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**Modeling of thermal distributions around a barrier at the interface of coating and substrate.**
*(English)*
Zbl 1470.80005

Summary: 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.

### MSC:

80A19 | Diffusive and convective heat and mass transfer, heat flow |

45G10 | Other nonlinear integral equations |

65R20 | Numerical methods for integral equations |

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\textit{A. Sahin}, Abstr. Appl. Anal. 2013, Article ID 968464, 8 p. (2013; Zbl 1470.80005)

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### References:

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