Time-fractional heat transfer equations in modeling of the non-contacting face seals

Abstract

The paper presents a mathematical model of a heat transfer process for non-contacting face seals. For a slewing ring (rotor), a time fractional Fourier law obtained from fractional calculus was applied. Heat exchange in the stator was described using Laplace’s equation. Heat flux generated in the medium layer separating the rings is discharged first to a working ring and the to a surrounding medium. Distribution of temperature fields in sealing rings was determined with the use of analytical methods, using integral transformation method. The fractional heat conduction equation (for the rotor) was considered in the light of the case 0<α⩽2 with the special attention paid to α=1 for the classical heat conduction equation.The proposed way of solving is very broad and involves many theoretical and practical problems, which were taken into account and described in the work. Finally, numerical results are presented graphically for various values of both operational and geometric parameters and order of fractional derivative.