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).

Electrokinetic-Driven Flow and Heat Transfer of a Non-Newtonian Fluid in a Circular Microchannel

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Ali Jabari Moghadam
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Flow Behavior ◽  
Length Scale ◽  
Surface Cooling ◽  
Flow Behavior Index ◽  
Circular Microchannel ◽  
Scale Ratio ◽  
Behavior Index

An analytical analysis is presented to explore the transport characteristics of electroosmotic flow and associated heat transfer of non-Newtonian power-law fluids in a circular microchannel. The approach selected here is based on the linearized Poisson–Boltzmann distribution equation to get analytical expressions for velocity and temperature profiles, the friction coefficient, and the fully-developed Nusselt number. The key parameters governing the problem include the flow behavior index, the length scale ratio (ratio of half channel diameter to Debye length), and the thermal scale ratio. The results reveal that increasing the length scale ratio tends to increase the friction coefficient. 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. Depending on the value of the thermal scale ratio, 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 infinity.

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 and Heat Transfer in Microchannels: A Closed Form Solution

2013 ◽  
Vol 319 ◽  
pp. 462-467 ◽  
Author(s):  
Chien Hsin Chen ◽  
Shen Jenn Hwang ◽  
Yunn Lin Hwang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Friction Coefficient ◽  
Flow Rate ◽  
Joule Heating ◽  
Closed Form Solution ◽  
Form Solution ◽  
Length Scale ◽  
Local Velocity ◽  
Scale Ratio

In this paper, an analysis has been conducted to explore the momentun and thermal transport characterastics of electroosmotic liquid flow in a microchannel under imposed constant wall heat flux boundary condition. The present formulation shows that the problem is governed by three parameters, namely, the length scale ratio (ratio of Debye length to half channel height), the Joule heating parameter (ratio of Joule heating to surface heat flux), and the Brinkman number. A closed form solution of the problem was obtained and the impact of viscous dissipation on the heat transfer behavior was investigated. Analytical exact solutions of dimensionless velocity and temperature profiles, normalized local velocity, volume flow rate, friction coefficient, mean fluid temperature, and the fully-developed Nusselt number were obtained as functions of the governing parameters. Especially, the effects of length scale ratio on major flow parameters (including the normalized local velocity, friction coefficient, and volumetric flow rate) were examined. Also, the viscous dissipation effect on thermal transport characteristics was discussed in depth.

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).

Non-Newtonian Fluid Flow and Heat Transfer in Microchannels

2013 ◽  
Vol 275-277 ◽  
pp. 462-465 ◽  
Author(s):  
Chien Hsin Chen ◽  
Yunn Lin Hwang ◽  
Shen Jenn Hwang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Joule Heating ◽  
Flow Behavior ◽  
Debye Length ◽  
Dimensionless Temperature ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Wide Range ◽  
Analytical Expressions

Convective heat transfer of non-Newtonian power-law fluids in a microchannel is investigated. The governing parameters include the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), the Joule heating parameter (ratio of Joule heating to surface heat flux), and the Brinkman number. Analytical expressions are presented for velocity and temperature profiles, as well as the Nusselt number. The flow and heat transfer parameters can be obtained by numerical integrations of the analytical expressions. The dimensionless temperature distribution across the microchannel and the fully-developed Nusselt number are illustrated for a wide range of governing parameters.

Thermal Transport Characteristics of Mixed Pressure and Electro-Osmotically Driven Flow in Micro- and Nanochannels With Joule Heating

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Chien-Hsin Chen
Keyword(s):  
Nusselt Number ◽  
Friction Factor ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Length Scale ◽  
Velocity Scale ◽  
Fluid Properties ◽  
Scale Ratio ◽  
Pressure Driven Flow ◽  
Pressure Driven

This study investigates convective transport phenomena of combined electro-osmotic and pressure-driven flow in a microchannel subject to constant surface heat flux, with Joule heating effect taken into account. The governing system of equations includes the electric potential field, flow field, and energy equations. Analytical solutions are obtained for constant fluid properties, while numerical solutions are presented for variable fluid properties. For constant properties, the problem is found to be governed by three ratios: the length scale ratio (the ratio of Debye length to half channel height), the velocity scale ratio (the ratio of pressure-driven velocity to electro-osmotic velocity), and the ratio of Joule heating to surface heat flux. A small length scale ratio corresponds to a microchannel, while finite length scale ratio represents a nanochannel. For electro-osmotic flow only, the momentum transport is solely a function of the length scale ratio. For combined electro-osmotic and pressure-driven flow, the velocity profile and therefore the friction factor depend on both the length scale ratio and the velocity scale ratio. Assuming a thermally fully developed flow, analytical expressions for the normalized temperature profile and Nusselt number are developed. The representative results for the friction factor, normalized temperature profile, and Nusselt number are illustrated for some typical values of the three ratios. For purely electro-osmotic flow, it is found that the Nusselt number increases with decreasing ε, approaching the value for slug flow as the length scale ratio approaches zero. For mixed flow with a given length scale ratio, the results show that the Nusselt number decreases with the velocity scale ratio, approaching the classical Poiseuille flow as the velocity scale ratio approaches infinite. When the effects of variable fluid properties are included in the analysis, numerical solutions are generated to explore the influence of thermal conductivity and viscosity variations with local temperature on the hydrodynamic and thermal characteristics of the fluid. These temperature-dependent property variations would initially develop pressure-driven flow, and correspondingly the dimensionless velocity and volume flow rate increase to account for such variations. The friction factor reduces considerably with viscosity variation, while the Nusselt number increases gently. Although the influence of thermal conductivity variation on the hydrodynamic characteristics is not impressive, it has certain impact on the heat transfer results; more specifically, increasing the conductivity variation will produce a sensible increase in Nusselt number but a small decrease in the normalized temperature.

