The Minimum Meniscus Radius and Capillary Heat Transport Limit in Micro Heat Pipes

1998 ◽  
Vol 120 (1) ◽  
pp. 227-233 ◽  
Author(s):  
H. B. Ma ◽  
G. P. Peterson
Keyword(s):  
Experimental Data ◽  
Contact Angle ◽  
Pressure Drop ◽  
Heat Transport ◽  
Heat Pipes ◽  
Momentum Conservation ◽  
Shear Stresses ◽  
Channel Angle ◽  
Micro Heat Pipes ◽  
Better Than

Based on the momentum conservation and Laplace-Young equations, an analytical expression for the minimum meniscus radius was derived and an expression for the maximum capillary heat transport limit in micro/small heat pipes was obtained. These expressions incorporated the shear stresses at the liquid/solid and liquid/vapor interfaces, contact angle effects, vapor pressure drop, tilt angle, groove dimensions, and channel angle effects. In order to verify the expressions derived herein, comparisons with experimental data from triangular grooves and micro heat pipes were made; they demonstrated that these equations can be used to predict the maximum capillary heat transport in the micro/small triangular grooves or micro heat pipes with a higher degree of accuracy, and they can explain the behavior better than previously developed models.

The Heat Transport Capacity of Micro Heat Pipes

1998 ◽  
Vol 120 (4) ◽  
pp. 1064-1071 ◽  
Author(s):  
J. M. Ha ◽  
G. P. Peterson
Keyword(s):  
Experimental Data ◽  
Heat Pipe ◽  
Heat Transport ◽  
Heat Pipes ◽  
Original Model ◽  
Semiempirical Model ◽  
Transport Capacity ◽  
Predictive Tool ◽  
Maximum Heat ◽  
Micro Heat Pipes

The original analytical model for predicting the maximum heat transport capacity in micro heat pipes, as developed by Cotter, has been re-evaluated in light of the currently available experimental data. As is the case for most models, the original model assumed a fixed evaporator region and while it yields trends that are consistent with the experimental results, it significantly overpredicts the maximum heat transport capacity. In an effort to provide a more accurate predictive tool, a semi-empirical correlation has been developed. This modified model incorporates the effects of the temporal intrusion of the evaporating region into the adiabatic section of the heat pipe, which occurs as the heat pipe approaches dryout conditions. In so doing, the current model provides a more realistic picture of the actual physical situation. In addition to incorporating these effects, Cotter’s original expression for the liquid flow shape factor has been modified. These modifications are then incorporated into the original model and the results compared with the available experimental data. The results of this comparison indicate that the new semiempirical model significantly improves the correlation between the experimental and predicted results and more accurately represents the actual physical behavior of these devices.

Experimental Investigation of the Maximum Heat Transport in Triangular Grooves

1996 ◽  
Vol 118 (3) ◽  
pp. 740-746 ◽  
Author(s):  
H. B. Ma ◽  
G. P. Peterson
Keyword(s):  
Experimental Investigation ◽  
Heat Transport ◽  
Heat Pipes ◽  
Effective Area ◽  
Experimental Results ◽  
Test Facility ◽  
Working Fluid ◽  
Maximum Heat ◽  
Pressure Losses ◽  
Micro Heat Pipes

An experimental investigation was conducted and a test facility constructed to measure the capillary heat transport limit in small triangular grooves, similar to those used in micro heat pipes. Using methanol as the working fluid, the maximum heat transport and unit effective area heat transport were experimentally determined for ten grooved plates with varying groove widths, but identical apex angles. The experimental results indicate that there exists an optimum groove configuration, which maximizes the capillary pumping capacity while minimizing the combined effects of the capillary pumping pressure and the liquid viscous pressure losses. When compared with a previously developed analytical model, the experimental results indicate that the model can be used accurately to predict the heat transport capacity and maximum unit area heat transport when given the physical characteristics of the working fluid and the groove geometry, provided the proper heat flux distribution is known. The results of this investigation will assist in the development of micro heat pipes capable of operating at increased power levels with greater reliability.

