A Numerical Study on Convective Heat Conduction Problems for Anisotropic FGMs of Space-Time Dependent Properties

The study focuses on analysing two-dimensional transient problems in anisotropic functionally graded materials (FGMs) using a differential equation with time-space dependent coefficients. By employing a transformation technique, the equation with space-time dependent coefficients is simplified to an equation with time-dependent coefficients. Applying a Laplace transform results in a constant coefficients equation that can be expressed as boundary-only integral equations and solved using the boundary element method (BEM). The BEM solutions are then transformed back to obtain solutions in the time variable through numerical calculations. Various problems involving trigonometric, exponential and quadratic grading of materials with compressible or incompressible flow are successfully solved. The obtained numerical solutions demonstrate high accuracy.