A NUMERICAL STUDY OF PULSATILE POWER LAW FLUID FLOW IN A POROUS CHANNEL

2009 ◽  
Vol 09 (03) ◽  
pp. 437-447
Author(s):  
B. V. RATHISH KUMAR ◽  
SHALINI ◽  
MOHIT NIGAM ◽  
VIVEK SANGWAN ◽  
S. V. S. S. N. V. G. KRISHNA MURTHY
Keyword(s):  
Power Law ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Time Discretization ◽  
Darcy Number ◽  
Flow Properties ◽  
Power Law Fluid ◽  
Discretization Schemes ◽  
Homogeneous Porous Medium ◽  
Power Law Index

The pulsatile flow characteristics of a power law fluid in a channel filled with a homogeneous porous medium are investigated by employing the Darcy–Brinkman–Forchheimer model. Finite element method in conjunction with β-family of time discretization schemes for parabolic equation have been used to numerically solve the model for analyzing the flow. Influence of various parameters, such as power law index (n), Darcy number (Da*), Forchheimer coefficient (Γ), pulsatile amplitude parameter (A), and Womerseley parameter (α), on the flow properties have been analyzed. Increasing Γ or decreasing Da* leads to decrease in velocities and shear stress for all values of n.

scholarly journals Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yazan Taamneh ◽  
Reyad Omari
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Skin Friction ◽  
Knudsen Number ◽  
Power Law ◽  
Slip Flow ◽  
Darcy Number ◽  
Power Law Fluid ◽  
Flow And Heat Transfer ◽  
Power Law Index

This study aims to numerically examine the fluid flow and heat transfer in a porous microchannel saturated with power-law fluid. The governing momentum and energy equations are solved by using the finite difference technique. The present study focuses on the slip flow regime, and the flow in porous media is modeled using the modified Darcy-Brinkman-Forchheimer model for power-law fluids. Parametric studies are conducted to examine the effects of Knudsen number, Darcy number, power law index, and inertia parameter. Results are given in terms of skin friction and Nusselt number. It is found that when the Knudsen number and the power law index decrease, the skin friction on the walls decreases. This effect is reduced slowly while the Darcy number decreases until it reaches the Darcy regime. Consequently, with a very low permeability the effect of power law index vanishes. The numerical results indicated also that when the power law index decreases the fully-developed Nusselt number increases considerably especially, in the limit of high permeability, that is, nonDarcy regime. As far as Darcy regime is concerned the effects of the Knudsen number and the power law index of the fully-developed Nusselt number is very little.

Onset of Convection in a Horizontal Porous Layer Saturated by a Power-Law Fluid

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Z. Alloui ◽  
N. Ben Khelifa ◽  
H. Beji ◽  
P. Vasseur
Keyword(s):  
Rayleigh Number ◽  
Newtonian Fluid ◽  
Power Law ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Governing Equations ◽  
Onset Of Convection ◽  
Power Law Index

This paper investigates the onset of motion, and the subsequent finite-amplitude convection, in a shallow porous cavity filled with a non-Newtonian fluid. A power-law model is used to characterize the non-Newtonian fluid behavior of the saturating fluid. Constant fluxes of heat are imposed on the horizontal walls of the layer. The governing parameters of the problem under study are the Rayleigh number R, the power-law index n, and the aspect ratio of the cavity A. An analytical solution, valid for shallow enclosures (A ≫ 1), is derived on the basis of the parallel flow approximation. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. For dilatant fluids (n > 1), it is found that the onset of motion is linearly unstable, i.e., always occurs provided that the supercritical Rayleigh number RCsup≥0. For pseudoplastic fluids (n < 1), the supercritical Rayleigh number for the onset of motion is RCsup=∞. However, it is demonstrated, on the basis of the nonlinear parallel flow theory, that the onset of motion occurs above a subcritical Rayleigh number RCsub which depends upon the power-law index n. For finite-amplitude convection, the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.

A Numerical Study of Dean Instability in Non-Newtonian Fluids

2005 ◽  
Vol 128 (1) ◽  
pp. 34-41 ◽  
Author(s):  
H. Fellouah ◽  
C. Castelain ◽  
A. Ould El Moctar ◽  
H. Peerhossaini
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Power Law ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Newtonian Fluids ◽  
Dean Number ◽  
Bingham Number ◽  
Curved Channels ◽  
Power Law Index

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar 180deg curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

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.

scholarly journals Travelling-Wave Similarity Solution for Gravity-Driven Rivulet of a Non-Newtonian Fluid

2018 ◽  
Vol 7 (2.15) ◽  
pp. 38
Author(s):  
Siti Sabariah Abas ◽  
Yazariah Mohd Yatim ◽  
. .
Keyword(s):  
Power Law ◽  
Similarity Solution ◽  
Travelling Wave ◽  
Global Maximum ◽  
Surface Tension Effect ◽  
Power Law Fluid ◽  
Transverse Profile ◽  
Strong Surface ◽  
Gravity Driven ◽  
Power Law Index

Unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained. The flow is driven by gravity with strong surface-tension effect. The solution predicts that at any time  and position , the rivulet widens or narrows according to , where  is velocity of a rivulet, and the film thickens or thins according to a free parameter , independent of power-law index . The rivulet also has a quartic transverse profile which always has a global maximum at its symmetrical axis.  

scholarly journals Finite Volume Simulation of Natural Convection for Power-Law Fluids with Temperature-Dependent Viscosity in a Square Cavity with a Localized Heat Source

2021 ◽  
Vol 39 (5) ◽  
pp. 1405-1416
Author(s):  
Hamza Daghab ◽  
Mourad Kaddiri ◽  
Said Raghay ◽  
Ismail Arroub ◽  
Mohamed Lamsaadi ◽  
...  
Keyword(s):  
Natural Convection ◽  
Heat Source ◽  
Finite Volume ◽  
Power Law ◽  
Numerical Study ◽  
Staggered Grid ◽  
Cooling Performance ◽  
Coupled Equations ◽  
Power Law Fluids ◽  
Power Law Index

In this paper, numerical study on natural convection heat transfer for confined thermo-dependent power-law fluids is conducted. The geometry of interest is a fluid-filled square enclosure where a uniform flux heating element embedded on its lower wall is cooled from the vertical walls while the remaining parts of the cavity are insulated, without slipping conditions at all the solid boundaries. The governing partial differential equations written in terms of non-dimensional velocities, pressure and temperature formulation with the corresponding boundary conditions are discretized using a finite volume method in a staggered grid system. Coupled equations of conservation are solved through iterative Semi Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The effects of pertinent parameters, which are Rayleigh number (103 ≤ Ra ≤ 106), power-law index (0.6 ≤ n ≤ 1.4), Pearson number (0 ≤ m ≤ 20) and length of the heat source (0.2 ≤ W ≤ 0.8) on the cooling performance are investigated. The results indicate that the cooling performance of the enclosure is improved with increasing Pearson and Rayleigh numbers as well as with decreasing power-law index and heat source length.

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