An explicit analytical solution for temperature rise in a half-space induced by ellipsoidal inclusions and its application for problems related to friction heating

Abstract

Green functions for temperature rise in a semi-infinite space containing an ellipsoidal inclusion are obtained in the present study. Explicit expression for disturbed temperature rise generated by eigen-temperature gradients uniformly distributed within a domain is derived. Further, the proposed analytical solution method is utilized to deal with temperature rise in heterogeneous half-space subjected to friction heating via applying the equivalent inclusion method (EIM), whose results are proven to be in good agreements with those of the benchmarks. Influences of heat load velocity, spatial orientation and aspect ratio of ellipsoidal inhomogeneity on temperature rise in a semi-infinite space are discussed. Finally, a model of semi-infinite medium with embedded dispersed ellipsoidal inhomogeneities of arbitrary spatial orientation is adopted to explore the application scope of the proposed solution method.

Keywords:

• Analytical solution
• ellipsoidal inclusion
• friction heating
• half-space
• temperature rise

Additional information

Funding

The authors would like to acknowledge the support from National Natural Science Foundation of China (No. 51875373), the Science and Technology Foundation of Sichuan (2019YJ0093) and the CAST-BISEE Foundation (2019-006). Q.Z. would also like to acknowledge the supports from the China Postdoctoral Science Foundation (No. 2018M643469, 2019T120836).