Unsteady diffusion of fluids through a non-linearly elastic cylindrical annulus

Abstract The unsteady radial diffusion motions of an incompressible fluid through an isotropic and transversely isotropic non-linearly elastic cylindrical annulus are studied by using the recent theory developed by Tao et al . [ Mathematical Models and Methods in Applied Sciences 1 (1991)]. As the fluid diffuses through the solid, ahead of it there is a pure solid while behind the diffusing front there is a mixture of a fluid and a solid. Governing equations for both the constituents, within the content of the theory of mixture, are used in the mixture region. On the diffusing front, the evolution equations are used based on the previous work of Tao et al . [ Mathematical Models and Methods in Applied Sciences 1 (1991)]. The problems are solved numerically using a finite difference method.