Effects of Greek Pomegranate Extracts in the Antioxidant Properties and Storage Stability of Kefir

2019 ◽  
Vol 15 (4) ◽  
pp. 437-441 ◽  
Author(s):  
Vasiliki Lagouri ◽  
Georgia Dimitreli ◽  
Aikatarini Kouvatsi
Keyword(s):  
Antioxidant Activity ◽  
Dairy Products ◽  
Storage Time ◽  
Storage Stability ◽  
Flow Behavior ◽  
Antioxidant Properties ◽  
Flow Behavior Index ◽  
Ph Values ◽  
Dpph Activity ◽  
Behavior Index

Background: Oxidation reactions are known to shorten the shelf life and cause damage to foods rich in fat, such as dairy products. One way to limit oxidation and increase the shelf life of fermented dairy products is to use natural antioxidants. The aim of this study was to examine the effect of adding pomegranate extracts in the antioxidant properties, rheological characteristics and the storage stability of the fermented product of kefir. Methods: The Pomegranate Juice (PGJ) and Peel Extracts (PGPE) (5%, 10% w/v) were added to kefir and the antioxidant properties were evaluated by using the methods of radical scavenging activity (DPPH) and Ferric Reducing Antioxidant Power Activity (FRAP). Spectrophotometric and instrumental methods were used to determine the Total Phenols (TPs), pH values, viscosity and flow behavioral index values of enriched with pomegranate kefir samples. The same properties were tested when kefir samples stored at 4°C for 7, 14, 21 and 28 days. Results: The addition of PGJ and PGPE results in an increase in the antioxidant activity (DPPH, FRAP) and total phenol content (TPs) of kefir samples. Increasing the concentration of the added PGJ and PGPE, results in an increase in the TP content and the DPPH activity of kefir. As far as the storage time is concerned, the results showed an increase in the amount of TP at 7th day and a reduction in the DPPH activity in the 14th day of storage. In contrary to the DPPH method, the increase in storage time has resulted in a reduction in antioxidant activity by the FRAP method. The addition of PGJ and PGPE in kefir results in a decrease in pH values while the pH of kefir samples increased during storage at 4°C for 28 days. The addition of PGJ and PGPE to kefir samples results to a decrease in viscosity and an increase in the flow behavior index. Increasing storage time results in increased flow behavior index of kefir samples. Conclusion: The addition of PGJ and PGPE increased the antioxidant activity and total phenols of the kefir product and preserved its properties during the total storage time of 28 days at 4°C.

scholarly journals Uncertainties Analysis on the Prediction of Flow and Heat Transfer of Liquid Sodium with CFD Technology

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanwei Liu ◽  
Xinyu Li ◽  
Tenglong Cong ◽  
Rui Zhang ◽  
Lingyun Zheng ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Liquid Sodium ◽  
Heat Transfer Characteristics ◽  
Backward Facing Step ◽  
Heating Wall ◽  
Transfer Characteristics ◽  
Cfd Models ◽  
Flow And Heat Transfer

The prediction of flow and heat transfer characteristics of liquid sodium with CFD technology is of significant importance for the design and safety analysis of sodium-cooled fast reactor. The accuracies and uncertainties of the CFD models should be evaluated to improve the confidence of the numerical results. In this work, the uncertainties from the turbulent model, boundary conditions, and physical properties for the flow and heat transfer of liquid sodium were evaluated against the experimental data. The results of uncertainty quantization show that the maximum uncertainties of the Nusselt number and friction coefficient occurred in the transition zone from the inlet to the fully developed region in the circular tube, while they occurred near the reattachment point in the backward-facing step. Furthermore, in backward-facing step flow, the maximum uncertainty of temperature migrated from the heating wall to the geometric center of the channel, while the maximum uncertainty of velocity occurred near the vortex zone. The results of sensitivity analysis illustrate that the Nusselt number was negatively correlated with the thermal conductivity and turbulent Prandtl number, while the friction coefficient was positively correlated with the density and Von Karman constant. This work can be a reference to evaluate the accuracy of the standard k-ε model in predicting the flow and heat transfer characteristics of liquid sodium.

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.

Hall Effects on Unsteady Magnetohydrodynamic Flow of a Nanofluid Past an Oscillatory Vertical Rotating Flat Plate Embedded in Porous Media

2021 ◽  
Vol 10 (2) ◽  
pp. 259-269
Author(s):  
M. Veera Krishna ◽  
N. Ameer Ahamad ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Local Nusselt Number ◽  
Hall Current ◽  
Skin Friction Coefficient ◽  
Engineering Industry ◽  
Hall Effects ◽  
The Impact

In the current investigative paper, the impact of Hall current on an unsteady magnetohydrodynamic liberated convection revolving flow of a nanofluid restricted with a uniform absorbent medium over an oscillatory moving vertical smooth plate with convective as well as diffusive frontier conditions has been reviewed. The non-dimensionalized governing differential equations by the appropriate frontier conditions are resolved by the perturbations technique. The impacts of the physical constants on the flow as well as the heat transfer features are displayed graphically and analyzed for Cu as well as Al2O3 nanoparticles. For the engineering industry, the skin friction coefficient, local Nusselt number, along with the Sherwood’s number are examined numerically in detail.

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