Analysis of non-Fickian diffusion problems in a composite medium

Abstract

The one-dimensional non-Fickian diffusion problems in a two-layered composite medium for finite and semi-infinite geometry are analyzed by using a hybrid application of the Laplace transform technique and control-volume method in conjunction with the hyperbolic shape functions, where the effect of the potential field is taken into account. The Laplace transform method used to remove the time-dependent terms in the governing differential equation and boundary conditions, and then the transformed equations are discretized by the control volume scheme. To evidence the accuracy of the present numerical method, a comparison between the present numerical results and analytical solution is made for the constant potential gradient. Results show that the present numerical results are accurate for various values of the potential gradient, relaxation time ratio, and diffusion coefficient ratio. It can be found that these values play an important role in the present problem. An interesting finding is that when the mass wave encounters an interface of the dissimilar materials, a portion of the wave is reflected and the rest is transmitted. The speed of propagation can change owing to the penetration of the mass wave into the region of the different material. The wave nature is significant only for short times and quickly dissipates with time.