Theoretical Analysis of the Maximum Heat Transport in Triangular Grooves: A Study of Idealized Micro Heat Pipes

1996 ◽  
Vol 118 (3) ◽  
pp. 731-739 ◽  
Author(s):  
G. P. Peterson ◽  
H. B. Ma
Keyword(s):  
Heat Pipe ◽  
Heat Transport ◽  
Control Volume ◽  
Flow Characteristics ◽  
Heat Pipes ◽  
Vapor Flow ◽  
Transport Capacity ◽  
Maximum Heat ◽  
Micro Heat Pipes ◽  
Theoretical Minimum

A mathematical model for predicting the minimum meniscus radius and the maximum heat transport in triangular grooves is presented. In this model, a method for determining the theoretical minimum meniscus radius was developed and used to calculate the capillary heat transport limit based on the physical characteristics and geometry of the capillary grooves. A control volume technique was employed to determine the flow characteristics of the micro heat pipe, in an effort to incorporate the size and shape of the grooves and the effects of the frictional liquid–vapor interaction. In order to compare the heat transport and flow characteristics, a hydraulic diameter, which incorporated these effects, was defined and the resulting model was solved numerically. The results indicate that the heat transport capacity of micro heat pipes is strongly dependent on the apex channel angle of the liquid arteries, the contact angle of the liquid flow, the length of the heat pipe, the vapor flow velocity and characteristics, and the tilt angle. The analysis presented here provides a mechanism whereby the groove geometry can be optimized with respect to these parameters in order to obtain the maximum heat transport capacity for micro heat pipes utilizing axial grooves as the capillary structure.

Thermocapillary Flow and Evaporation Near Contact Lines in Micro Heat Pipes

2004 ◽  
Author(s):  
Vladimir S. Ajaev ◽  
M. Markos Gebresilassie
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Contact Line ◽  
Heated Surface ◽  
Heat Pipes ◽  
Apparent Contact Angle ◽  
Thermocapillary Flow ◽  
Contact Lines ◽  
Moving Contact ◽  
Micro Heat Pipes

We develop a mathematical model for heat transfer and fluid flow near a contact line on a heated surface in the presence of thermocapillary flow and evaporation. The coupled heat transfer and flow problem is reduced to an equation for local thickness, which is then solved numerically. The steady-state results indicate that thermocapillary stresses act to reduce the rate of liquid flow towards the contact line and increase interfacial curvature there. We also discuss solutions than involve moving contact lines, applicable to studies of start-up and shut-down operations of heat pipes. The velocity of the contact line and the apparent contact angle are found as functions of the Marangoni number. Thermocapillary effect is shown to reduce contact line speed and increase the apparent contact angle. Finally, the local solution is incorporated into global solutions for curvature variations of an evaporating three-dimensional meniscus in a corner. This configuration is typically encountered in proposed designs of micro heat pipes. Interface curvature is found as a function of the axial coordinate for the case of linear axial temperature variation in the corner.

Thermal analysis of Al2O3/water nanofluid-filled micro heat pipes

RSC Advances ◽  
2015 ◽  
Vol 5 (34) ◽  
pp. 26716-26725 ◽  
Author(s):  
Jie Sheng Gan ◽  
Yew Mun Hung
Keyword(s):  
Thermal Analysis ◽  
Thermal Resistance ◽  
Heat Transport ◽  
Performance Indicators ◽  
Heat Pipes ◽  
Physical Significance ◽  
Transport Capacity ◽  
Micro Heat Pipes

The comparison of heat transport capacity and the thermal resistance as the performance indicators provides valuable insights into the underlying physical significance of the use of a nanofluid on the performance of micro heat pipes.

Estimating ink mileage of dry toners in electrophotography

TAPPI Journal ◽  
2013 ◽  
Vol 12 (3) ◽  
pp. 9-14
Author(s):  
RENMEI XU ◽  
CELESTE M. CALKINS
Keyword(s):  
Experimental Data ◽  
Curve Fitting ◽  
Graphite Furnace ◽  
Atomic Absorption Spectrometer ◽  
Density Region ◽  
Coated Papers ◽  
Graphite Furnace Atomic Absorption ◽  
S Model ◽  
Better Than ◽  
Film Weight

