Convective Heat Conduction in Anisotropic FGMs: A Numerical Simulation

A combination of the Laplace transform (LT) and domain-boundary element method (DBEM) was employed to find numerical solutions for an unsteady diffusion-convection (DC) equation with spatial and temporal coefficients, considering arbitrary initial conditions and source terms. This method addresses problems in a unique class of anisotropic functionally graded materials (FGMs). The procedure involves converting the variable coefficient equation to a constant coefficient equation, Laplace transform and then deriving a domain-boundary integral equation. Numerical solutions were obtained using the standard domain-boundary element method and the Stehfest algorithm. This study examines cases involving compressible or incompressible flows, showcasing the precision of the numerical solutions.