Effect of the potential field on non-Fickian diffusion problems in a sphere

The present study applies a hybrid numerical method to investigate the effect of a potential field on one-dimensional non-Fickian diffusion problems in a sphere. This hybrid numerical scheme involves the Laplace transform technique and the control volume method in conjunction with the suitable hyperbolic shape functions. The Laplace transform method is used to remove the timedependent terms in the governing differential equation and boundary conditions, and then the transformed equations are discretized by the control volume scheme. It is worth noting that the boundary condition at r=0 should be carefully established for the present problems to determine an accurate numerical result. To evidence the accuracy of the present numerical method, a comparison of the mass concentration distribution between the present numerical results and the analytic solutions is made for the potential gradient dV/dr=0. The results show that the present numerical results agree well with the analytic solutions and do not exhibit numerical oscillations in the vicinity of the jump discontinuity for various potential values. The important findings are that dV/dr has a great effect on the mass concentration distribution, and the strength of the jump discontinuity can decrease with increasing the value of the dimensionless potential gradient.