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Abstract and Applied Analysis
Volume 2013, Article ID 968464, 8 pages
Research Article

Modeling of Thermal Distributions around a Barrier at the Interface of Coating and Substrate

Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey

Received 7 March 2013; Accepted 2 August 2013

Academic Editor: Adem Kılıçman

Copyright © 2013 Ali Sahin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Due to constant heat flux, the thermal distribution around an insulated barrier at the interface of substrate and functionally graded material (FGM) which are essentially two-phase particulate composites is examined in such a way that the volume fractions of the constituents vary continuously in the thickness direction. Using integral transform method, two-dimensional steady-state diffusion equation with variable conductivity is turned into constant coefficient differential equation. Reducing that equation to a singular integral equation with Cauchy type, the temperature distribution around the barrier is obtained by defining an unknown function, which is called density function, as a series expansion of orthogonal polynomials. Results are shown for different thickness and nonhomogeneity parameters of FGM.