Heat Exchanger Circuitry Design by Decision Diagrams

  • Nikolaos Ploskas
  • Christopher Laughman
  • Arvind U. Raghunathan
  • Nikolaos V. SahinidisEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11494)


The interconnection pattern between the tubes of a tube-fin heat exchanger, also referred to as its circuitry, has a significant impact on its performance. We can improve the performance of a heat exchanger by identifying optimized circuitry designs. This task is difficult because the number of possible circuitries is very large, and because the dependence of the heat exchanger performance on the input (i.e., a given circuitry) is highly discontinuous and nonlinear. In this paper, we propose a novel decision diagram formulation and present computational results using the mixed integer programming solver CPLEX. The results show that the proposed approach has a favorable scaling with respect to number of tubes in the heat exchanger size and produces configurations with 9% higher heat capacity, on average, than the baseline configuration.


Optimization Decision diagram Heat exchanger design Refrigerant circuitry Heat capacity 


  1. 1.
    Ploskas, N., Laughman, C., Raghunathan, A.U., Sahinidis, N.V.: Optimization of circuitry arrangements for heat exchangers using derivative-free optimization. Chem. Eng. Res. Des. 131, 16–28 (2018). Scholar
  2. 2.
    Hewitt, G.F., Shires, G.L., Bott, T.R.: Process Heat Transfer, vol. 113. CRC Press, Boca Raton (1994)Google Scholar
  3. 3.
    Fax, D.H., Mills, R.R.: Generalized optimal heat exchanger design. ASME Trans. 79, 653–661 (1957)Google Scholar
  4. 4.
    Hedderich, C.P., Kelleher, M.D., Vanderplaats, G.N.: Design and optimization of air-cooled heat exchangers. J. Heat Transfer 104, 683–690 (1982)CrossRefGoogle Scholar
  5. 5.
    Liang, S.Y., Wong, T.N., Nathan, G.K.: Study on refrigerant circuitry of condenser coils with exergy destruction analysis. Appl. Therm. Eng. 20, 559–577 (2000). Scholar
  6. 6.
    Wang, C.C., Jang, J.Y., Lai, C.C., Chang, Y.J.: Effect of circuit arrangement on the performance of air-cooled condensers. Int. J. Refrig. 22, 275–282 (1999). Scholar
  7. 7.
    Yun, J.Y., Lee, K.S.: Influence of design parameters on the heat transfer and flow friction characteristics of the heat exchanger with slit fins. Int. J. Heat Mass Transf. 43, 2529–2539 (2000). Scholar
  8. 8.
    Liang, S.Y., Wong, T.N., Nathan, G.K.: Numerical and experimental studies of refrigerant circuitry of evaporator coils. Int. J. Refrig. 24, 823–833 (2001). Scholar
  9. 9.
    Matos, R.S., Laursen, T.A., Vargas, J.V.C., Bejan, A.: Three-dimensional optimization of staggered finned circular and elliptic tubes in forced convection. Int. J. Therm. Sci. 43, 477–487 (2004). Scholar
  10. 10.
    Domanski, P.A., Yashar, D., Kim, M.: Performance of a finned-tube evaporator optimized for different refrigerants and its effect on system efficiency. Int. J. Refrig. 28, 820–827 (2005). Scholar
  11. 11.
    Domanski, P.A., Yashar, D., Kaufman, K.A., Michalski, R.S.: An optimized design of finned-tube evaporators using the learnable evolution model. HVAC&R Res. 10, 201–211 (2004). Scholar
  12. 12.
    Domanski, P.A., Yashar, D.: Optimization of finned-tube condensers using an intelligent system. Int. J. Refrig. 30, 482–488 (2007). Scholar
  13. 13.
    Wu, Z., Ding, G., Wang, K., Fukaya, M.: Application of a genetic algorithm to optimize the refrigerant circuit of fin-and-tube heat exchangers for maximum heat transfer or shortest tube. Int. J. Therm. Sci. 47, 985–997 (2008). Scholar
