A new problem of hydrodynamic lubrication with temperature and viscosity variations in gap height direction

Numerous Authors of scientific papers occurring in hydrodynamic theory of slide bearing lubrication, up to now almost always had neglected the oil dynamic viscosity variations caused by temperature, adhesion forces, capillary forces, or hydrogen ion concentration across the film thickness by virtue of the statement of the constant temperature as well constant adhesion as capillary forces in the thin bearing gap height direction. In addition, simultaneously by virtue of boundary layer simplifications for energy equation and by virtue of new measurements performed in micro and nano- level follows that oil temperature gradients and its values differences and adhesion or capillary gradients of forces in bearing gap height directions are not negligible small. The contemporary hydrodynamic theory of lubrication for non-isothermal lubricant flow is unfortunately based on the assumption of constant viscosity values across the film thickness, despite abovementioned self-evident contradiction between the fact of constant viscosity and simultaneously temperature variations in gap height direction. Such problem was up to now not sufficient critical examined and explained in practical and theoretical sense. After Authors, knowledge by virtue of above problem the most scientific papers in the domain of non-isothermal and lamellar hydrodynamic slide bearing or biobearing lubrication were up to now not sufficient correctly solved. It denotes that the main hydrodynamic lubrication solutions presenting for example hydrodynamic pressure by the modified Reynolds equation and temperature by the energy conservation equation are not sufficiently correctly obtained and next not correctly solved. Therefore are assumed simultaneously the temperature T and oil dynamic viscosity variations in length, width and bearing gap- height directions. From this assumption follows, that the energy equation must be solved simultaneously with the equations of motion i.e. consequently with pressure equation where viscosity depends on temperature and temperature depends on the coordinate in gap height direction.