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.

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.

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).

Mixed Electroosmotic Pressure Driven Flow and Heat Transfer of Power Law Fluid in a Hydrophobic Microchannel

2017 ◽  
Author(s):  
Ainul Haque ◽  
Ameeya Kumar Nayak
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Joule Heating ◽  
Scientific Data ◽  
Channel Height ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Hydrophobic Microchannel ◽  
Pressure Driven Flow ◽  
Pressure Driven

In this paper, a mathematical model has been developed to analyze the combined electroosmotic and pressure driven flow of power law fluids in a micro channel in the presence of Joule heating effects. The effects of Navier slip boundary condition and thermal radiation is examined for effective heat transfer in a hydrophobic microchannel. The analytical treatment has been performed for fluid flow and heat transfer effects in terms of flow governing parameters. This study highlights the effect of channel height to the electric double layer thickness and observed the flow variation due to heat transfer effect with the available scientific data. For a pure EOF, velocity slip have more significant role to get a maximum flow rate as expected. For both pseudo-plastic and dilatent fluids Nusselt number is decreased with the increment of the hydrophobic parameter and dimensionless pressure gradient where as increment in Joule heating effect enhance the heat transfer rate.

Heat Transfer and Pressure Drop Correlation for Helicoidal Pipes of Rectangular Cross Section

2009 ◽  
Author(s):  
Christopher Katinas ◽  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Friction Factor ◽  
Cross Section ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Dean Number ◽  
Curvature Effects ◽  
The Impact

In this study, flow and heat transfer for laminar flow in curved channels of rectangular cross section is examined. The focus of the numerical solutions is on rectangular cross sections with an aspect ratio less than one, since little information is available for heat transfer in curved rectangular pipes whose width is greater than height. The study examines the impact of the aspect ratio and Dean number on both friction factor and Nusselt number. The results show that although both friction factor and Nusselt number increase as a result of curvature effects, the heat transfer enhancements significantly outweigh the friction factor penalty. Numerical solutions in this study consider the more realistic case of hydrodynamically developed and thermally developing flow.

Numerical Simulation of Heat Transfer in Mixed Electroosmotic Pressure-Driven Flow in Straight Microchannels

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Amir Shamloo ◽  
Arshia Merdasi ◽  
Parham Vatankhah
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Zeta Potential ◽  
Electric Potential ◽  
Uniform Heat Flux ◽  
Electric Potentials ◽  
Circular Flows ◽  
Flow Through ◽  
Pressure Driven Flow ◽  
Pressure Driven

This paper investigates two-dimensional, time-independent elecroosmotic pressure-driven flow generated by a direct current electric potential with asymmetrical and symmetrical zeta potential distributions along the microchannel walls. Fluid flow through the horizontal microchannel is simulated using a numerical method. Two different cases are proposed to study the effect of electric potential on the flow field. First, negative electric potential is applied on the microchannel walls. In this case, large segments with negative electric potential are initially placed on the first half of the microchannel walls with two different arrangements. Afterward, smaller segments with negative electric potential are placed on the microchannel walls. Next, negative electric potential is replaced by positive electric potential on the microchannel walls in the similar manner. It is shown that applying positive potential on the walls contributes to the localized circular flows within the microchannel. The size of these vortices is also proved to considerably vary with the applied zeta potential magnitude. Finally, the effect of wall zeta potential on heat transfer was studied for all the four types of microchannels by imposing a constant uniform heat flux on the walls. The Nusselt number plots indicate how heat transfer varies along the microchannel walls. The Nusselt number fluctuation can be observed where the positive and negative electric potentials are located.