  14. 14.
    Bendaoud, A.L., Ouzzane, M., Aidoun, Z., Galanis, N.: A new modeling procedure for circuit design and performance prediction of evaporator coils using CO2 as refrigerant. Appl. Energy 87, 2974–2983 (2010). Scholar
  15. 15.
    Lee, W.J., Kim, H.J., Jeong, J.H.: Method for determining the optimum number of circuits for a fin-tube condenser in a heat pump. Int. J. Heat Mass Transf. 98, 462–471 (2016). Scholar
  16. 16.
    Yashar, D.A., Lee, S., Domanski, P.A.: Rooftop air-conditioning unit performance improvement using refrigerant circuitry optimization. Appl. Therm. Eng. 83, 81–87 (2015). Scholar
  17. 17.
    Cen, J., Hu, J., Jiang, F.: An automatic refrigerant circuit generation method for finned-tube heat exchangers. Can. J. Chem. Eng. (2018). Scholar
  18. 18.
    Andersen, H.R., Hadzic, T., Hooker, J.N., Tiedemann, P.: A constraint store based on multivalued decision diagrams. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 118–132. Springer, Heidelberg (2007). Scholar
  19. 19.
    Behle, M.: Binary decision diagrams and integer programming. Ph.D. thesis, Saarland University (2007)Google Scholar
  20. 20.
    Bergman, D., Cire, A.A., van Hoeve, W.J., Hooker, J.N.: Discrete optimization with decision diagrams. INFORMS J. Comput. 28(1), 47–66 (2016). Scholar
  21. 21.
    Bergman, D., Cire, A.A., van Hoeve, W.J., Hooker, J.N.: Decision Diagrams for Optimization. Artificial Intelligence: Foundations, Theory, and Algorithms, 1st edn. Springer, Cham (2016). Scholar
  22. 22.
    Bergman, D., Cire, A.A.: Discrete nonlinear optimization by state-space decompositions. Manage. Sci. 64(10), 4700–4720 (2017). Scholar
  23. 23.
    Cire, A.A., van Hoeve, W.J.: Multivalued decision diagrams for sequencing problems. Oper. Res. 61(6), 1411–1428 (2013). Scholar
  24. 24.
    Davarnia, D., van Hoeve, W.J.: Outer approximation for integer nonlinear programs via decision diagrams (2018).
  25. 25.
    Haus, U.U., Michini, C., Laumanns, M.: Scenario aggregation using binary decision diagrams for stochastic programs with endogenous uncertainty. CoRR abs/1701.04055, (2017)
  26. 26.
    Hooker, J.N.: Decision diagrams and dynamic programming. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 94–110. Springer, Heidelberg (2013). Scholar
  27. 27.
    Lozano, L., Smith, J.C.: A binary decision diagram based algorithm for solving a class of binary two-stage stochastic programs. Math. Program. (2018).
  28. 28.
    Morrison, D.R., Sewell, E.C., Jacobson, S.H.: Solving the pricing problem in a branch-and-price algorithm for graph coloring using zero-suppressed binary decision diagrams. INFORMS J. Comput. 28(1), 67–82 (2016). Scholar
  29. 29.
    Raghunathan, A.U., Bergman, D., Hooker, J.N., Serra, T., Kobori, S.: Seamless multimodal transportation scheduling. CoRR abs/1807.09676 (2018)
  30. 30.
    Serra, T., Hooker, J.N.: Compact representation of near-optimal integer programming solutions (2017).
  31. 31.
    Tjandraatmadja C., van Hoeve, W.J.: Target cuts from relaxed decision diagrams. INFORMS J. Comput. (2018, to appear)Google Scholar
  32. 32.
    Jiang, H., Aute, V., Radermacher, R.: CoilDesigner: a general-purpose simulation and design tool for air-to-refrigerant heat exchangers. Int. J. Refrig. 29, 601–610 (2006). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Informatics and Telecommunications EngineeringUniversity of Western MacedoniaKozaniGreece
  2. 2.Mitsubishi Electric Research LaboratoriesCambridgeUSA
  3. 3.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations