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).

Heat Transfer Analysis of Mixed Electro-osmosis Pressure-Driven Flow for Power-Law Fluids Through a Microtube

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Chien-Hsin Chen
Keyword(s):  
Nusselt Number ◽  
Pressure Gradient ◽  
Joule Heating ◽  
Flow Behavior ◽  
Surface Cooling ◽  
Flow Behavior Index ◽  
Dimensionless Pressure ◽  
Scale Ratio ◽  
Pressure Driven Flow ◽  
Behavior Index

In this work, convection heat transfer for combined electro-osmotic and pressure driven flow of power-law fluid through a microtube has been analyzed. Typical results for velocity and temperature distributions, friction coefficient, and Nusselt number are illustrated for various values of key parameters such as flow behavior index, length scale ratio (ratio of Debye length to tube radius), dimensionless pressure gradient, and dimensionless Joule heating parameter. The results reveal that friction coefficient decreases with increasing dimensionless pressure gradient, and classical Poiseuille solutions can be retrieved as the dimensionless pressure gradient approaches to infinite. To increase the length scale ratio has the effect to reduce Nusselt number, while the influence of this ratio on Nusselt number diminishes as the pressure gradient increases. With the same magnitude of dimensionless Joule heating parameter, Nusselt number can be increased by increasing both the flow behavior index and dimensionless pressure gradient for surface cooling, while the opposite behavior is observed for surface heating. Also, singularities occurs in the Nusselt number variations for surface cooling as the ratio of Joule heating to wall heat flux is sufficiently large with negative sign.

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.

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.

Rheological effects on the levelling dynamics of thin fluid films

2015 ◽  
Vol 25 (8) ◽  
pp. 1850-1867 ◽  
Author(s):  
Gulraiz Ahmed ◽  
Mathieu Sellier ◽  
Yeaw Chu Lee ◽  
Mark Jermy ◽  
Michael Taylor
Keyword(s):  
Flow Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Lubrication Approximation ◽  
Fluid Films ◽  
Flow Behavior Index ◽  
Shear Thickening Fluid ◽  
Content Type ◽  
Shear Thinning Fluid ◽  
Behavior Index

Purpose – The purpose of this paper is to investigate numerically the effect of rheology on the leveling of thin fluid films on horizontal solid substrates. Design/methodology/approach – A mathematical model based on the lubrication approximation which defines non-Newtonian rheology using a Power-law model is presented. The rheology is described by two parameters: the consistency factor and the flow behavior index. The resulting highly non-linear coupled set of equations is discretized using Finite-Difference and the resulting algebraic system is solved via an efficient Multigrid algorithm. Findings – Importantly, the non-dimensionalization process leads to a pair of Partial Differential Equations which depends on one parameter only, the flow behavior index. The authors show that the consistency factor only affects the time scale of the leveling process, hence stretching or contracting the time line. Results for the leveling of sinusoidal perturbations of the fluid film highlights important differences between the leveling of shear-thinning and shear-thickening fluids. In a normalized time frame, the onset of leveling occurs earlier for the shear-thinning fluid than for the shear-thickening one. However, the dimensionless leveling rate is higher for the shear-thickening fluid than the shear-thinning one. This results in a “threshold thickness” which delimits two regimes: the shear-thinning fluid levels to a thickness above this threshold faster than the shear-thickening fluid but the opposite is true for a film thickness below this threshold. An important aspect of this study is the verification of the numerical implementation using the Method of Manufactured Solutions (MMS), a first in the context of thin film studies. The paper also highlights differences between the leveling of two-dimensional and three-dimensional thickness perturbations. Originality/value – The study of the leveling of disturbances at the free surface of a liquid film using a Power-law rheological model does not appear to have been covered in the literature. Also, the paper uses the MMS to test the validity of the implementation. This appears to be the first time it has been used in the context of the lubrication approximation. Finally, unlike most prior studies, the work does away with the planar assumption.

Static Rheological Study of Ocimum basilicum Seed Gum

2015 ◽  
Vol 11 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Fakhreddin Salehi ◽  
Mahdi Kashaninejad
Keyword(s):  
Power Law ◽  
Flow Behavior ◽  
Shear Thinning ◽  
Power Law Model ◽  
Rotational Viscometer ◽  
Flow Behavior Index ◽  
Consistency Coefficient ◽  
Salt Addition ◽  
Seed Gum ◽  
Behavior Index

Abstract A rotational viscometer was used to investigate the effect of different sugars (sucrose, glucose, fructose and lactose, 1–4% w/w) and salts (NaCl and CaCl2, 0.1–1% w/w), on rheological properties of Basil seed gum (BSG). The viscosity was dependent on type of sugar and salt addition. Interactions between BSG gum and sugars improved the viscosity of solutions, whereas the viscosity of the BSG solutions decreased in the presence of salts. Power law model well-described non-Newtonian shear thinning behavior of BSG. The consistency index was influenced by the sugars and salts content. Addition of sucrose, glucose, lactose and salts to BSG led to increases in flow behavior index (less shear thinning solutions), whereas fructose increased shear thinning of solutions. Flow behavior index values of the power law model vary as follows: 0.43–0.49, 0.53–0.64, 0.21–0.26, and 0.57–0.67 for sucrose, glucose, fructose and lactose, respectively. The consistency coefficient (k) of BSG was affected by sugars and salts. It decreased from 0.14 to 0.09 Pa.sn with increasing CaCl2 from 0 to 4% w/w (20°C, 0.2% w/w BSG). The consistency coefficient values vary as follows: 0.094–0.119, 0.075–0.098, 0.257–0.484, and 0.056–0.074 for sucrose, glucose, fructose and lactose, respectively.

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.

Electro-Osmotic Heat Transfer of Non-Newtonian Fluid Flow in Microchannels

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Chien-Hsin Chen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Joule Heating ◽  
Slug Flow ◽  
Flow Behavior ◽  
Length Scale ◽  
Flow Behavior Index ◽  
Scale Ratio ◽  
Behavior Index

A theoretical analysis is presented to explore the transport characteristics of electro-osmotic flow and associated heat transfer of non-Newtonian power-law fluids in a parallel plate microchannel. The formulation shows that the key parameters governing the current problem include the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), and the Joule heating parameter (ratio of Joule heating to surface heat flux). Analytical expressions are presented for velocity and temperature profiles, the friction coefficient, and the fully developed Nusselt number. In particular, closed-form solutions are obtained for several special values of the flow behavior index. The results reveal that reducing the length scale ratio tends to increase the friction coefficient, and the friction coefficient approaches infinite for slug flow. The increase in the friction coefficient due to increasing the flow behavior index is more noticeable for a smaller length scale ratio. For surface heating, increasing the flow behavior index amplifies the temperature difference between the wall and the fluid, and thus the temperature distribution broadens; while the opposite trend is observed for surface cooling with sufficiently large Joule heating parameter with negative sign. Depending on the value of Joule heating parameter, the fully developed Nusselt number can be either increased or decreased by increasing the flow behavior index and/or the length scale ratio. The effect of flow behavior index on the Nusselt number vanishes as the length scale ratio approaches zero (the limiting case for slug flow).

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