Submicron Superhydrophobic Surface Treatment Suitable for High Performance Condensers: A Modeling

2009 ◽  
Author(s):  
Sunwoo Kim ◽  
Kwang J. Kim ◽  
John M. Kennedy ◽  
Jiong Liu ◽  
Ganesh Skandan
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Theoretical Model ◽  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution ◽  
Condensation Heat Transfer ◽  
Dropwise Condensation ◽  
Superhydrophobic Coating ◽  
Single Droplet

The effect of the drop-contact angle on dropwise condensation heat transfer of saturated steam on a single horizontal copper tube with the superhydrophobic coating was investigated theoretically. The theoretical model is established by combining heat transfer through a single droplet with a well-known drop size distribution theory. The analysis of single droplet heat transfer incorporates resistances due to vapor-liquid interface, drop curvature, conduction through the drop, and conduction through the superhydrophobic coating layer. Each resistance is expressed as a function of the contact angle. The total resistance for a drop with a fixed radius increases as the contact angle increases. A population balance model is used to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from the empirical equation proposed by Le Fevre and Rose (1966). The results indicate that the contact angle has a strong correlation with the maximum drop radius, which plays a pivotal role in determining drop size distribution. A high contact angle leads to a significant reduction in the radius of the largest drop that is about to fall down due to gravity and sweep away drops in its path. Thus, there are more areas on the condensing surface for small drops, allowing for greater heat transfer. Also, it is shown that surface wettability affects the performance of dropwise condensation heat transfer and our theoretical model successfully predicts this phenomenon.

Dropwise Condensation Modeling Suitable for Superhydrophobic Surfaces

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Sunwoo Kim ◽  
Kwang J. Kim
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Size Distribution ◽  
Drop Size ◽  
Contact Angles ◽  
Drop Size Distribution ◽  
Balance Model ◽  
Dropwise Condensation ◽  
Interfacial Resistance ◽  
Single Droplet

A mathematical model is developed to represent and predict the dropwise condensation phenomenon on nonwetting surfaces having hydrophobic or superhydrophobic (contact angle greater than 150 deg) features. The model is established by synthesizing the heat transfer through a single droplet with the drop size distribution. The single droplet heat transfer is analyzed as a combination of the vapor-liquid interfacial resistance, the resistance due to the conduction through the drop itself, the resistance from the coating layer, and the resistance due to the curvature of the drop. A population balance model is adapted to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from a well-known empirical equation. The evidence obtained suggests that both the single droplet heat transfer and drop distribution are significantly affected by the contact angle. More specifically, the model results indicate that a high drop-contact angle leads to enhancing condensation heat transfer. Intense hydrophobicity, which produces high contact angles, causes a reduction in the size of drops on the verge of falling due to gravity, thus allowing space for more small drops. The simulation results are compared with experimental data, which were previously reported.

A Theoretical Approach to Dropwise Condensation Using Population Balance Concept

2004 ◽  
Author(s):  
S. Vemuri ◽  
K. J. Kim ◽  
B. D. Wood ◽  
T. W. Bell
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Theoretical Model ◽  
Size Distribution ◽  
Drop Size ◽  
Population Balance ◽  
Theoretical Formula ◽  
Dropwise Condensation ◽  
Sweeping Effect ◽  
Direct Condensation

A model using the population balance concept is used to derive a theoretical formula to predict the drop-size distribution of small drops which grow mainly by direct condensation. All the important resistances to heat transfer such as the heat conduction through the drop, vapor-liquid interface are considered in developing this model. By knowing the contact angle of the drop made with the condensing surface and the maximum drop radius the sweeping effect of large falling drops could be calculated which is also incorporated into the model. This is combined with the well known size distribution for large drops proposed by Le Fevre and Rose (1966) which grow mainly by coalescence and with the growth rate of single drops to compute the heat flux during the process of dropwise condensation. The data obtained from this theoretical model is compared to that of the data obtained from our experimentation. There has been a satisfactory agreement between our experimental data and the present theoretical model.

A Heat Transfer Model of Dropwise Condensation Underneath a Horizontal Substrate

2011 ◽  
Vol 199-200 ◽  
pp. 1604-1608
Author(s):  
Yun Fu Chen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Contact Angle ◽  
Fractal Model ◽  
Condensation Heat Transfer ◽  
Droplet Growth ◽  
Transfer Model ◽  
Dropwise Condensation ◽  
Small Contact Angle ◽  
Horizontal Substrate

For finding influence of the condensing surface to dropwise condensation heat transfer, a fractal model for dropwise condensation heat transfer has been established based on the self-similarity characteristics of droplet growth at various magnifications on condensing surfaces with considering influence of contact angle to heat transfer. It has been shown based on the proposed fractal model that the area fraction of drops decreases with contact angle increase under the same sub-cooled temperature; Varying the contact angle changes the drop distribution; higher the contact angle, lower the departing droplet size and large number density of small droplets; dropwise condensation translates easily to the filmwise condensation at the small contact angle ;the heat flux increases with the sub-cooled temperature increases, and the greater of contact angle, the more heat flux increases slowly.

