Hyperbolic heat conduction at a microscopic sliding contact with account of adhesion-deformational heat generation and wear

Abstract

Different non-Fourier models were proposed to simulate temperatures in materials subjected to extremely fast thermal disturbances, when the speed of heat propagation should be concerned. The present study investigated temperature and heat balance at a microscopic sliding contact during a single frictional interaction based on the Cattaneo-Vernotte hyperbolic heat conduction equation. Two fundamental features of friction, namely, adhesion-deformational heat generation and wear, were taken into account. By applying the Laplace transform approach, non-stationary temperature expressions were derived for the hyperbolic and classical parabolic heat conduction equations. Parametric analysis was then done for parameter ranges typical of brake materials. It was found that the hyperbolic heat conduction generally results in a higher temperature at the sliding surface compared to the parabolic heat conduction. The influence of the heat propagation speed can be significant for thermal relaxation time of the order above microsecond. It becomes stronger with an increase in the contribution of the adhesive heat generation. Another finding obtained is that a considerable fraction of heat is removed from the contact zone along with wear debris, resulting in a lower temperature. This fraction is larger for the hyperbolic heat conduction.