Thermal effects in externally pressurized porous conical bearings with variable viscosity

Summary The present paper analyzes the porous constant gap externally pressurized conical bearings when the slider is rotating with uniform angular velocity. The lubricant is assumed to be incompressible, and its viscosity varies exponentially with temperature. The lubricant inertia due to rotation of the slider is considered but the convective inertia is neglected. The energy equation is used to determine the temperature generated in the lubricant film. The governing system of coupled momentum and energy equation is solved numerically, using finite difference method, to determine various bearing characteristics. It is observed that for the surfaces which are highly porous the inlet pressure decreases remarkably, resulting in reduced load capacity of the bearing, and the torque remains unaffected with respect to variation in the permeability.Notation c specific heat of the fluid - D dissipation parameter - E a type of Eckert number - h lubricant film thickness - h _p thickness of the porous matrix - H=h _p/h nondimensional thickness of the porous matrix - k thermal conductivity - permeability - L load capacity of the bearing - M torque on the bearing surface - p gauge pressure - p ^* pressure in the porous matrix - Pr Prandtl number - Q flow rate - R rotational parameter - Re Reynolds number - Re^* modified Reynolds number - T temperature of the lubricant - T _i, T_u temperature of the pad and the slider, respectively - u, v, w velocity components in thex, y and directions, respectively - u ^*, v^*, w^* velocity components in the porous matrix - U, V, W reference quantities for the velocity components - x, y, conical coordinate system - x _in, x₀ inlet, outlet positions - angle between stationary pad surface and a plane perpendicular to the bearing axis - viscosity-temperature exponent - viscosity of the lubricant - density of the lubricant - v ₀ kinematic viscosity of the lubricant - ₀ viscosity of the lubricant at pad temperature - angular velocity of the slider