# Interdisciplinary Applied Mathematics

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Previous models for the generalized Reynolds equation predict the pressure distribution and load capacity on the slider. However, it is impossible to predict    the    skin friction    distribution    and    viscous    drag    on    the    runner

(stationary) and slider (moving) surfaces, which are important in predicting the pitch and roll moments. In addition, accurate prediction of viscous forces enables robust head suspension design and calculation of actuator power consumption. To address this need, Bahukudumbi and Beskok (2003) developed a modified Reynolds equation to accurately predict the velocity and shear stress distribution, pressure profile, and load capacity in slider bearings for a wide range of Knudsen numbers (Kn < 12). Their approach is a superposition of the unified Poiseuille flow model of Section 4.2.2 with the linear Couette flow model of Section 3.2. Neglecting the thermal creep effects Qp, the one-dimensional generalized Reynolds equation becomes

###### d

dX

where Qp is due to the pressure-driven flow, and it is dependent on the local Kn. Following the model presented in Section 4.2.2, we have

#### 57 Qp

where a is the rarefaction parameter. In Section 4.2.2 we determined a using the volumetric flowrate for duct and pipe flows as a function of Kn. In this section, we choose a by matching the volumetric flowrate data for twodimensional pressure-driven flows in the entire Knudsen regime, obtained from the solutions of the linearized Boltzmann equation. Therefore, the current modified Reynolds equation (6.12) is identical to that of Fukui and Kaneko (1988). However, there is an important difference between the two approaches. The model presented in (Bahukudumbi and Beskok, 2003), is able to predict the local velocity profile and shear stress. For example, the local velocity distribution for Poiseuille flow is given by

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