zbMATH — the first resource for mathematics

Analytical exact solutions of heat conduction problems for a three-phase elliptical composite. (English) Zbl 1231.80008
Summary: 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.

80A20 Heat and mass transfer, heat flow (MSC2010)
74E30 Composite and mixture properties
Full Text: DOI