuated beds of fine powders. 

In Table 15 the fully developed Nusselt numbers for trapezoidal microchannels in which rarefied gases flow under the HI boundary craidition with four heated sides (4bc) are quoted. These values are obtained for a gas having Pr = 0.7 by neglecting viscous dissipation, axial conduction and flow work and using in the slip boundary conditions (Eq. 8 and 19) ol = = ol, = a, =. ... 

Rarefied analyses of thermal coupling between the micro-nozzle with the surrounding substrate have also been reported [10]. In this work, steady low Reynolds number gas flows were again modeled by the DSMC approach, and the substrate transient thermal response was governed by the heat conduction equation. It was shown that propulsive efficiencies of the micronozzle decreased with higher nozzle wall temperatures and vice versa. These results are in agreement with the continuum-based heat transfer results previously discussed. 

---