Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media

2015 ◽  
Vol 26 (04) ◽  
pp. 1550045 ◽  
Author(s):  
Xiao-Hua Tan ◽  
Xiao-Ping Li ◽  
Lie-Hui Zhang ◽  
Jian-Yi Liu ◽  
Jianchao Cai
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Pressure Gradient ◽  
Power Law ◽  
Transient Flow ◽  
Power Law Fluid ◽  
Fractal Properties ◽  
Pressure Changes ◽  
Power Law Index ◽  
Starting Pressure Gradient

A transient flow model for power-law fluid in fractal porous media is derived by combining transient flow theory with the fractal properties of tortuous capillaries. Pressure changes of transient flow for power-law fluid in fractal porous media are related to pore fractal dimension, tortuosity fractal dimension and the power-law index. Additionally, the starting pressure gradient model of power-law fluid in fractal porous media is established. Good agreement between the predictions of the present model and that of the traditional empirical model is obtained, the sensitive parameters that influence the starting pressure gradient are specified and their effects on the starting pressure gradient are discussed.

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.

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.

A Numerical Model for Edge Effect Correction of the Mooney Rheometer

2009 ◽  
Vol 82 (4) ◽  
pp. 401-417
Author(s):  
Sergio A. Montes
Keyword(s):  
Experimental Data ◽  
Edge Effect ◽  
Power Law ◽  
Power Law Fluid ◽  
One Dimensional ◽  
Complex Shear ◽  
Theoretical Predictions ◽  
Power Law Index ◽  
Significant Concentration ◽  
Finite Difference Techniques

Abstract The flow of a power law fluid within the cavity of a multi-speed Mooney rheometer is studied by means of finite difference techniques with the aim of quantifying the edge effects that occur in the vicinity of the rotor corner. As expected, a significant concentration of shear stress occurs near the rotor edge. As the power law index varies, significant stagnation zones are found within the cavity, which combined with thin-shearing behavior near the moving surfaces, yield complex shear rate distributions. However, when torque is calculated, the edge effect can be described by a factor which is numerically very similar to a factor obtained from one-dimensional models described in the literature. Comparison of theoretical predictions and experimental data was found to be satisfactory.

Developing and Fully Developed Non-Newtonian Fluid Flow and Heat Transfer Through Concentric Annuli

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Mohammad Sefid ◽  
Ehsan Izadpanah
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Convection Heat Transfer ◽  
Channel Length ◽  
Laminar Flows ◽  
Rheological Parameter ◽  
Power Law Fluid ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Power Law Index

Developing and fully developed laminar flows of power law fluid with forced convection heat transfer through a concentric annular duct are numerically analyzed. The results are presented for the following ranges: 0.2 ≤ n ≤ 1.8 (power law index), 10 ≤ Re ≤ 1000 (Reynolds number), and r* = 0.2, 0.5, 0.8 (aspect ratio). In addition, the influences of different thermal boundary conditions on the thermal performance are delineated. The effects of rheological parameter on the developing length, friction factor, temperature distribution, velocity profile, and Nusselt number along the channel length are investigated. The results are compared with earlier research and excellent agreement was observed.

Unsteady Flow of a Power–Law Fluid past a Shrinking Sheet with Mass Transfer

2012 ◽  
Vol 67 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Nor Azizah Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Power Law ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Shrinking Sheet ◽  
Power Law Fluid ◽  
Suction Parameter ◽  
Shooting Technique ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Power Law Index

The unsteady two-dimensional boundary layer flow past a shrinking sheet in a non-Newtonian power-law fluid is investigated. The governing partial differential equations are transformed into a nonlinear ordinary differential equation using a similarity transformation before being solved numerically by the Runge-Kutta-Fehlberg method and the NAG Fortran library subroutine DO2HAF with shooting technique. The results obtained by both methods are in good agreement. It is found that dual solutions exist for a certain range of the unsteadiness parameter and the suction parameter. Moreover, by increasing the power-law index n, the skin friction coefficient is enhanced.

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks

2015 ◽  
Vol 29 (19) ◽  
pp. 1550135 ◽  
Author(s):  
Xiao-Hua Tan ◽  
Xiao-Ping Li ◽  
Jian-Yi Liu ◽  
Lie-Hui Zhang ◽  
Jianchao Cai
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Heterogeneous Porous Media ◽  
Flow In Porous Media ◽  
Inversion Method ◽  
Type Curves ◽  
Fractal Properties ◽  
Proposed Model ◽  
The Laplace Transform ◽  
Fractal Characteristics

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks was presented based on the fractal properties of tree-shaped capillaries and generalized Darcy's law. The dimensionless expression of flowing pressure was developed using the Laplace transform and Stehfest numerical inversion method. The bilogarithmic type curves were illustrated and the influences of different fractal factors on dimensionless flowing pressure were also discussed. The presented study indicated that the fractal characteristics for the tree-shaped fractal networks should be considered in analysis of transient flow in the heterogeneous porous media. The proposed model may be conducible to a better understanding of the mechanism for transient flow in the multi-porosity porous media.

Sign in / Sign up

Export Citation Format

Share Document