Open Access

ARTICLE

Analytical Exact Solutions of Heat Conduction Problems for a Three-Phase Elliptical Composite

Ching Kong Chao^1,2, Chin Kun Chen¹, Fu Mo Chen³

1 Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taiwan
2 Corresponding author, E-mail: ckchao@mail.ntust.edu.tw
3 Department of Mechanical Engineering, Nan-Kai University of Technology, Taiwan.

Computer Modeling in Engineering & Sciences 2009, 47(3), 283-298. https://doi.org/10.3970/cmes.2009.047.283

Abstract

Analytical exact solutions of a fundamental heat conduction problem for a three-phase elliptical composite under a remote uniform heat flow are provided in this paper. The steady-state temperature and heat flux fields in each phase of an elliptical composite are analyzed in detail. Investigations on the present heat conduction problem are tedious due to the presence of material inhomogeneities and geometric discontinuities. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and heat flux are derived explicitly in a closed form. Some numerical results of the temperature and heat flux distributions are discussed in detail and provided in full-field configurations. The heat flux concentration factor around the geometric discontinuity is introduced to quantify the amount of the local energy accumulation.

---

Keywords

---