Dropwise Condensation Heat Transfer Model: Effect of the Liquid-Solid Surface Free Energy Difference

2006 ◽  
Author(s):  
Xue-Hu Ma ◽  
Zhong Lan ◽  
Yu Zhang ◽  
Xing-Dong Zhou ◽  
Tian-Yi Sun
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Free Energy ◽  
Heat Transfer Coefficient ◽  
Energy Difference ◽  
Interfacial Interaction ◽  
Condensation Heat Transfer ◽  
Dropwise Condensation ◽  
Free Energy Difference ◽  
Simulation Results

Dropwise condensation heat transfer performance depends not only on the condensing conditions, but also on the interfacial interaction between condensate and condensing surface material. Based on the well-established Rose’s model, a modified model of dropwise condensation heat transfer is proposed by considering the interfacial interaction between liquid and solid, and established by rebuilding the space conformation of drop distributing into time conformation. The simulation results indicate that the heat transfer coefficient increases with the surface free energy difference increasing and the contact angle hysteresis decreasing. The larger contact angle and the smaller departure drop size result in the higher heat transfer coefficient. Different interfacial effect gives rise to the different heat transfer curves. For the identical solid-liquid-vapor system, the simulation results agree very well with the present experimental data and those reported in literature. The controversy among experimental results in literature might be well understood with the concept of the present paper.

scholarly journals Effect of Contact Angle on Steam Dropwise Condensation: A Simulation Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Milad Nahavandi ◽  
Arjomand Mehrabani-Zeinabad
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Distribution Coefficient ◽  
Size Distribution ◽  
Atmospheric Pressure ◽  
Simulated Data ◽  
Condensation Process ◽  
Dropwise Condensation

Dropwise condensation process on surface of a vertical polytetrafluouroethylene (PTFE) plate at atmospheric pressure was simulated. Comparison of simulated data with experimental and theoretical results indicates that performed simulation results confirm experimental data, although they deviated from existing proposed correlations. For calculation of heat transfer coefficient and droplets size distribution, simulation of condensation process over vertical copper and PTFE surfaces at atmospheric pressure was performed. By considering the effect of contact angle on heat transfer resistances of droplets, the gained data were optimized in order to evaluate droplets size distribution coefficient. This distribution coefficient was used in a new correlation for prediction of heat transfer coefficient for dropwise condensation process. Comparison of experimental results with the correlation shows a good agreement, 11% relative error.

A Theoretical Study of Dropwise Condensation

1975 ◽  
Vol 97 (1) ◽  
pp. 72-78 ◽  
Author(s):  
Hiroaki Tanaka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Size Distribution ◽  
General Expression ◽  
Drop Size ◽  
Theoretical Study ◽  
Dropwise Condensation ◽  
Fundamental Equations ◽  
The Heat Transfer Coefficient

The so-called steady dropwise condensation consists of the transient dropwise condensation occurring repeatedly from place to place on the tracks of departing drops. By taking statistical and geometrical conditions into account, the author derives fundamental equations describing the process of this transient dropwise condensation. By solving these equations, the existence of a universal drop-size distribution is predicted. Further, by introducing a model for the cycle of drop departure, a general expression for the heat-transfer coefficient under the so-called steady dropwise condensation is obtained.

Influence of Surface Wettability on Dropwise Condensation Heat Transfer

2011 ◽  
Vol 228-229 ◽  
pp. 869-873
Author(s):  
Yun Fu Chen
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Surface Wettability ◽  
Condensation Heat Transfer ◽  
Size Distributions ◽  
Dropwise Condensation ◽  
Number Density ◽  
Drop Radius ◽  
Proposed Model ◽  
Drop Size Distributions

For finding influence of the surface wettability on dropwise condensation heat transfer, a model for dropwise condensation heat transfer has been established based on the drop size distributions and the heat transfer rate through a single drop with considering influence of contact angle to heat transfer. It has been shown based on the proposed model that up to a drop radius of 5μm, the rate of decrease in the drop population density is not as steep as the rate for a drop radius greater than 10μm, because coalescence between drops starts taking place. Varying the contact angle changes the drop distribution; higher the contact angle, lower the departing droplet size and large number density of small droplets. Heat flux first increases and then decreases with increasing contact angle under the temperature difference condition.

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