Solving direct and inverse heat conduction problems in functionally graded materials using an accurate and robust numerical method

Abstract In this study we present a numerical approach to solve steady-state heat conduction problems in functionally graded materials (FGMs). Two different types of material gradations are considered for spatially varying thermal conductivity FGM: (1) Quadratic gradation; (2) Exponential gradation. The proposed procedure is based on finite-difference method and developed the equation over general two-dimensional (irregular) conducting body (FGM) with Dirichlet, Neumann, Robin boundary conditions. addition presenting an accurate solution considering irregular shape variety conditions, other novel aspect identify constant parameters accurately by inverse analysis thereby determining form novelty lies proposing efficient explicit sensitivity scheme. main advantage scheme that it not involved adjoint all coefficients can be explicitly computed only one direct solution. conjugate gradient (CGM) used reduce mismatch between temperature part simulated measured distribution. accuracy, efficiency, robustness demonstrated through two test cases.