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Abstract
This article deals with a numerical investigation of fluid inertia effects on inclined slider bearings lubricated by couple stress fluids. Convective inertial forces are considered in the film fluid. A reduced version of the Navier-Stokes equations is thus derived. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing partial differential equations are discretized by finite differences based on boundary layer–type equations. The resulting algebraic equations are solved using a Gauss-Seidel method. Compared to the case of the non-inertia Newtonian lubricant, the couple effects of fluid inertia forces and non-Newtonian couple stresses provide a significant improvement in slider bearing load capacity.
Nomenclature
| a | = | Aspect ratio, a = he/hs |
| Cf | = | Friction coefficient, Cf = |τ|/W |
| h | = | Fluid film thickness (m) |
| he | = | Fluid film thickness at the bearing inlet (m) |
| hs | = | Fluid film thickness at the bearing outlet (m) |
| h* | = | Dimensionless fluid film thickness, h* = h/hs |
| L | = | Bearing length (m) |
| l | = | Couple stress parameter, |
| M | = | Number of mesh intervals in the bearing sliding direction |
| N | = | Number of mesh intervals in the cross-film direction |
| p | = | Fluid film pressure (Pa) |
| p* | = | Dimensionless fluid film pressure, |
| Q | = | Volumetric flow rate per unit width (m2/s) |
| Q* | = | Dimensionless volumetric flow rate, |
| Re | = | Reynolds number in the fluid film, |
| U | = | Sliding velocity of the lower surface (m/s) |
| u | = | Velocity component in the bearing sliding direction (m/s) |
| u* | = | Dimensionless velocity component in the bearing sliding direction, |
| W | = | Load capacity (N) |
| W* | = | Dimensionless load capacity |
| w | = | Velocity component in the cross-film direction (m/s) |
| w* | = | Dimensionless velocity component in the cross-film direction, |
| x | = | Cartesian coordinate in the bearing sliding direction |
| x* | = | Dimensionless Cartesian coordinate in the bearing sliding direction, |
| Δx* | = | Mesh step size in bearing sliding direction (m) |
| z | = | Cartesian coordinate in the cross-film direction |
| z* | = | Dimensionless Cartesian coordinate in the cross-film direction, |
| Δz* | = | Mesh step size in the cross-film direction (m) |
| ϵ | = | Scale ratio, |
| η | = | Material constant responsible of the couple stress property (Pa s m2) |
| λ | = | Characteristic length of the size of solid particles suspended in fluid (m), |
| μ | = | Fluid dynamic viscosity (Pa s) |
| ρ | = | Fluid density (kg/m3) |
| τ | = | Total viscous force on the sliding surface (N) |
| τ* | = | Dimensionless total viscous force on the sliding surface |
| τxz | = | Shear stress (N/m2) |