Nonlinear Transient Heat Transfer and Optimisation of Multidirectional (1D/2D/3D) Functionally Graded Porous Composites

In this paper, the steady and transient heat transfer behaviours of multidirectional (1D/2D/3D) functionally graded composite plates are investigated. Also, two different porosity types, i.e., even and uneven distributions, are considered along with material gradation. Here, the spatial/temperature-dependent effective material properties of these highly heterogeneous composites with porosity are evaluated using the extended Voigt’s homogenisation scheme via multi-variable power-law functions and further verified with the representative volume element (RVE) scheme. In continuation, generalised mathematical models are developed by including material nonlinearity using the cubic-polynomial-based temperature-dependent constitutive model. The Poisson’s and Laplace’s equations are utilised for steady and transient heat transfer problems, respectively, and the weak form is derived using the Galerkin method. Further, coupled finite element method (FEM)–finite difference method (FDM) is adopted via Picard’s successive iteration and Crank–Nicolson technique to compute the nonlinear transient temperature. The proposed model is verified by comparing it with the previously reported results. In addition, the effects of heterogeneity, porosity, power-law indices and boundary conditions on the steady/transient heat transfer responses of multidirectional functionally graded plates are examined and discussed in detail. At last, the optimum material distributions are obtained using the response surface methodology (RSM) by minimising the heat transfer responses.