Analysis of Temperature Fields in FGM Micro/Nano Solids by Moving Finite Element Method

This paper deals with the higher-grade theory of heat conduction in micro/nano solids with functionally graded material (FGM) properties. Making use the variation principles, the mathematical formulation of the boundary value problems is derived within higher-grade theory of heat conduction, i.e. the governing equation and the physically admissible boundary conditions are derived. Applying the developed formulation for FGM solid structures we can derive rather complex governing equation with variable coefficients and higher order derivatives of field variables. It is well known the high order derivatives of field variables can lead to decreasing of accuracy of the numerical solution. To eliminate this problem, the decomposition of the original governing partial differential equation (PDE) into the system of PDEs with lower order derivatives is proposed. For the numerical implementation the novel Moving Finite Element approximation method is utilized. Several numerical simulations are devoted to study the influence of micro-length scale parameter as well as the parameters of gradation of material parameters on the temperature field.