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Heat Transfer Engineering, 29(7):597–607, 2008 C Taylor and Francis Group, LLC Copyright  ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630801922337

Application of a Genetic Algorithm for Thermal Design of Fin-and-Tube Heat Exchangers GONGNAN XIE,1 QIUWANG WANG,1 and BENGT SUNDEN2 1 2

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, China Division of Heat Transfer, Lund University, Lund, Sweden

Instead of the traditional trial-and-error process, a genetic algorithm (GA) is successfully applied to thermal design of fin-and-tube heat exchangers (FTHEs). The design method uses a GA to search and optimize structure sizes of FTHEs. The minimum total weight or total annual cost of FTHEs is taken as the objective function in the GA, respectively. Seven design parameters are varied for the optimization objectives. The implementation of the design method consists of a GA routine and a thermal design routine. In the GA routine, binary coding for tournament selection, uniform crossover, and one-point mutation is adopted. In the thermal design routine, thermal design of the FTHE is carried out according to the conditions of the structure sizes that the genetic algorithm generated, and the log-mean temperature difference method is used to determine the heat transfer area under the combined structure sizes for a given heat duty. Optimization shows that it is possible to achieve a great reduction in cost or weight, whenever such objectives have been chosen for minimization. The method is universal and may be used for thermal design and optimization of FTHEs under different specified duties.

INTRODUCTION Compact heat exchangers (CHEs), including two types of heat exchangers such as plate-fin types and fin-and-tube (tubefin) types, are widely used for gas-gas or gas-liquid applications. CHEs are compact, highly effective, small volume, and low in weight and cost. Fin-and-tube heat exchangers (FTHEs) are employed in many power engineering and chemical engineering applications, such as compressor intercoolers, air coolers, and fan coils. Plate-fin heat exchangers (PFHEs) are widely used in gas-gas applications such as regenerators and recuperators in microturbines [1, 2]. The FTHE (as shown in Figure 1) is one of the successful improvements of tubular heat exchangers. Because a relatively large thermal resistance is encountered on the gas side (generally, air side), fins are employed on the gas side to enlarge the heat exchanger surface and increase the disturbance of the flow. In addition, if the operating pressure is high on the other side, it generally is economical to use tubes. In the last 10 years, many high-performance fin structures have been developed and Address correspondence to Qiuwang Wang, State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China. E-mail: [email protected]

applied to industrial engineering applications. For gas-liquid heat exchangers, fins can be used outside the tubes, or even inside tubes, based on different operating conditions and fluid types. For gas-gas heat exchangers, fins can be employed on both sides. Heat exchanger design is a traditional and classical issue. It can be based on previous design experience and industrial requirements. The design of heat exchangers, in general, including geometrical parameters and operating specifications, cost estimation, and optimization, represents a complex process. The geometrical parameters are chosen first for a specified heat duty under conditions of fouling. These parameters then are changed manually by a trial-and-error process to satisfy the condition on allowable pressure drop. Subsequently, the heat transfer coefficients (i.e., the heat duty) and friction factors (i.e., the pressure drop) are recalculated until both the heat duty and pressure drop meet specified requirements. Thus, the design task is a complex trial-and-error process and there is always the possibility that the designed results are not the optimum. In this sense, novel design and optimization methods as well as optimization techniques for design of processes need to be developed. In recent years, much literature has appeared on the design and method of shell-and-tube exchangers [3–6], platefin/plate heat exchangers [7–10], and air-cooled heat exchangers [11–14].

