The heat conduction in nanosized structures
Thermal transport cannot be well described by classical Fourier’s law in nanosized structures. A novel gradient theory is developed in such structures adopting the size effect of heat conduction. This is achieved by considering the second derivatives of temperature in the constitutive equation for the high-order heat flux in an advanced continuum model. The variational principle is applied to derive the governing equations. The general two-dimensional boundary-value problem for heat conduction is analyzed by the finite element method (FEM). A mixed FEM with two independent C<sup>0</sup> continuous interpolations for temperature and temperature gradients is developed. The constraints between temperature and its gradients are performed by the collocation approach. Parametric studies are given to evaluate the influence of the internal size on the temperature distribution.