Frictional contact results in dissipation of energy, wherein one part is transformed into thermal energy. This leads to heating under the surface, where the resulting transient temperature fields at short times and high Peclet numbers are of interest. Therefore, the numerical method of finite elements with space‐time stabilization technique is applied on the 2D hyperbolic heat conduction equation of Cattaneo‐Vernotte with respect to a moving frame. It is shown, that the combination of the θ‐Method with Streamline‐Upwind‐Petrov‐Galerkin‐FEM gives satisfying solutions for a wide broadband of Peclet numbers.
The hyperbolic wave equation of heat conduction with respect to Christov's formulation is utilized with the Streamline-Upwind-Petrov-Galerkin method in space and the Θ, Houbolt, linear acceleration, Wilson-Θ and Newmark methods in time. The derivation of this equation and its matrix formulation are shown. A 2D transient finite element simulation of a generic asperity with an infinite line heat source in an interface, either as a heat flux density q or temperature distribution T , is performed for Ma th = [0.5; 1.0]. A sensitivity study is presented for the mentioned numerical schemes. The temperature jump in the solution is interpreted as an indicator for a thermal shock.
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