# Interdisciplinary Applied Mathematics

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Л = 61.6 and M = 0.08. As evident from Figure 6.6, very good agreement is found between the generalized Reynolds equation and the DSMC results. The pressure profile predicted by the first-order slip model exhibits significant deviations from the DSMC data. Predictions using a second-order slip model (not shown on the figure) also result in considerable errors (Liu and Ng, 2001). In Figure 6.6 (b), we consider a slider bearing with an identical geometric configuration as in case (a). However, the bearing number is increased to Л = 758 by increasing the plate speed to sonic conditions

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FIGURE 6.4. Nondimensional Poiseuille flow velocity profiles in the upper half of a channel for к = у/к/2 Kn = 0.1,1.0, and 10.0 flow. The “current model” in the figure is from (Bahukudumbi and Beskok, 2003).

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U

0.9 0.8

>-

0.7 0.6 0.5

FIGURE 6.5. Variation of the Poiseuille flowrate coefficient Qp as a function of the inverse Knudsen number at the exit of the channel. The “current model” in the figure is from (Bahukudumbi and Beskok, 2003).

(c)

FIGURE 6.6.    Slider    bearing    pressure    profiles    for    different    Knudsen    number    and

bearing number combinations. The DSMC results are from (Alexander et al., 1994), and the Fukui and Kaneko data are from (Fukui and Kaneko, 1988). The “Current model” in the figure is from (Bahukudumbi and Beskok, 2003).

(M = 1.0). Surprisingly, the pressure distributions predicted by different models are very similar. This is because of the high bearing number. Since the bearing number is the ratio of the Couette and Poiseuille flow rates, the Couette flow is    dominant    at    high Л    values.    In    Figure    6.6    (c),    we    con

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