No abstract

This paper presents approximate analytical solutions for the diffusion problems of a cylindrical hole in an infinite medium and a slot in an infinite medium with properly prescribed boundary conditions and initial conditions. These solutions have much simpler forms than those of exact analytical solutions, and asymptotically approach the exact solutions with increasing time or the material point moving away from the internal boundary. The approximate analytical solution for the diffusion problem of a slot in an infinite medium is applied to establish a shape function for the infinite elements. Good agreement is found in comparison of our results with those presented by Li and Huang and Cinco‐Ley et al. Finally, an example simulating a primary recovery procedure in hydraulic fracturing technique for an oil field is presented.