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REFERENCES [18] [1] McDonald, C. F, Low-Cost Compact Primary Surface Recuperator Concept for Microturbines, Applied Thermal Engineering, vol. 20, pp. 471–497, 2000. [2] McDonald, C. F, Recuperator Considerations for Future Higher Efficiency Microturbines, Applied Thermal Engineering, vol. 23, pp. 1463–1487, 2003. [3] Poddar, T. K., and Polley, G. T., Optimize Shell-and-Tube Heat Exchanger Design, Chemical Engineering Progress, vol. 96, no. 9, pp. 41–46, 2000. [4] Bell, K. J., Heat Exchanger Design for the Process Industries, ASME Journal of Heat Transfer, vol. 126, no. 6, pp. 877–885, 2004. [5] Serna, M., and Jimenez, A., An Efficient Method for the Design of Shell and Tube Heat Exchangers, Heat Transfer Engineering, vol. 25, no. 2, pp. 5–16, 2004. [6] Unuvar, A., and Kargici, S., An Approach for the Optimum Design of Heat Exchangers, International Journal of Energy Research, vol. 28, no. 15, pp. 1379–1392, 2004. [7] Jia, R., Sunden, B., and Xuan, Y., Design and Optimization of Compact Heat Exchangers, 3rd International Conference on Compact Heat Exchangers and Enhancement Technology for the Process Industries, Eds: Shah, R. K., Davos, Switzerland, pp. 135– 142, 2001. [8] Jia, R., and Sunden, B., Optimal Design of Compact Heat Exchangers by an Artificial Neural Network Method, Proceedings of HT2003, ASME Summer Heat Transfer Conference, paper no. HT2003-47141, 2003. [9] Wang, L., and Sunden, B., Design Methodology for Multistream Plate-Fin Heat Exchangers in Heat Exchanger Networks, Heat Transfer Engineering, vol. 22, no. 1, pp. 3–11, 2001. [10] Wang, L., and Sunden, B., Optimal Design of Plate Heat Exchangers with and without Pressure Drop Specifications, Applied Thermal Engineering, vol. 23, no. 3, pp. 295–311, 2003 [11] Mukherjee, R., Effectively Design Air-Cooled Heat Exchangers, Chemical Engineering Progress, vol. 93, no. 1, pp. 26–47, 1997. [12] Gonzalez, M. T., Petracci, N. C., and Urbicain, M. J., Air-cooled Heat Exchanger Design Using Successive Quadratic Programming, Heat Transfer Engineering, vol. 22, no. 1, pp. 11–16, 2001. [13] Xie, G. N., Chen, Q. Y., Tang, L. H., Zeng, M., and Wang, Q. W., Thermal Design and Comparison of two Fin-And-Tube Heat Exchangers, Proceedings of 2nd Chinese Heat Transfer Technology, November 8–11, 2005, Hainan, China, 2005. (in Chinese) [14] Xie, G. N., Chen, Q. Y., Zeng, M., and Wang, Q. W., Thermal Design of Heat Exchanger with Fins inside and outside of Tubes, Pro-

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ceedings of GT2006, ASME Turbo Expo 2006, May 8–11, 2006, Barcelona, Spain. Paper No. GT2006-90260, 2006. Sen, M., and Yang, K. T., Applications of Artificial Neural Networks and Genetic Algorithms in Thermal Engineering, In: Kreith, F., (Eds), The CRC Handbook of Thermal Engineering, CRC Press, Boca Raton, FL, pp. 620–661, 2000. Pacheco-Vega, A., Sen, M.,Yang, K.T., and McClain, R. L., Genetic Algorithms-based Predictions of Fin-Tube Heat Exchanger Performance, Proceedings of 11th International Heat Transfer Conference, August 23–28, Kyongju, Korea. Vol. 6, pp. 137–142, 1998. Ozkol, I., and Komurgoz, G., Determination of The Optimum Geometry of the Heat Exchanger Body via a Genetic Algorithm, Numerical Heat Transfer, Part A, vol. 48, pp. 283–296, 2005. Xie, G. N., and Wang, Q. W., Geometrical Optimization of PlateFin Heat Exchanger using Genetic Algorithms, Proceedings of the Chinese Society for Electical Engineering, vol. 26, no. 7, pp. 53– 57, 2006. (in Chinese) Mishra, M., Das, P. K., and Sarangi, S., Optimum Design of Crossflow Plate-Fin Heat Exchangers through Genetic Algorithm, International Journal of Heat Exchangers, vol. 5, no. 2, pp. 379–401, 2004 Selbas, R., Kizilkan, O., and Reppich, M., A New Design Approach for Shell-and-Tube Heat Exchangers using Genetic Algorithms from Economic Point of View, Chemical Engineering and Processing, vol. 45, no. 4, pp. 268–275, 2006. Liang, H. X., Xie, G. N., Zeng, M., Wang, Q. W., and Feng, Z. P., Application Genetic Algorithm to Optimization Recuperator in Micro-Turbine, The 2nd International Symposium on Thermal Science and Engineering, October 23–25, Beijing, China, 2005. Wang, Q. W., Liang, H. X., Xie, G. N., Zeng, M., Luo, L. Q., and Feng, Z. P., Genetic Algorithm Optimization for Primary Surfaces Recuperator of Microturbine, ASME Journal of Engineering for Gas Turbines and Power, vol. 129, pp. 436–442, 2007. Pacheco-Vega, A., Sen, M.,Yang, K. T., and McClain, R. L., Correlations of Fin-Tube Heat Exchanger Performance Data Using Genetic Algorithms Simulated Annealing and Interval Methods, Proceedings of ASME the Heat Transfer Division, November 11– 16, New York, USA, Vol. 369–5, pp. 143–151, 2001. Pacheco-Vega, A., Sen, M., and Yang, K. T., Simultaneous Determination of In-and-over-Tube Heat Transfer Correlations in Heat Exchangers by Global Regression, International Journal of Heat and Mass Transfer, vol. 46, no. 6, pp. 1029–1040, 2003. Jegede, F. O., and Polley, G. T., Optimum Heat Exchanger Design, Trans. IChemE, vol. 70, pp. 133–141, 1992. Muralikrishna, K., and Shenoy, U. V., Heat Exchanger Design Targets for Minimum Area and Cost, Trans. IChemE, vol. 78, Part A, pp. 161–167, 2000. Jafari Nasr, M. R., and Polley, G. T., An Algorithm for Cost Comparison of Optimized Shell-and-Tube Heat Exchangers with Tube Inserts and Plain Tubes, Chemical Engineering Technology, vol. 23, no. 3, pp. 267–272, 2000. Wang, L., Performance Analysis and Optimal Design of Heat Exchangers and Heat Exchanger Networks, PhD thesis, Division of Heat Transfer, Department of Heat and Power Engineering, Lund Institute of Technology, 2001. Holland, J. H., Adaption in Nutrual and Aritifical Systems, University of Michigan Press, Ann Arbor, 1975.

