Heat transfer analysis of irradiation-induced gas bubble in tungsten from a fractal dimension perspective

Abstract

The mechanism of heat transfer profoundly depends on the microscopic topological structure. In reality, the intrinsic nature of (un)-irradiated metals possesses the fractal characteristic that repeats a pattern at different scales and sizes regardless of the complexity. Herein we combine the conventional thermal conduction model with the analytical fractal solution in order to understand the effect of fractal parameter on estimating the proportion of each phase in dual- and triple-phase microstructures, the role of gaseous pressure in conducting heat, and the variation of effective thermal conductivity of the bubble-containing tungsten. The fractal dimension obtained from the differential box-counting (DBC) method is quantitatively compared with that from the classical box-counting (BC) method, and the relevance between two approaches in assessing the fractal dimension is analyzed and discussed. Importantly, the basic porosity-fractal dimension formula is qualitatively modified by introducing a regulatory factor to identify the microstructure with striking characteristic. This study provides evidence from the analytical fractal model that the effective thermal conductivity changes with grain size and bubble density. Meanwhile, the predicted results from the proposed model match well with the previous experimental data and the corresponding results predicted from the numerical finite element simulation. Focusing on the heat performance of (un)-irradiated material, the specific procedure allows us to extract the valuable data effectively and efficiently.