This work investigates the ink mileage of dry toners in electrophotography (EP). Four different substrates were printed on a dry-toner color production Xerox iGen3 EP press. The print layout contained patches with different cyan, magenta, yellow, and black tonal values from 10% to 100%. Toner amounts on cyan patches were measured using an analytical method. Printed patches and unprinted paper samples, as well as dry toners, were dissolved in concentrated nitric acid. The copper concentrations in the dissolved solutions were analyzed by a Zeeman graphite furnace atomic absorption spectrometer. Analytical results were calculated to determine the toner amounts on paper for different tonal values. Their corresponding reflection densities were also measured. All data were plotted with OriginPro® 8 software, and four mathematical models were used for curve fitting. It was found that the C-S model fitted the experimental data of the two uncoated papers better than the other three models. None of the four models fitted the experimental data of the two coated papers, while the linear model was found to fit the data well. Linear fitting was the best in the practical density region for the two coated papers. Ink mileage curves obtained from curve fitting were used to estimate how much ink was required to achieve a target density for each paper; hence, the ink mileage was calculated. The highest ink mileage was 3.39 times the lowest ink mileage. The rougher the paper surface, the higher the requirement for ink film weight, and the lower ink mileage. No correlation was found between ink mileage and paper porosity.

scholarly journals The effect of ultrafiltration transmembrane permeation on the flow field in a surrogate system of an artificial kidney

2021 ◽  
Vol 2 ◽  
Author(s):  
Matilde De Pascale ◽  
Monica Faria ◽  
Cristiana Boi ◽  
Viriato Semiao ◽  
Maria Norberta de Pinho
Keyword(s):  
Pressure Drop ◽  
Artificial Kidney ◽  
Shear Stresses ◽  
Removal Rates ◽  
Permeable Membrane ◽  
Fluid Removal ◽  
Renal Replacement Therapies ◽  
Extracorporeal Blood Circulation ◽  
Conventional Hemodialysis ◽  
Upper Chamber

Abstract Renal Replacement Therapies generally associated to the Artificial Kidney (AK) are membrane-based treatments that assure the separation functions of the failing kidney in extracorporeal blood circulation. Their progress from conventional hemodialysis towards high-flux hemodialysis (HFHD) through the introduction of ultrafiltration membranes characterized by high convective permeation fluxes intensified the need of elucidating the effect of the membrane fluid removal rates on the increase of the potentially blood-traumatizing shear stresses developed adjacently to the membrane. The AK surrogate consisting of two-compartments separated by an ultrafiltration membrane is set to have water circulation in the upper chamber mimicking the blood flow rates and the membrane fluid removal rates typical of HFHD. Pressure drop mirrors the shear stresses quantification and the modification of the velocities profiles. The increase on pressure drop when comparing flows in slits with a permeable membrane and an impermeable wall is ca. 512% and 576% for $ \mathrm{CA}22/5\%{\mathrm{SiO}}_2 $ and $ \mathrm{CA}30/5\%{\mathrm{SiO}}_2 $ membranes, respectively.

Thermohydraulics of Laminar Flow Through Rectangular and Square Ducts With Transverse Ribs and Twisted Tapes

2006 ◽  
Vol 128 (10) ◽  
pp. 1070-1080 ◽  
Author(s):  
Debashis Pramanik ◽  
Sujoy K. Saha
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Laminar Flows ◽  
Short Length ◽  
Full Length ◽  
Twisted Tape ◽  
Twisted Tapes ◽  
Square Ducts ◽  
Better Than

The heat transfer and the pressure drop characteristics of laminar flow of viscous oil through rectangular and square ducts with internal transverse rib turbulators on two opposite surfaces of the ducts and fitted with twisted tapes have been studied experimentally. The tapes have been full length, short length, and regularly spaced types. The transverse ribs in combination with full-length twisted tapes have been found to perform better than either ribs or twisted tapes acting alone. The heat transfer and the pressure drop measurements have been taken in separate test sections. Heat transfer tests were carried out in electrically heated stainless steel ducts incorporating uniform wall heat flux boundary conditions. Pressure drop tests were carried out in acrylic ducts. The flow was periodically fully developed in the regularly spaced twisted-tape elements case and decaying swirl flow in the short-length twisted tapes case. The flow characteristics are governed by twist ratio, space ratio, and length of twisted tape, Reynolds number, Prandtl number, rod-to-tube diameter ratio, duct aspect ratio, rib height, and rib spacing. Correlations developed for friction factor and Nusselt number have predicted the experimental data satisfactorily. The performance of the geometry under investigation has been evaluated. It has been found that on the basis of both constant pumping power and constant heat duty, the regularly spaced twisted-tape elements in specific cases perform marginally better than their full-length counterparts. However, the short-length twisted-tape performance is worse than the full-length twisted tapes. Therefore, full-length twisted tapes and regularly spaced twisted-tape elements in combination with transverse ribs are recommended for laminar flows. However, the short-length twisted tapes are not recommended.

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