Abstract
In this work, Finite Element Method (FEM) is applied to obtain the condition at the boundary of the interface between a channel and a porous medium. The boundary conditions that should be applied to the inhomogeneous interface zone between the two homogeneous regions of free fluid and porous medium are derived. The comparison has been performed for porous material characterizations to provide the velocity at the inhomogeneous interface zone with variable permeability between the two homogeneous regions of free fluid and porous medium. Also, the dependence of the slip coefficient on the thickness of the transition zone is established and the values of the thickness are so justified that the numerical results and the numerical results of our proposed technique are found to be in good agreement with experimental results in the literature.
Highlights
Several authors have discussed the boundary condition at the interface between a free fluid and a porous medium [1], boundary conditions at a naturally permeable wall [2], boundary condition at the interface of a porous medium [3], and numerical simulations of pressure jump interface law for Stokes–Darcy coupling [4]
The boundary conditions that should be applied to the inhomogeneous interface zone with variable permeability between the two homogeneous regions of free fluid and porous medium are derived
The up scaled Navier-Stokes equation that is used to describe the flow in the two homogeneous regions is assumed to hold in the inhomogeneous interface zone with variable permeability
Summary
Several authors have discussed the boundary condition at the interface between a free fluid and a porous medium [1], boundary conditions at a naturally permeable wall [2], boundary condition at the interface of a porous medium [3], and numerical simulations of pressure jump interface law for Stokes–Darcy coupling [4]. Poiseuille flow over a permeable block is studied in Reference [11] and the boundary conditions that must be applied to the inhomogeneous interface zone between the free fluid and porous medium are derived using the matched asymptotic expansions method, without specifying the porosity–dependent function and permeability–dependent function at the interface zone. The Finite element method has been employed in Reference [13] to show that variation of the energy storage efficiency of Copper oxide nanoparticles and V shaped fins is involved in a storage unit to expedite the solidification. In Reference [14], the finite element method is recalled to obtain the outputs, which are the roles of radiation parameter (Rd), Darcy number (Da), nanofluid volume fraction (Φ), Rayleigh number (Ra), and supplied voltage (Δφ). In this work thethe authors show to which this the condition canapplicable be applied.is In other words, condition deduced hereofusing the technique of FiniteThe
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