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.

中文翻译：

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椭球夹杂引起的半空间温升的显式解析解及其在摩擦热相关问题中的应用

摘要 本研究获得了包含椭球体包裹体的半无限空间中温升的格林函数。推导出由均匀分布在域内的特征温度梯度产生的扰动温升的显式表达式。此外，通过应用等效包含法（EIM），所提出的解析解方法被用于处理受到摩擦加热的异质半空间中的温升，其结果被证明与基准的结果非常吻合。讨论了热负荷速度、椭球不均匀性的空间取向和纵横比对半无限空间中温升的影响。最后，