engleski

A Formulation of Boundary Element Method for Two-Dimensional Steady Heat Conduction

The paper presents a formulation of boundary element method for solving of steady heat conduction problems in two-dimensional homogeneous space. Described method can be used to find the temperature field on the boundary of machine elements that are exposed to predetermined heat sources generated by friction, for example, on the hydrostatic and hydrodynamic bearings, gears, etc. A formulation of presented method is observed step by step. Governing integral equation, that is derived from Laplace differential equation, originates a set of integral equations. Two of them are used in formulation of boundary integral equation, that represents equilibrium between predetermined and unknown boundary conditions (heat flux and temperature). By splitting the boundary into the boundary elements, boundary integral equation transforms to the ordinary system of linear equations, which solution determines unknown boundary conditions. Once, when boundary conditions are completely defined, it is easy to find temperature at any point within the body. Developed equations differs from usual one, involve reductions of final expressions, and consequently reduction of round-off error.

heat conduction; heat flux; temperature; Laplace differential equation; boundary element method; machine elements; bearings; gears; friction

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