A description of anisotropic porous nanocrystals filled by a fluid flow in the framework of extended thermodynamics with internal variables

In a previous paper a non conventional model for fluid-saturated porous crystals was derived in the framework of non-equilibrium thermodynamics introducing in the thermodynamic state vector, as internal variables describing the porous defects, a structural permeability tensor a la Kubik, ` ri j, its gradient, ri j,k, and its flux, Vi jk. Here, we work out for nanocrystals with porous channels filled by fluid flow, in the anisotropic and linear case, the constitutive relations for the stress tensor, the entropy density, the chemical potentials for the concentration of the fluid and for the defects field, and the rate equations for the ri j, Vi jk, the fluid and the heat fluxes, describing disturbances propagating with finite velocity. Also, the closure of the system of equations describing the behaviour of these nanosystems with defects is discussed, presenting the linearized temperature and internal energy equations. The obtained results may have relevance in important advanced studies on nanostructures, where their defects have a direct influence on mechanical and transport properties, in particular on thermal conductivity. Inside these nanomaterials there are situations of high-frequency waves propagation and the phenomena are fast.