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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

## Abstract

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.

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## References

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## Figures

Fig. 1

A schematic diagram for counter-flow cooling tower

Fig. 6

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

Fig. 2

Heating and humidification process (triangle similarity between air properties)

Fig. 3

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

Fig. 5

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

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

## Errata

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