Cooling towers, enthalpy potential, NTU, Merkel equation, evaporative cooling


Accurate performance analysis of direct-contact air-water counterflow cooling towers is important in practice for energy conservation and cost savings purposes. In general, accurate analysis can often be made using Merkel’s theory. However, a simple and accurate analytical solution of the Merkel equation is not yet available.  In this paper, a novel and accurate analytical solution is presented, obtained from direct integration of the Merkel equation. The new method gives excellent agreement when compared with the use of standard Merkel’s method when predicting the outlet water temperatures with maximum root-mean-square error of 0.2% for a practical range of operating conditions. The new method also predicts the outlet water temperatures for four experimental cooling towers with maximum root-mean-square error of 0.8%. A limited validation shows that the method is also applicable to performance analysis of an actual crossflow cooling tower. The new method is a valuable addition to the existing methods of solving the Merkel equation.


ASHRAE. 2020. ASHRAE Handbook of HVAC Systems and Equipment. Atlanta: American Society of Heating, Refrigerating, and Air-Conditioning Engineers Inc.

Merkel, F. 1925. Verdunstungskühlung. VDI-Zeitschrift. 70: 123-128.

Baker, D. A, and H. A. Shryock. 1961. A Comprehensive Approach to the Analysis of Cooling Tower Performance. ASME Journal of Heat Transfer. 83(3): 339-350. https://doi.org/10.1115/1.3682276.

Simpson, W. M., and T. K. Sherwood. 1946. Performance of Small Mechanical Draft Cooling Towers. Refrigerating Engineering. 52(6): 535-543,574-576.

Jaber, H., and R. L. Webb. 1989. Design of Cooling Towers by the Effectiveness-NTU Method. ASME Journal of Heat Transfer. 111: 837-843. https://doi.org/10.1115/1.3250794.

Braun, J. E., S. A. Klein, and J. W. Mitchell. 1989. Effectiveness Models for Cooling Towers and Cooling Coils. AHSRAE Transactions. 95(2): 164-174.

Kloppers, J. C., and D. G. Kroger. 2005. Cooling Tower Performance Evaluation: Merkel, Poppe, and e-NTU Methods of Analysis. Journal of Engineering for Gas Turbines and Power. 127: 1-7. https://doi.org/10.1115/1.1787504.

Kloppers, J. C., and D. G. Kroger. 2005. A Critical Investigation into the Heat and Mass Transfer Analysis of Counterflow Wet-Cooling Towers. International Journal of Heat Mass Transfer. 48: 765-777.


Kloppers, J. C. 2003. A Critical Evaluation and Refinement of the Performance Prediction of Wet-Cooling Towers. PhD Thesis. University of Stellenbosch, South Africa.

Cooling Technology Institute. 2000. Acceptance Test Code for Water-Cooling Towers ATC-105. Houston, TX: Cooling Technology Institute.

Singh, K., and R. Das. 2017. Simultaneous Optimization of Performance Parameters and Energy Consumption in Induced Draft Cooling Towers. Chemical Engineering Research and Design. 123: 1-13.


Benton, D. J., M. Hydeman, C. F. Bowman, and P. Miller. 2002. An Improved Cooling Tower algorithm for the CoolToolsTM simulation model. AHSRAE Transactions. 108(1): 760-768.

Stoecker, W. F., and J. W. Jones. 1982. Refrigeration and Air Conditioning. 2nd Edition. Singapore: McGraw-Hill.

Tomas, A. C. C., S. D. O. Araujo, M. D. Paes, A. R. M. Primo, J. A. P. Da Costa, and A. A. V. Ochoa. 2018. Experimental Analysis of the Performance of New Alternative Materials for Cooling Tower Fill. Applied Thermal Engineering. 144: 444-456. https://doi.org/10.1016/j.applthermaleng.2018.08.076.

Sutherland, J. W. 1983. Analysis of Mechanical-Draught Counterflow Air/Water Cooling Towers. ASME Journal of Heat Transfer. 105: 576-583.


Mansour, M. K., and M. A. Hasab. 2014. Innovative Correlation for Calculating Thermal Performance of Wet-Cooling Tower. Energy. 74: 855-862.


Picardo, J. R., and J. E. Variyar. 2012. The Merkel Equation Revisited: A Novel Method to Compute the Packed Height of a Cooling Tower. Energy Conversion and Management. 57: 167-172.


Costelloe, B., and D. P. Finn. 2009. Heat Transfer Correlations for Low Approach Evaporative Cooling Systems in Buildings. Applied Thermal Engineering. 29: 105-115.


Serna-Gonzalez, M., J. M. Ponce-Ortega, and A. Jimenez-Gutierrez. 2010. MINLP Optimization of Mechanical Draft Counter Flow Wet-Cooling Towers. Chemical Engineering Research and Design. 88: 614-625.


Pontes, R. F. F., W. M. Yamauchi, and E. K. G. Silva. 2019. Analysis of the Effect of Seasonal Climate Changes on Cooling Tower Efficiency, and Strategies for Reducing Cooling Tower Power Consumption. Applied Thermal Engineering. 161: 1-10.


Mohiuddin, A. K. M., and K. Kant. 1996. Knowledge Base for the Systematic Design of Wet Cooling Towers, Part 1: Selection and Tower Characteristics. International Journal of Refrigeration. 19(1): 43-51.


Navaro, P., J. Ruiz, M. Hernandez, A. S. Kaiser, and M. Lucas. 2022. Critical Evaluation of Thermal Performance Analysis of a New Cooling Tower Prototype. Applied Thermal Engineering. 213: 1-12.


Ruiz, J., P. Navaro, M. Hernandez, M. Lucas, and A. S. Kaiser. 2022. Thermal Performance and Emissions Analysis of a New Cooling Tower. Applied Thermal Engineering. 206: 1-10. https://doi.org/10.1016/j.applthermaleng.2022.118065.

Threlkeld, J. L. 1970. Thermal Environmental Engineering. 2nd Edition. New Jersey: Prentice-Hall Inc.

Clouse, R. L. 1971. Preliminary Design of a Mechanical-Draft Counterflow Cooling Tower AEDC-TR-71-213. Tennessee: Arnold Engineering Development Center, Arnold Air Force Station, USA.

Maclaine-cross, I. L., and P. J. Banks. 1981. A General Theory of Wet Surface Heat Exchangers and its Application to Regenerative Cooling. Journal of Heat Transfer. 103: 579-585. https://doi.org/10.1115/1.3244505.

ASHRAE. 2021. ASHRAE Handbook of Fundamentals. Atlanta: American Society of Heating, Refrigerating, and Air-Conditioning Engineers Inc.

Yu, F. W., and K. T. Chan. 2008. Optimization of Water-cooled Chiller System with Load-based Speed Control. Applied Energy. 85: 931-950.






Science and Engineering

How to Cite

A NOVEL ANALYTICAL SOLUTION OF MERKEL EQUATION FOR COUNTERFLOW COOLING TOWERS. (2024). Jurnal Teknologi, 86(3), 13-20. https://doi.org/10.11113/jurnalteknologi.v86.20849