Study of non-Fickian diffusion problems with the potential field in the cylindrical co-ordinate system

The present study applies a hybrid numerical scheme of the Laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the e ect of a potential eld on the one-dimensional non-Fickian di usion problems in the cylindrical co-ordinate system. The Laplace transform method is used to remove the time-dependent terms in the governing di erential equation and the boundary conditions, and then the resulting equations are discretized by the control volume scheme. The primary di culty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities. Results show that the present numerical results do not exhibit numerical oscillations and the potential eld plays an important role in the present problem. The strength of the jump discontinuity can be reduced by increasing the value of the potential gradient. The propagation speed of mass wave is independent of the potential gradient and the boundary condition.