2 - Dimensional analysis and analytical solutions

Abstract

An analytical solution helps in the validation of numerical methods/solutions as well as the comprehension of mechanisms and physical effects. Analytical solutions of the problem of flow in porous media, magnetic flow in porous media, nanoparticles transport in porous media, and magnetic nanoparticles transport in porous media are addressed in this chapter. Also, dimensional analysis is vital in handling problems regardless of their actual dimensions, which is helpful in large-scale problems such as hydrocarbon reservoirs. Therefore, this chapter also introduces a simplified one-dimensional model of nanoparticle transport in porous media and its generalized nondimensional form that will be solved analytically and numerically to obtain physical insight.