A study on transient flow formation in concentric porous annuli filled with porous material having variable porosity

Abstract

This research explores the transient flow formation in concentric porous annuli filled with porous material having variable porosity. The study focuses on the fluid flow between two horizontal concentric cylinders, assuming the fluid is viscous and incompressible. To solve the governing partial differential equation, the Laplace transform technique is applied, transforming it into an ordinary differential equation in the Laplace domain. Exact solutions are obtained in the Laplace domain, and then inverted to the time-dependent domain using the Riemann-sum approximation method.The accuracy of the Riemann-sum approximation method is validated by comparing the numerical values obtained with those of the exact solution for steady-state flow and transient solution. The results are presented graphically, illustrating the variations of velocity and skin friction with respect to the Darcy number and suction/injection parameter.The study reveals that suction accelerates the flow, while injection retards it. The Darcy number, which represents the permeability of the porous medium, significantly affects the flow characteristics. The skin friction, which is a measure of the shear stress at the surface, is also influenced by the suction/injection parameter.The findings of this study have implications for various engineering applications, such as groundwater flow, oil reservoirs, and chemical engineering processes. Understanding the transient flow formation in porous annuli can help optimize the design and operation of these systems.The use of the Laplace transform technique and Riemann-sum approximation method provides an efficient and accurate solution to the problem. The graphical representation of the results allows for a clear understanding of the flow characteristics and the effects of various parameters. The list of symbols, notation and meaning of parameters can be found in appendix A and B attached in section below.