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.


80A19 Diffusive and convective heat and mass transfer, heat flow
45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations
Full Text: DOI


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