An LT-BEM for an unsteady diffusion-convection problem of another class of anisotropic FGMs

Abstract

An LT-BEM is used to find numerical solutions to an unsteady variable coefficients diffusion-convection equation governing problems of another class of anisotropic functionally graded media. A boundary-only integral equation is derived, following a transformation of the variable coefficients equation to a constant coefficients equation. The boundary-only integral equation is used to find the numerical solutions. Some problems considered are those for several new types of functionally graded materials of compressible or incompressible flow. The effects of the anisotropy and inhomogeneity of the considered materials on the solutions are also shown as to say that it is very important to take the anisotropy and inhomogeneity into account in experimental or practical studies for any applications.

Keywords:

• Variable coefficients
• anisotropic functionally graded materials
• unsteady diffusion-convection equation
• Laplace transform
• boundary element method

2010 Mathematics Subject Classifications:

• 65N38
• 35K51
• 44A10
• 35N10

Acknowledgments

The first author was supported by Hasanuddin University and Ministry of Research and Technology / National Research and Innovation Agency of Indonesia.

Data Availability

The data that supports the findings of this study are available within the article and its supplementary material.