International Journal of Heat and Mass Transfer. Vol. 51, Nos. 11-12, pp. 3018-3024, 2008
H.M. Yina,b,*, G.H. Paulinoa, W.G. Buttlara, L.Z. Sunc
a Department of Civil and Environmental Engineering, Newmark
Laboratory, 205 North Mathews Avenue,
University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States
b Office of Flexible Pavement Materials, Transportation Laboratory, 5900 Folsom Boulevard, California Department of Transportation, Sacramento, CA 95819, United States
c Department of Civil and Environmental Engineering, 4139 Engineering Gateway, University of California, Irvine, CA 92697, United States
Abstract
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.
KEY WORDS: Functionally graded materials; Equivalent inclusion method; Inhomogeneity; Thermal conduction; Heat transfer