Finsler geometry for nonlinear path of fluids flow through porous media

Nonlinear paths of the fluids flow determined by the Finsler geometry conforming to Darcy's law have been investigated through inhomogeneous porous media. Geodesics in a Finsler space are used to determine the nonlinear paths of a fluid flow in inhomogeneous anisotropic porous medium. Significant differences occur between the Riemannian and Finslerian geodesics due to the directional dependence of Darcy's flow of fluids. In an optimum path (a geodesic) in physical space, it guarantees the maximum flux or shortest transition time of the fluid through inhomogeneous porous medium. Fermat's variational principle is used to minimizing the total resistance through inhomogeneous porous medium. The fluid streamlines move between areas exposed to minimal resistance. Therefore, the path of Darcy's flows of fluid can be defined by geodesics in Finsler geometry (Yajima & Nagahamab, 2015). The various functional properties of the hydraulic conductivity of porous media are examined and given graphically. In this study, various functional structures of hydraulic resistance of the inhomogeneous porous media are examined and the results obtained are given graphically.