Research Papers

On the Merkel Equation: Novel ε-Number of Transfer Unit Correlations for Indirect Evaporative Cooler Under Different Lewis Numbers

[+] Author and Article Information
M. Khamis Mansour

Department of Mechanical Engineering,
Faculty of Engineering,
Beirut Arab University,
Beirut 115020, Lebanon;
Department of Mechanical Engineering,
Faculty of Engineering,
Alexandria University,
Alexandria 21526, Egypt
e-mail: m.mansour@bau.edu.lb

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received June 1, 2016; final manuscript received February 22, 2017; published online April 19, 2017. Assoc. Editor: Srinath V. Ekkad.

J. Thermal Sci. Eng. Appl 9(4), 041005 (Apr 19, 2017) (8 pages) Paper No: TSEA-16-1159; doi: 10.1115/1.4036204 History: Received June 01, 2016; Revised February 22, 2017

An innovative relationship between the effectiveness (ε) and number of transfer unit (NTU) was presented in this work for indirect evaporative cooler (IEC). This relationship is featured by its simplicity in use and has noniterative procedure to be implemented as the traditional one in the literature. The new model can be implemented in sizing and rating design of the IEC at different Lewis numbers with a reasonable accuracy. General integral equation, which is similar to that of Merkel equation, is developed in this model. The new relationship was verified through comparison with experimental and numerical work reported in the available literature for closed or indirect cooling tower (ICT), as an example of IEC. Additionally, the predicted results of the present model were compared to those obtained from the traditional numerical models at different Lewis numbers. The simulated results from the new model show a satisfactory agreement with those obtained from the experimental work of less than 10%. The new correlations can be implemented easily in predicting the thermal design and performance of IEC in any simulation program or in real site.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Khamis Mansour, M. , and Hassab, M. A. , 2016, “ Novel Lumped Modeling for Determining Thermal Performance of DX Evaporator Under Partially-Wet and Fully-Wet Conditions,” Appl. Therm. Eng., 98, pp. 1025–1035. [CrossRef]
Khamis Mansour, M. , 2016, “ Practical Effectiveness-NTU Model for Cooling and Dehumidifying Coil With Non-Unit Lewis Factor,” Appl. Therm. Eng., 100, pp. 1111–1118. [CrossRef]
Riffat, S. B. , Gan, G. , Shao, L. , and Doherty, P. , 2001, “ Application of CFD to Closed-Wet Cooling Towers,” Appl. Therm. Eng., 21(1), pp. 79–92. [CrossRef]
Zheng, W.-Y. , Zhu, D.-S. , Song, J. , Zeng, L.-D. , and Zhou, H.-J. , 2012, “ Experimental and Computational Analysis of Thermal Performance of the Oval Tube Closed Wet Cooling Tower,” Appl. Therm. Eng., 35, pp. 233–239. [CrossRef]
Budihardjo, N. , and Nugraha, M. H. , 2015,” Experimental and Simulation Study on the Performance of Counter Flow Closed Cooling Tower Systems,” Int. J. Technol., 6(3), pp. 365–379. [CrossRef]
Xia, Z. Z. , Chen, C. J. , and Wang, R. Z. , 2011, “ Numerical Simulation of a Closed Wet Cooling Tower With Novel Design,” Int. J. Heat Mass Transfer, 54(11–12), pp. 2367–2374. [CrossRef]
Qureshi, B. A. , and Zubair, S. M. , 2006, “ A Comprehensive Design and Rating Study of Evaporative Coolers and Condensers. Part I. Performance Evaluation,” Int. J. Refrig., 29(4), pp. 645–658. [CrossRef]
Chengqin, R. A. , and Hongxing, Y. , 2006, “ An Analytical Model for the Heat and Mass Transfer Processes in Indirect Evaporative Cooling With Parallel/Counter Flow Configurations,” Int. J. Heat and Mass Transfer, 49(3–4), pp. 617–627. [CrossRef]
