Solutions of Laminar Jet Flow Problems for Non-Newtonian Power-Law Fluids

1978 ◽  
Vol 100 (3) ◽  
pp. 363-366 ◽  
Author(s):  
E. M. Mitwally
Keyword(s):  
Power Law ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Free Jets ◽  
Free Jet ◽  
Laminar Jet ◽  
Flow Problems ◽  
Power Law Fluids ◽  
Flow Configurations ◽  
Behavior Index

Solutions are presented for laminar flow of non-Newtonian power-law fluids. The flow configurations cover the two-dimensional plane and radial free jets, the axisymmetrical (circular) free jet, and the plane and radial wall jets. When the flow behavior index is unity, the present results agree well with those already published for the case of Newtonian fluids.

Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel

2009 ◽  
Author(s):  
Cunlu Zhao ◽  
Chun Yang
Keyword(s):  
Shear Stress ◽  
Double Layer ◽  
Power Law ◽  
Dynamic Viscosity ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Power Law Fluids ◽  
Hyperbolic Cosine ◽  
Behavior Index

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson–Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity and velocity distributions. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a mathematical expression for the average electroosmotic velocity is derived for large values of the dimensionless electrokinetic parameter, κH, in a fashion similar to the Smoluchowski equation. Hence, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Finally, calculations are performed to examine the effects of κH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

Shear Rate Corrections for Herschel-Bulkley Fluids in Couette Geometry

2008 ◽  
Vol 18 (3) ◽  
pp. 34482-1-34482-11 ◽  
Author(s):  
Vassilios C. Kelessidis ◽  
Roberto Maglione
Keyword(s):  
Flow Behavior ◽  
Flow Equation ◽  
Oil Field ◽  
Rheological Parameters ◽  
Concentric Cylinder ◽  
Flow Behavior Index ◽  
Shear Rates ◽  
Power Law Fluids ◽  
Good Agreement ◽  
Behavior Index

AbstractA methodology is presented to invert the flow equation of a Herschel-Bulkley fluid in Couette concentric cylinder geometry, thus enabling simultaneous computation of the true shear rates, γ̇HB, and of the three Herschel-Bulkley rheological parameters. The errors made when these rheological parameters are computed using Newtonian shear rates, γ̇N, as it is normal practice by research and industry personnel, can then be estimated. Quantification of these errors has been performed using narrow gap viscometer data from literature, with most of them taken with oil-field rheometers. The results indicate that significant differences exist between the yield stress and the flow behavior index computed using γ̇HB versus the parameters obtained using γ̇N and this is an outcome of the higher γ̇HB values. Predicted true shear rates and rheological parameters are in very good agreement with results reported by other investigators, who have followed different approaches to invert the flow equation, both for yield-pseudoplastic and power-law fluids.

Thermally Fully Developed Electroosmotic Flow of Power-Law Fluids in a Circular Microchannel

2013 ◽  
Vol 29 (4) ◽  
pp. 609-616 ◽  
Author(s):  
Y.-J. Sun ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Power Law ◽  
Joule Heating ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Mathematic Model ◽  
Dimensionless Temperature ◽  
Fluid Temperature ◽  
Navier Stokes Equation ◽  
Power Law Fluids ◽  
Behavior Index

ABSTRACTThis study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

Non-Newtonian Fluid Flow and Heat Transfer in a Semicircular Microtube Induced by Electroosmosis and Pressure Gradient

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Mehdi Karabi ◽  
Ali Jabari Moghadam
Keyword(s):  
Nusselt Number ◽  
Pressure Gradient ◽  
Flow Behavior ◽  
Velocity Ratio ◽  
Shear Thinning ◽  
Fluid Viscosity ◽  
Flow Behavior Index ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Behavior Index

The hydrodynamic and thermal characteristics of electroosmotic and pressure-driven flows of power-law fluids are examined in a semicircular microchannel under the constant wall heat flux condition. For sufficiently large values of the electrokinetic radius, the Debye length is thin; the active flow within the electric double layer (EDL) drags the rest of the liquid due to frictional forces arising from the fluid viscosity, and consequently a plug-like velocity profile is attained. The velocity ratio can affect the pure electrokinetic flow as well as the flow rate depending on the applied pressure gradient direction. Since the effective viscosity of shear-thinning fluids near the wall is quite small compared to the shear-thickening fluids, the former exhibits higher dimensionless velocities than the later close to the wall; the reverse is true at the middle section. Poiseuille number increases with increasing the flow behavior index and/or the electrokinetic radius. Due to the comparatively stronger axial advection and radial diffusion in shear-thinning fluids, better temperature uniformity is achieved in the channel. Reduction of Nusselt number continues as far as the fully developed region where it remains unchanged; as the electrokinetic radius tends to infinity, Nusselt number approaches a particular value (not depending on the flow behavior index).

