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.

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.

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).

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.

Enhanced Electro-Osmotic Flow of Power-Law Fluids in Hydrophilic Patterned Nanochannel

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
M. Majhi ◽  
A. K. Nayak ◽  
A. Banerjee
Keyword(s):  
Power Law ◽  
Enhancement Factor ◽  
Random Phase ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Osmotic Flow ◽  
Power Law Fluids ◽  
Dilatant Fluid ◽  
Electro Osmotic Flow

Abstract In this paper, electro-osmotic flow (EOF) enhancement of non-Newtonian power-law fluids in a modulated nanochannel with polarized wall is proposed. The channel walls are embedded with periodically arranged rectangular grooves, placed vertically with the direction of electric field. The key aspect of the present study is to achieve enhanced EOF of power-law fluids due to periodic groove patterns. The flow characteristics are studied through Poisson–Nernst–Plank-based Navier–Stokes model associated with electrochemical boundary conditions. Some random-phase differences between the grooves in both the walls are allowed to find the best configuration for the EOF enhancement in case of both Pseudo-plastic fluid, Dilatant fluid, and compared to Newtonian fluid. A notable enhancement factor is observed when groove width is much larger than its depth along with overlapped EDL. It is also found that EOF enhancement for shear-thinning fluid is quite better than the other fluids, for the same set of physical parameters. A comparison of enhancement factor for power-law fluid is also presented when the grooves are replaced with hydrophobic strips. It is worth to mention here that the present study assumes no-slip condition which is true for wetting (hydrophilic) surface over nonwetting (hydrophobic) strips which is common occurrence in regards to nanoconfinements.

The Laminar Far Wake Flow of a Non-Newtonian Power-Law Fluid

1979 ◽  
Vol 101 (3) ◽  
pp. 331-334 ◽  
Author(s):  
E. M. Mitwally
Keyword(s):  
Power Law ◽  
Order Approximation ◽  
Flow Behavior ◽  
Wake Flow ◽  
Third Order ◽  
Flow Behavior Index ◽  
Power Law Fluids ◽  
Dimensional Object ◽  
Third Order Approximation ◽  
Far Wake

Asymptotic solutions are presented for the laminar flow far behind a two-dimensional object for incompressible non-Newtonian power-law fluids. The solutions are given up to the third order approximation with a note on higher order approximations. When the flow behavior index tends to unity, the present solutions reduce to those already published for the Newtonian laminar far wake flow.

Forced convection heat transfer study of a blunt-headed cylinder in non-Newtonian power-law fluids

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jaspinder Kaur ◽  
Roderick Melnik ◽  
Anurag Kumar Tiwari
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Drag Coefficient ◽  
Power Law ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Total Drag ◽  
Shear Thinning Fluids ◽  
Power Law Fluids

Abstract In this present work, forced convection heat transfer from a heated blunt-headed cylinder in power-law fluids has been investigated numerically over the range of parameters, namely, Reynolds number (Re): 1–40, Prandtl number (Pr): 10–100 and power-law index (n): 0.3–1.8. The results are expressed in terms of local parameters, like streamline, isotherm, pressure coefficient, and local Nusselt number and global parameters, like wake length, drag coefficient, and average Nusselt number. The length of the recirculation zone on the rear side of the cylinder increases with the increasing value of Re and n. The effect of the total drag coefficient acting on the cylinder is seen to be higher at the low value of Re and its effect significant in shear-thinning fluids (n < 1). On the heat transfer aspect, the rate of heat transfer in fluids is increased by increasing the value of Re and Pr. The effect of heat transfer is enhanced in shear-thinning fluids up to ∼ 40% and it impedes it’s to ∼20% shear-thickening fluids. In the end, the numerical results of the total drag coefficient and average Nusselt number (in terms of J H −factor) have been correlated by simple expression to estimate the intermediate value for the new application.

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.

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