Multi-Objective Optimization of Force Convective Heat Transfer in a Stack of Horizontal Channels Using CFD and Genetic Algorithms: a Comparison with Asymptotic Method Results

Document Type : Article


Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156-88349, Iran


In this paper, by combining the computational fluid dynamics (CFD) and NSGA II algorithm, the forced convective heat transfer flow in a stack of horizontal parallel plates has been multi-objectively optimized. In the optimization process, the distance between the plates in the set of parallel channels has been changed so as to simultaneously optimize the amount of heat transfer between the plates and fluid and the pressure drop of the fluid (maximization of heat transfer and minimization of pressure drop). The Pareto front, which illustrate the changes of the heat transfer from the plates and the pressure drop of fluid simultaneously, have been presented in the results section. This result contains important information regarding the thermal designing of stack of channels subjected to forced convective heat transfer. The Pareto front have been obtained for four different fluids that have different Prandtl (Pr) numbers (mercury, air, water and oil), and the results related to each fluid have been discussed. Finally, the multi-objective optimization results obtained in this paper have been compared with the results of the asymptotic analysis method (which is a single-objective method aimed at increasing the amount of heat transfer from plates) for internal fluid flows; and useful information has been obtained.


Main Subjects

1. Bejan, A. and Sciubba, E. \The optimal spacing of parallel plates cooled by forced  convection", International Journal of Heat and Mass Transfer, 35, pp. 3259-3264 (1992).
2. Wei, X., and Joshi, Y. \Optimization study of stacked micro-channel heat sinks for micro-electronic cooling", IEEE Transactions Components Packaging Technologies, 26(1), pp. 156-169 (2003).
3. Bejan, A., Fowler, A.J. and Stanescu, D. \The optimal spacing between horizontal cylinders in a xed volume cooled by natural convection", International Journal of Heat and Mass Transfer, 38, pp. 2047-2055 (1995).
4. Goshayeshi, H.R. and Ampofo, F. \Heat transfer by
natural convection from a vertical and horizontal surfaces
using vertical ns", Energy Power Engineering,
1(2), pp. 85-89 (2009).
5. Bar-Cohen, A. and Rohsenow, W.M. \Optimal internal
structure of volumes cooled by single-phase forced
and natural convection", Journal of Heat Transfer,
106, pp. 106-116 (1984).
6. Buonomo, B. and Manca, O. \Natural convection slip

ow in a vertical microchannel heated at uniform heat

ux", International Journal of Thermal Sciences, 49,
pp. 1333-1344 (2010).
7. Sa khani, H., Abbassi, A., Khalkhali, A. and Kalteh
M. \Multi-objective optimization of nano
at tubes using CFD, arti cial neural networks
and genetic algorithms", Advanced Powder Technology,
25(5), pp. 1608-1617 (2014).
8. Sada , M.H., Hosseini, R., Sa khani, H., Bagheri, A.
and Mahmoodabadi, M.J. \Multi-objective optimization
of solar thermal energy storage using hybrid of
particle swarm optimization, multiple crossover and
mutation operator", International Journal of Engineering
Transaction B, 24, pp. 367-376 (2011).
9. Khalkhali, A., Sada , M., Rezapour, J. and Sa khani,
H. \Pareto based multi-objective optimization of solar
thermal energy storage using genetic algorithms",
Transactions of the Canadian Society for Mechanical
Engineering, 34(3-4), p. 463 (2010).
10. Sa khani, H. and Dolatabadi, H. \Multi-objective
optimization of cooling of a stack of vertical minichannels
and conventional channels subjected to natural
convection", Applied Thermal Engineering, 96, pp.
144-150 (2016).
11. Sa khani, H. and Eiamsa-ard, S. \Pareto based multiobjective
optimization of turbulent heat transfer
in helically corrugated tubes", Applied Thermal Engineering,
95, pp. 275-280 (2016).
12. Sa khani, H. and Eiamsa-Ard, S. \Multi-objective
optimization of turbulent tube
ows over diamondshaped
turbulators", Heat Transfer Engineering,
37(18), pp. 1579-1584 (2016).
13. Hao, P., Wang, B. and Li, G. \Surrogate-based optimum
design for sti ened shells with adaptive sampling",
AIAA Journal, 50(11), pp. 2389-2407 (2012).
H. Sa khani and Z. Shirazi/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 221{229 229
14. Hao, P., Wang, B., Tian, K. and Li, G. \Optimization
of curvilinearly sti ened panels with single cutout
concerning the collapse load", International Journal
of Structural Stability and Dynamics, 16, pp. 155-169
15. Wang, B., Tian, K., Hao, P., Cai, Y., Li, Y. and Sun,
Y. \Hybrid analysis and optimization of hierarchical
sti ened plates based on asymptotic homogenization
method", Composite Structures, 132, pp. 136-147
16. Deb, K., Agrawal, S., Pratap, A. and Meyarivan, T.
\A fast and elitist multi-objective genetic algorithm:
NSGA-II", IEEE Trans Evolutionary Computation, 6,
pp. 182-197 (2002).
17. Sa khani, H., Akhavan-Behabadi, M.A., Nariman-
Zadeh, N. and Mahmoodabadi, M.J. \Modeling and
multi-objective optimization of square cyclones using
CFD and neural networks", Chemical Engineering
Research and Design, 89, pp. 301-309 (2011).
18. Sa khani, H., Hajiloo, A. and Ranjbar, M.A. \Modeling
and multi-objective optimization of cyclone separators
using CFD and genetic algorithms", Computers
and Chemical Engineering, 35, pp. 1064-1071 (2011).
19. Amanifard, N., Nariman-Zadeh, N., Borji, M.,
Khalkhali, A. and Habibdoust, A. \Modeling and
Pareto optimization of heat transfer and
ow coef-
cients in micro channels using GMDH type neural
networks and genetic algorithms", Energy Conversion
and Management, 49, pp. 311-325 (2008).
20. Bejan, A., Convection Heat Transfer, Wiley (2004).