Modification of the fundamental theorem for transport phenomena in porous media
| Autor: | Yasuyuki Takatsu |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Fluid Flow and Transfer Processes
Physics Convection Fundamental theorem Point particle Mechanical Engineering Mathematical analysis Divergence theorem Thermodynamics 02 engineering and technology 021001 nanoscience & nanotechnology Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Pressure-correction method 0103 physical sciences Reynolds transport theorem 0210 nano-technology Transport phenomena Porous medium |
| Zdroj: | International Journal of Heat and Mass Transfer. 115:1109-1120 |
| ISSN: | 0017-9310 |
| DOI: | 10.1016/j.ijheatmasstransfer.2017.08.067 |
| Popis: | To examine convection in porous media, numerous analyses and numerical simulations have been conducted based on the macroscopic governing equations. In deriving the macroscopic governing equations, the phenomena intrinsic to porous media, such as Darcy’s flow resistance, Forchheimer’s flow resistance, and dispersion, are modeled using the theorem of the local volume average of a gradient (or a divergence). The theorem has been widely accepted as fundamental in the theory of convection in porous media; however, certain questions relating to the correctness of the theorem (the continuous derivative of the volume average and the pressure correction for Darcy’s law) have been raised. In this study, we modify the conventional theorem for the local volume average of a gradient (or a divergence) to solve the aforementioned questions. First, we introduce the concept of a point mass to describe the reference point for the movement of the fluid phase, and we derive the Reynolds transport theorem in the macroscopic field that corresponds to the continuum of porous media. Then, we examine the definition of divergence at a point to obtain the relation between the microscopic description that employs the velocity vector u and quantity B of the fluid particle and the macroscopic description that employs the reference velocity vector u 0 and the reference quantity B 0 of the point-mass particle, and we derive the modified theorem for the local volume average of a gradient (or a divergence). Furthermore, we derive the governing equations for porous media with the aid of the modified theorem. |
| Databáze: | OpenAIRE |
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