scholarly journals Uncertainties quantification and modelling of different rheological models in estimation of pressure losses during drilling operation

2018 ◽  
Vol 7 (2) ◽  
pp. 694 ◽  
Author(s):  
Anawe P. A. L ◽  
Folayan J. Adewale
Keyword(s):  
Power Law ◽  
Averaging Method ◽  
Graphical Method ◽  
Flow Behavior ◽  
Drilling Fluids ◽  
Flow Behavior Index ◽  
Rheological Models ◽  
Pressure Losses ◽  
Pump Pressure ◽  
Behavior Index

The determination of pressure losses in the drill pipe and annulus with a very high degree of precision and accuracy is sacrosanct for proper pump operating conditions and correct bit nozzle sizes for maximum jet impact and forestalling of possible kicks and eventual blow outs during drilling operation. The two major uncertainties in pump pressure estimation that are being addressed in this research work are the flow behavior index (n) and the consistency index factor (k). It is in this light that the accuracy of various rheological models in predicting pump pressure losses as well as the uncertainties associated with each model was investigated. In order to come by with a decisive conclusion, two synthetic based drilling fluids were used to form synthetic muds known as sample A and B respectively. Inference from results shows that the Newtonian model underestimated the pump pressure by 78.27% for sample A and 82.961% by for sample B. While the Bingham plastic model overestimated the total pump pressure by 100.70% for sample A and 48.17% for sample B. Three different power law rheological model approaches were used to obtain the flow behavior index and consistency factor of the drilling fluids. For the power law rheological model approaches, an underestimation error of 23.5743% was encountered for the Formular method for sample A while the proposed consistency index averaging method reduces the error to 14.9306%. The Graphical method showed a reasonable degree of accuracy with underestimation error of 5.6435%. Sample B showed an underestimation error of 47.8234% by using the power law formula method while the Consistency averaging method reduced the error to 20.7508. The graphical method showed an underestimation error of 0.4318%.

Flow Resistance and Mass Transfer in Slow Non-Newtonian Flow Through Multiparticle Systems

1992 ◽  
Vol 59 (2) ◽  
pp. 431-437 ◽  
Author(s):  
M. G. Satish ◽  
J. Zhu
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Power Law ◽  
Cell Model ◽  
Flow Behavior ◽  
Solid Sphere ◽  
Power Law Fluid ◽  
Flow Behavior Index ◽  
Flow Through ◽  
Behavior Index

Finite difference solutions for a power-law fluid flow through an assemblage of solid particles at low Reynolds numbers are obtained using both the free-surface cell model and the zero-vorticity cell model. It is shown that, unlike in the case of power-law fluid flow past a single solid sphere, the flow drag decreases with decrease of flow behavior index, and that the degree of this reduction is more significant at low voidage. The results from this study are found to be in good agreement with the approximate solutions at slight pseudoplastic anomaly and the available experimental data. The results are presented in closed form and compare favorably with the variational bounds and the modified Blake-Kozeny equations. Numerical results show that a decrease in the flow behavior index leads to a slight increase in the mass transfer rate for an assemblage of solid spheres, but this increase is found to be small compared with that for a single solid sphere.

An Approximate Analytical Solution for Electro-Osmotic Flow of Power-Law Fluids in a Planar Microchannel

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Arman Sadeghi ◽  
Moslem Fattahi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Power Law ◽  
Flow Behavior ◽  
Heat Fluxes ◽  
Flow Behavior Index ◽  
Osmotic Flow ◽  
Flow Parameters ◽  
Wall Heating ◽  
Power Law Fluids ◽  
Electro Osmotic Flow

The present investigation considers the fully developed electro-osmotic flow of power-law fluids in a planar microchannel subject to constant wall heat fluxes. Using an approximate velocity distribution, closed form expressions are obtained for the transverse distribution of temperature and Nusselt number. The approximate solution is found to be quite accurate, especially for the values of higher than ten for the dimensionless Debye-Huckel parameter where the exact values of Nusselt number are predicted. The results demonstrate that a higher value of the dimensionless Debye-Huckel parameter is accompanied by a higher Nusselt number for wall cooling, whereas the opposite is true for wall heating case. Although to increase the dimensionless Joule heating term is to decrease Nusselt number for both pseudoplastic and dilatant fluids, nevertheless its effect on Nusselt number is more pronounced for dilatants. Furthermore, to increase the flow behavior index is to decrease the Nusselt number for wall cooling, whereas the contrary is right for the wall heating case. Depending on the value of flow parameters, a singularity is observed in the Nusselt number values of the wall heating case.

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