A Seminumerical Approach for Heat Diffusion in Heterogeneous Media: One Extension of the Analytical Quadrupole Method

• Published in: Numerical heat transfer. Part B, Fundamentals Vol. 42; no. 4; pp. 325 - 348
• Main Authors: Fudym, Olivier, Ladevie, Bruno, Batsale, Jean-Christophe
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Informa UK Ltd 01-10-2002; Taylor & Francis
• Subjects: Analytical and numerical techniques; Civil Engineering; Construction durable; Eco-conception; Engineering Sciences; Environment and Society; Environmental Sciences; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Materials; Mechanics; Physics; Thermics; Temperature distribution; Thermal diffusion; Stratified medium; Digital simulation; Analytical method; Matrix calculus; Inhomogeneous media; Boundary conditions; Two layer medium; Quadrupoles; Discretization method; Thermal conduction
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/10407790190053978

The analytical thermal quadrupole method is suitable for the modeling of multidimensional transient heat diffusion in homogeneous media, especially when applied to multilayered media. Here, we propose a new approach in order to extend the quadrupole frame to heterogeneous media. A seminumerical general solution is proposed for transient heat transfer in finite or semi-infinite media in both axial and radial coordinate systems, when the variation of thermal properties is one-dimensional. The presentation of the method is explained with a 2-D two-layer slab case. Some application examples are then presented from this basic case. The analytical expressions allow deep insight about the physical phenomenon.