FRACTAL ANALYSIS OF HYDRAULICS IN POROUS MEDIA WITH WALL EFFECTS

Fractals ◽  
2014 ◽  
Vol 22 (03) ◽  
pp. 1440001 ◽  
Author(s):  
MINGCHAO LIANG ◽  
BOMING YU ◽  
SHANSHAN YANG ◽  
MINGQING ZOU ◽  
LONG YAO
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Fractal Theory ◽  
Analytical Models ◽  
Wall Effects ◽  
Average Mass ◽  
Fractal Models ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Analytical Expressions

The analytical expressions for the normalized average mass flux and pressure drop for power law fluids for wall effects in porous media are presented by using the fractal theory and technique for porous media. The proposed models are expressed as functions of power law index and structure parameters. These model predictions show that the proposed models can provide a good agreement with the experimental and other analytical results. This indicates that the fractal models may be helpful to much better understand the mechanisms of flow than other analytical models for porous media.

scholarly journals Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Meijuan Yun
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Quantitative Description ◽  
Flow In Porous Media ◽  
Power Law Fluid ◽  
Related Data ◽  
Fractal Models ◽  
Fractal Properties ◽  
Seepage Characteristics ◽  
Analytical Expressions

We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.

POWER-LAW FLUIDS IN POROUS MEDIA

1987 ◽  
Vol 53 (1-6) ◽  
pp. 3-22 ◽  
Author(s):  
RICHARD PARNAS ◽  
YORAM COHEN
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Power Law Fluids

scholarly journals On power-law fluids with the power-law index proportional to the pressure

2016 ◽  
Vol 62 ◽  
pp. 118-123 ◽  
Author(s):  
J. Málek ◽  
K.R. Rajagopal ◽  
J. Žabenský
Keyword(s):  
Power Law ◽  
Power Law Fluids ◽  
Power Law Index

Advances and benefits of fractal models to predict streaming potentials in partially saturated porous media

2021 ◽  
Author(s):  
Damien Jougnot ◽  
Luong Duy Thanh ◽  
Mariangeles Soldi ◽  
Jan Vinogradov ◽  
Luis Guarracino
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Electrical Potential ◽  
Streaming Potential ◽  
Excess Charge ◽  
Distribution Law ◽  
Distribution Models ◽  
Streaming Potentials ◽  
Fractal Models ◽  
Partially Saturated Porous Media

<p>Understanding streaming potential generation in porous media is of high interest for hydrological and reservoir studies as it allows to relate water fluxes to measurable electrical potential distributions in subsurface geological settings. The evolution of streaming potential <span>stems</span> from electrokinetic coupling between water and electrical fluxes due to the presence of an electrical double layer at the interface between the mineral and the pore water. Two different approaches can be used to model and interpret the generation of the streaming potential in porous media: the classical coupling coefficient approach based on the Helmholtz-Smoluchowski equation, and the effective excess charge density. Recent studies based on both approaches use a mathematical up-scaling procedure that employs the so-called fractal theory. In these studies, the porous medium is represented by a bundle of tortuous capillaries characterized by a fractal capillary-size distribution law. The electrokinetic coupling between the fluid flow and electric current is obtained by averaging the processes that take place in a single capillary. In most cases, closed-form expressions for the electrokinetic parameters are obtained in terms of macroscopic hydraulic variables like permeability, saturation and porosity. In this presentation we propose a review of the existing fractal distribution models that predict the streaming potential in porous media and discuss their benefits compared against other published models.</p>

Internal Heat Transfer to Power-Law Fluid Flows Through Porous Media

2000 ◽  
Author(s):  
B. K. Rao ◽  
J. P. McDevitt ◽  
D. L. Vetter
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Power Law ◽  
Polymer Concentration ◽  
Internal Heat ◽  
Fluid Flows ◽  
Vertical Tube ◽  
Uniform Heat Flux ◽  
Power Law Fluid ◽  
Power Law Fluids

Abstract Heat transfer and pressure drop were measured for flow of aqueous solutions of Carbopol 934 through a vertical tube filled with porous media. The heated stainless steel test section has an inside diameter of 2.25 cm, and is 200 diameters long. The porosity was varied from 0.32 to 0.68 by using uniform spherical glass beads. Uniform heat flux thermal boundary condition was imposed bypassing direct electric current through the tube wall. Over a range of the parameters: 45 < Rea < 7,000, 21 < Pra < 58, 0.62<n (power-law exponent)<0.80, 0.22 < d/D < 0.6, and the polymer concentration from 250 to 500 parts per million, the friction factor data for power-law fluids agreed with the Newtonian predictions. Heat transfer to power-law fluids increases with increasing Rea and Prw and decreasing porosity. A new correlation was proposed for predicting heat transfer to power-law fluid flows through confined porous media.

Unsteady Flow of Power Law Fluids With Wall Slip in Microducts

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer ◽  
M'hamed Boutaous
Keyword(s):  
Power Law ◽  
Nonlinear Partial Differential Equation ◽  
Slip Flow ◽  
Wall Slip ◽  
Nonlinear Boundary Conditions ◽  
Velocity Profiles ◽  
Momentum Balance ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Pseudo Spectral

Unsteady laminar nonlinear slip flow of power law fluids in a microchannel is investigated. The nonlinear partial differential equation resulting from the momentum balance is solved with linear as well as nonlinear boundary conditions at the channel wall. We prove the existence of the weak solution, develop a semi-analytical solution based on the pseudo-spectral-Galerkin and Tau methods, and discuss the influence and effect of the slip coefficient and power law index on the time-dependent velocity profiles. Larger slip at the wall generates increased velocity profiles, and this effect is further enhanced by increasing the power law index. Comparatively, the velocity of the Newtonian fluid is larger and smaller than that of the power law fluid for the same value of the slippage coefficient if the power index is smaller and larger, respectively, than one.

Numerical Simulation for Heat Transfer of Nanofluid in a Rotating Circular Groove Using a Continuous Finite Element Scheme

2014 ◽  
Vol 1081 ◽  
pp. 175-179 ◽  
Author(s):  
Yong Yue Jiang ◽  
Ping Lin ◽  
Bo Tong Li ◽  
Lin Li
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Power Law ◽  
Initial Time ◽  
The Finite Element Method ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Circular Groove ◽  
Power Law Fluids ◽  
Power Law Index

In this paper, we investigate the heat transfer of the power-law-fluids-based nanofluids in a rotating circular groove. The circular groove rotates with a constant speed and the temperature on the wall of the groove is different from the temperature inside in the initial time. The effects of thermophoresis and Brownian are considered. The thermal conductivity of the nanofluids is taken as a constant. We solve the model with the finite element method directly and discretize them using a continuous finite element scheme in space and a modified midpoint scheme in time. From the results we can find that the heat transfer enhancement of the nanofluids increases as the power law index of the base fluid decreases.

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