Three-dimensional problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

The analytical solution of three-dimensional heat conduction problem, including the temperature and thermal flux fields, is one important problems that have not been completely solved in solid mechanics. Considering dependence material parameters makes problem more difficult. In this paper, we first reduce temperature-dependent to Laplace equation by introducing intermediate function. Then, generalized ternary function proposed, general given. Finally, solutions three specific are obtained corresponding temperature-thermal fields discussed. results show field dependent same as classical constant conductivity approach result, while different from result. Thermal at a planar defect boundary has r-1/2 singularity, its intensity proportional fourth root width. On other hand, when blocked defect, distribution will re-adjusted so it overflows rate all parts boundary.