Temperature fluctuation from incomplete fluid mixing induces fatigue damages on structures of nuclear components, which should be prevented. For rational analyses of this phenomenon, the authors have developed a frequency response function of thermal stress and extended to multi-dimensional spatial fluctuations of fluid temperature. This function is formulated by a product of the effective heat transfer and the effective thermal stress functions, and enables us to quickly calculate the thermal stresses induced by both local and global temperature distributions in structures. Furthermore, it can evaluate sensitivities of thermal stress to frequencies of temperature fluctuation, Biot number and constraint conditions of structures. Applicability of this function was verified for multi-dimensional problems such as thermal stratification problems and hot/cold spot ones.

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