An experimental study of the effect of uniform strain on thermal fluctuations in grid-generated turbulence

1980 ◽  
Vol 99 (3) ◽  
pp. 545-573 ◽  
Author(s):  
Z. Warhaft
Keyword(s):  
Heat Flux ◽  
Decay Rate ◽  
Time Scale ◽  
Cross Correlation ◽  
Thermal Fluctuation ◽  
Thermal Fluctuations ◽  
Length Scale ◽  
Scale Size ◽  
Velocity Scale ◽  
Scale Ratio

The effect of homogeneous strain on passive scalar fluctuations, and the resultant evolution of the scalar field when the strain is removed, is experimentally studied by passing thermal fluctuations in decaying grid turbulence through a four-to-one axisymmetric contraction. Using amandoline(Warhaft & Lumley 1978a) to vary the scale size of the initial thermal fluctuations and hence the pre-contraction mechanical/thermal time-scale ratio,r, it is shown, for values ofrgreater than unity, that asris increased so is the post-contraction thermal decay rate, i.e. the contraction does not cause the thermal-fluctuation decay rate to equilibrate to a constant value. In these experiments the post-contraction thermal decay rate is always greater than the pre-contraction decay rate, i.e. the contraction accelerates the thermal-fluctuation decay. Moreover, the mechanical/thermal time-scale ratio in the post-contraction region is driven further from unity. In terms of scale size the uniform strain has the effect of increasing the thermal length scale by an amount equal in value to the contraction ratio if the pre-contraction thermal length scale is comparable to that of the pre-contraction velocity scale. However, if the pre-contraction thermal length scale is smaller than the pre-contraction velocity scale then the effect of the contraction on the thermal scale is less marked. The contraction induces significant negative cross-correlation ρuθbetween the longitudinal velocityuand thermal fluctuations θ even if the pre-contraction cross-correlation is close to zero. The magnitude of ρuθand hence the post-contraction heat flux is varied and the coherence structure is studied. It is shown that the thermal-fluctuation decay rate is insensitive to the magnitude of the heat flux, the latter of which decays rapidly compared to the relatively slow decay of turbulence energy in the post-contraction region. It is also shown that ρuθtends towards zero in this axisymmetric homogeneous flow at a faster rate than in isotropic turbulence. In accord with previous investigations, the return toward isotropy of the velocity field is very slow.

Laminar Heat Transfer in Rotating Eccentric Annuli

1974 ◽  
Vol 16 (5) ◽  
pp. 306-309 ◽  
Author(s):  
B. E. Launder ◽  
W. M. Ying
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Prandtl Number ◽  
Friction Factor ◽  
Numerical Solutions ◽  
Elliptic Partial Differential Equations ◽  
Method Of Solution ◽  
Eccentric Annuli

The paper presents numerical solutions to the problem of laminar heat transfer in eccentric annuli with the inner cylinder rotating. The method of solution is based on the general finite-difference procedure for solving elliptic partial differential equations developed by Gosman et al.(1)‡. The solutions show that, for an eccentricity of 0.5, even modest levels of swirl greatly reduce the large circumferential variation in Nusselt number that is present without swirl. Moreover rotation appears to offer a particularly effective way of increasing the level of heat transfer since, for a Prandtl number of 0.7, the Nusselt number is raised by twice as much as the friction factor.

Flow Characteristics in Helical Pipes of Various Coil Geometries With Rectangular Cross Section

2010 ◽  
Author(s):  
Christopher Katinas ◽  
Ahmad Fakheri
Keyword(s):  
Nusselt Number ◽  
Friction Factor ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Flow Characteristics ◽  
Dimensional Parameter ◽  
Aspect Ratios ◽  
Curved Pipes ◽  
Coil Diameter ◽  
Industrial Operations

Although curved pipes are commonly used in industrial operations, such as chemical reactors and heat exchangers, few investigations have been performed to develop an understanding of how tightly wound coils impact the heat transfer rate and friction factor in the laminar flow regime. Small coil radius geometries exhibit interesting characteristics that impact both Nusselt number and friction factor. Numerical solutions are presented for rectangular ducts of various coil diameters and aspect ratios which are compared with available experimental and analytical solutions to determine their applicabilty to tightly wound coils. A new non-dimensional parameter called the modified friction factor is presented and correlated to the results presented in this study. Additionally, a correlation for Nusselt number is presented for a variety of coil diameter ratios for curved square channels.

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.

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