Zheng, W.-Y. , Zhu, D.-S. , Zhou, G.-Y. , Wu, J.-F. , and Shi, Y.-Y. , 2012, “ Thermal Performance Analysis of Closed Wet Cooling Towers Under Both Unsaturated and Supersaturated Conditions,” Int. J. Heat Mass Transfer, 55(25–26), pp. 7803–7811. [CrossRef]
Jafari Nasr, M. R. , and Behfar, R. A. , 2010, “ Novel Design for Evaporative Fluid Coolers,” Appl. Therm. Eng., 30(17–18), pp. 2746–2752. [CrossRef]
Goodman, W. , 1938, “Performance of Coils for Dehumidifying Air,” Heating, Piping and Air Conditioning, 10(11), pp. 697–707.
Threlkeld, J. L. , 1968, Thermal Environmental Engineering, 1st ed., Prentice-Hall, Englewood Cliffs, NJ.
Facao, J. , and Oliveira, A. C. , 2000, “ Thermal Behavior of Closed Wet Cooling Towers for Use With Chilled Ceilings,” Appl. Therm. Eng., 20(13), pp. 1225–1236. [CrossRef]
Facao, J. , and Oliveira, A. C. , 2004, “ Heat and Mass Transfer Correlations for the Design of Small Indirect Contact Cooling Towers,” Appl. Therm. Eng., 24(14–15), pp. 1969–1978. [CrossRef]
Braun, J. E. , Klein, S. A. , and Mitchell, J. W. , 1989, “ Effectiveness Models for Cooling Towers and Cooling Coils,” ASHRAE Trans., 95(2), pp. 3270–3280.
Khamis Mansour, M. , and Hassab, M. A. , 2014, “ Innovative Correlation for Calculating Thermal Performance of Counterflow Wet-Cooling Tower,” Energy, 74, pp. 855–862. [CrossRef]
Stabat, P. , and Marchio, D. , 2004, “ Simplified Model for Indirect-Contact Evaporative Cooling-Tower Behavior,” Appl. Energy, 78(4), pp. 433–451. [CrossRef]
Hasan, A. , 2012, “ Going Below the Wet-Bulb Temperature by Indirect Evaporative Cooling: Analysis Using a Modified e-NTU Method,” Appl. Energy, 89(1), pp. 237–245. [CrossRef]
Kim, M.-H. , Jeong, D.-S. , and Jeong, J.-W. , 2015, “ Practical Thermal Performance Correlations for a Wet-Coil Indirect Evaporative Cooler,” Energy Build., 96, pp. 285–298. [CrossRef]
Xia, Y. P. , and Jacobi, A. M. , 2005, “ Air-Side Data Interpretation and Performance Analysis for Heat Exchangers With Simultaneous Heat and Mass Transfer: Wet and Frosted Surfaces,” Int. J. Heat Mass Transfer, 48(25–26), pp. 5089–5102. [CrossRef]
Xia, L. , Chan, M. Y. , Deng, S. M. , and Xu, X. G. , 2010, “ Analytical Solutions for Evaluating the Thermal Performances of Wet Air Cooling Coils Under Both Unit and Non-Unit Lewis Factors,” Energy Convers. Manage., 51(10), pp. 2079–2086. [CrossRef]
Hasan, A. , and Siren, K. , 2002, “ Theoretical and Computational Analysis of Closed Wet Cooling Towers and Its Applications in Cooling of Buildings,” Energy Build., 34(5), pp. 477–486. [CrossRef]


Grahic Jump Location
Fig. 1

A schematic diagram for counter-flow cooling tower

Grahic Jump Location
Fig. 6

Comparison between the results obtained by the present model and those obtained from the traditional integration model

Grahic Jump Location
Fig. 2

Heating and humidification process (triangle similarity between air properties)

Grahic Jump Location
Fig. 3

Comparison between the present model and the traditional ε-NTU method

Grahic Jump Location
Fig. 5

Comparison between the results obtained by the present model, traditional integration model, and those of Facao and Oliveira [13]

Grahic Jump Location
Fig. 4

Comparison between the results obtained by the present model and those of Hasan and Siren [22] in terms of (a) process water temperature and (b) air temperature and enthalpy



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In