A three dimensional thermohydrodynamic lubrication model which couples the Reynolds and energy equations is developed. The model uses the streamline upwind Petrov-Galerkin (SUPG) method to solve the non-symmetric stiffness matrix that results from the convective-dominated flow. Model results indicate that the peak temperature is not on the mid-plane surface, a fact that cannot be predicted with two dimensional models. This position shifts towards the mid-plane as the width to length ratio is reduced from ten to one (square slider) as well as when pressure boundary conditions are altered in such a way that the inlet/outlet pressure is higher than the side pressure. The square slider has a peak temperature 4°K less than the wider slider. This is due to the higher side flow in the square slider.
Three-Dimensional Thermal Field in Slider Bearings
Zengeya, M, Gadala, M, & Segal, G. "Three-Dimensional Thermal Field in Slider Bearings." Proceedings of the World Tribology Congress III. World Tribology Congress III, Volume 1. Washington, D.C., USA. September 12–16, 2005. pp. 427-428. ASME. https://doi.org/10.1115/WTC2005-63076
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