Accession Number : ADA119621

Title :   Finite-Element Method for Heat Transfer Problem in Hydrodynamic Lubrication.

Descriptive Note : Research and development rept.,

Corporate Author : DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD SHIP PERFORMANCE DEPT

Personal Author(s) : Bai,Kwang June

PDF Url : ADA119621

Report Date : Apr 1982

Pagination or Media Count : 36

Abstract : Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearing used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. It has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain (lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical computations, numerical convergency errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubricant problem are presented for a second numerical model. (Author)

Descriptors :   *Heat transfer, *Finite element analysis, *Numerical analysis, *Mathematical models, Hydrodynamics, Lubrication, Thrust bearings, Thermal diffusion, Equations, Stability, Thermal radiation, Parabolas

Subject Categories : Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE