MATHEMATICAL MODEL FOR NANOFIBERS’ DIFFUSION IN A NANOFLUID AND NUMERICAL SIMULATION

The diffusion process of the nanofibers in a nanofluid displays a combination of diffusion and wave characteristics. The wave-like behavior is attributed to the large aspect ratio of the nanofiber, which can be modeled as a bead-spring chain system, exhibiting wave-like properties. In order to describe this mixed diffusion-wave phenomenon, a fractional diffusion-wave equation is proposed, wherein multiple time fractional derivatives are employed. By appropriately regulating the fractional time terms, the model can be transformed into either the traditional diffusion equation or the traditional wave equation, as required. A numerical schedule is developed through the implementation of suitable time and space discretization, and a stability analysis is conducted. The numerical results substantiate the reliability of the numerical schedule and its applicability to other fractional differential equations.