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G. XIE ET AL. [30] Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Boston, USA, 1989. [31] Michalewicz, Z., and Fogel, D. B., How to Solve it: Modern Heuristics. New York, Springer, 2000. [32] Wang, C. C., Recent Progress on the Air-Side Performance of Fin-and-Tube Heat Exchangers, International Journal of Heat Exchangers, vol. 2, pp. 57–84, 2000. [33] Wang, C. C., Heat Exchanger Design, Wunan Press, Taiwan, China, Chap. 4, 2003. [34] Carroll, D. L., Chemical Laser Modeling with Genetic Algorithms, AIAA Journal, vol. 34, no. 2, pp. 338–346,1996. [35] Carroll, D. L., Genetic Algorithms and Optimizing Chemical Oxygen-Iodine Lasers, In: Wilson, H., Batra, R., Bert, C., Davis, A., Schapery, B., Stewart, B., and Swinson, F. (Eds). Developments in Theoretical and Applied Mechanics, Vol. XVIII, School of Engineering, The University of Alabama, pp. 411–424,1996. [36] Michalewicz, Z., Deb, K., Schmidt, M., and Stidsen, T., Test-case Generator for Constrained Parameter Optimization Techniques, IEEE Transactions on Evolutionary Computation, vol. 4, no. 3, pp. 197–215, 2000. [37] Gnielinski, V., New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flows, Ind Chem Eng, vol. 16, pp. 359– 368, 1976. [38] Martin, H., Economic Optimization of Compact Exchangers, 1st International Conference on Compact Heat Exchangers and Enhancement Technology for the Process Industries, Eds: Shah, R. K., Banff, Canada, pp. 75–80, 1999.

Gongnan Xie received his Ph.D in Power Engineering and Engineering Thermo Physics from the School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China. He received his M.S. degree in Thermal and Power Engineering from Guangdong Ocean University in 2002, Zhanjiang, China. His research interests include computational fluid dynamics, numerical heat transfer, compact heat exchangers and appli-

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cation of computational intelligence in thermal engineering. He is currently a post doc at Lund University. He has published more than 10 articles in international journals or conferences, and has participated in several projects.

Qiuwang Wang is a professor at the School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China. He received his Ph.D. degree in Engineering Thermophysics from the Xi’an Jiaotong University in 1996. He then joined the faculty of the university and took the professor post in 2001. His main research interests include computational fluid dynamics and numerical heat transfer, heat transfer enhancement, compact heat exchangers, building energy saving and indoor air quality, etc. He has published more than 100 journal papers, half of which have been published in international journals or conferences. He has also obtained 9 Invent Patents of China.

Bengt Sunden received his M.S. and Ph.D. from Chalmers University, G¨oteborg, Sweden. He is currently professor of heat transfer and department head at Lund University, Sweden. His main research interests are computational heat transfer, heat exchangers, transport phenomena in fuel cells, gas turbine heat transfer, combustionrelated heat transfer and enhanced heat transfer. Professor Sunden has published more than 350 articles in well-recognized journals, books and proceedings. He has edited twenty books. He is the editor-in-chief of the International Journal of Heat Exchangers, editor-in-chief for a book series Developments in Heat Transfer. In addition, he is on the editorial board for another four journals. He is a fellow of ASME and serves as associate editor of journal of Heat Transfer. He is an honorary professor of Xi’an Jiatong University, Xi’an, China.

vol. 29 no. 7 2008

Application of a Genetic Algorithm for Thermal Design ...

Apr 4, 2008 - Multiphase Flow in Power Engineering, School of Energy and Power. Engineering, Xi'an Jiaotong ... Exchanger Design, Chemical Engineering Progress, vol. 96, no. 9, pp. 41–46 ... Press, Boca Raton, FL, pp. 620–661, 2000.

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