A Study of Power-Law Non-Newtonian Fluid Flow
andHeat Transfer in
a
Porous Medium
1998
Masahiko Inoue
Two- and three-dimensional numerical calculations have been conducted to simulate the viscous and porous inertia effects on the pressure drop in a non-Newtonian fluid flow and heat transfer in a porous medium. Collections of aquare rods and cubes placed in a region of infinite extent have been proposed as two- and three-dimensional models of microscopic porous st$ctures, respectively. A full set of the momentum and evergy equations is treated along with the continuity equatioin at a pore scale, so as to simulate a flow through an infinite number of obstacles arranged in a regular pattern. The microscopic numerical results, thus obtained, are processed to extract the macroscopic relationship between the pressure gradient-mass flow rate. It has been found that the modified permeability determined by reading the intercept in the dimensionless pressure gradient versus Reynolds number plot closely follows Christopher and Middleman's formula based on a hydraulic radius concept. Upon comparing the results based on the two- and three-dimensinal models, it has been found that only the three-dimensional model can capture the porous inertia effects on the pressure drop, conectly.
Furthermore, thermal dispersion in power-law non-Newtonian fluid flow in a porous medium has been investigated both numerically and experimantally. A macroscopically uniform flow is imposed to pass through a collection of aquare rods, where a macroscopically linear temperature gradient is imposed perpendicularly to the flow direction. The numerical results, thus obtained at a pore scaleo are integrated over a unit structure to evaluate the thermal dispersion in a porous medium. It has been found that the resulting correlation obtained for a high Peclet number range agrees well with the experimental data.
