Heat flux field for one spherical inhomogeneity embedded in a functionally graded material matrix

The heat flux field for a single particle embedded in a graded material is derived by using the equivalent inclusion method. A linearly distributed prescribed heat flux field is introduced to represent the material mismatch between the particle and the surrounding graded materials. By using Green’s function technique, an explicit solution is obtained for the heat flux field in both the particle and the graded material. Comparison of the present solution with finite element results illustrates the accuracy and limitation of this solution.