Drying viscoelastic materials: a non-Fickian approach

In this paper, we study a system of partial differential equations defined in a moving domain. This system is defined by a heat equation and a diffusion equation for a concentration of non-Fickian type whose diffusion coefficient depends on the temperature, completed with suitable initial and boundary conditions. The non-Fickian mass flux is established considering the viscoelastic properties of the medium where the strain depends on the temperature and on the concentration. The initial boundary value problem (IBVP) analyzed can be used to describe the drying of viscoelastic materials where the internal structure offers a resistance to the movement of the moisture molecules and a consequent delay in the moisture removal. Due to heat transference into the materials and moisture removal, shrinkage of the medium occurs. The stability of the IBVP defined in a moving domain is analyzed and its qualitative behavior is numerically studied.