In this paper, a first-order slip boundary condition is derived using the Chapman-Enskog solution of the Boltzmann equation. In comparison with the existing slip models such as first, second, and 1.5-order slip models, the Poiseuille flow rate predicted by the new slip model shows better agreement with that calculated by the linearized Boltzmann equation. The slip boundary condition is also applied to predict the pressure field in gas lubrication problems.

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When numerical methods are applied in engineering, verification is essential. Test problems can help in meeting this requirement. This is especially so when these problems are tuned to the application at hand. Unfortunately, in practice such tuned test problems are not always directly available. For these cases, this paper describes an approach for constructing tuned test problems. The approach may be used on ordinary or partial differential equations, be they linear or non-linear. This is demonstrated on a number of applications drawn from dynamics, solid mechanics, and fluid mechanics.

In order to check the numerical analysis of Reynolds equation for gas lubricated bearings, it is desirable to have available exact analytical solutions. This note outlines the construction of some exact, two-dimensional, transient solutions for this purpose.

The current formulation of the Reynolds equation for lubrication problems in the rarefied gas flow regime breaks down when the pressure varies rapidly in the flow direction, which could often happen in the complicated modern hard-disk drive air bearings. In this paper the effect of rapid pressure change in a small distance is examined using a new nonlocal formulation of rarefied Poiseuille flow. The new formulation couples the pressure distribution and the velocity distributions via the Reynolds equation. Detailed numerical strategies required to solve the nonlocal pressure field are explained by analyzing a particular slider structure. Comparisons of the pressure field calculated using the proposed nonlocal formulation with the pressure predicted by the local formulation reveal significant differences between them in the region of large pressure variation. The nonlocal effect discussed in this paper could be significant for certain disk-drive air-bearing design that involves large pressure variations.