Abstract
The constructal optimizations of T-shaped fin with two-dimensional heat transfer model are carried out by finite element method and taking the minimization of equivalent thermal resistance based on entransy dissipation and the minimization of maximum thermal resistance as optimization objectives, respectively. The effects of the global parameter a (integrating the coefficient of convective heat transfer, the overall area occupied by fin and its thermal conductivity) and the volume fraction Φ of fin on the minimums of equivalent thermal resistance and maximum thermal resistance as well as their corresponding optimal configurations are analyzed. The comparison of the results based on the above two optimization objectives is conducted. The results show that the optimal structures based on the two optimization objectives are obviously different from each other. Compared with the optimization result by taking the minimization of maximum thermal resistance as the objective, the optimization result by taking the equivalent thermal resistance minimization as the objective can reduce the average temperature difference in the fin obviously. The increases of a and Φ can all improve the working status of local hot spot and the global heat transfer performance of the system. But the improvement effects of the increases of a and Φ on the minimization of equivalent thermal resistance are different from those on the minimization of maximum thermal resistance. For either objective, the effect of a is different from that of Φ. The T-shaped fin with minimum equivalent thermal resistance is much taller than that with minimum maximum thermal resistance; for either optimization objective, the stem of fin is thicker than the branches of fin, and the stem thickness is relatively close to branch thickness when the minimization of equivalent thermal resistance is taken as the optimization objective. The T-shaped fin with flat stem and slender branches can benefit the reduction of the maximum thermal resistance.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Guo Z Y, Li D Y, Wang B X. A novel concept for convective heat transfer enhancement. Int J Heat Mass Transfer, 1998, 41(14): 2221–2225
Guo Z Y. Mechanism and control of convective heat transfer-Coordination of velocity and heat flow fields. Chin Sci Bull, 2001, 46(7): 596–599
Guo Z Y, Wei S, Cheng X G. A novel method to improve the performance of heat exchanger — Temperature fields coordination of fluids. Chin Sci Bull, 2004, 49(1): 111–114
Li Z X, Guo Z Y. Field Synergy Principle of Heat Convection Optimization (in Chinese). Beijing: Science Press, 2010
Guo Z Y, Cheng X G, Xia Z Z. Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization. Chin Sci Bull, 2003, 48(4): 406–410
Guo Z Y, Zhu H Y, Liang X G. Entransy-A physical quantity describing heat transfer ability. Int J Heat Mass Transfer, 2007, 50(13–14): 2545–2556
Bejan A, Dan N. Constructal trees of convective fins. Trans ASME J Heat Transfer, 1999, 121(3): 675–682
Alebrahim A, Bejan A. Constructal trees of circular fins for conductive and convective heat transfer. Int J Heat Mass Transfer. 1999, 42(19): 3585–3597
Bejan A, Almogbel M. Constructal T-shaped fins. Int J Heat Mass Transfer, 2000, 43(12–15): 2101–2115
Rocha L A O, Montanari G C, dos Santos E D, et al. Constructal design applied to the study of cavities into a solid conducting wall. ENCIT 2004, Brazil: Rio de Janeiro, 2004
Biserni C, Rocha L A O, Bejan A. Inverted fins: geometric optimization of the intrusion into a conducting wall. Int J Heat Mass Transfer, 2004, 47(12–13): 2577–2583
Rocha L A O, Lorenzini E, Biserni C. Geometric optimization of shapes on the basis of Bejan’s Constructal theory. Int Comm Heat Mass Transfer, 2005, 32(10): 1281–1288
Lorenzini G, Rocha L A O. Constructal design of Y-shaped assembly of fins. Int J Heat Mass Transfer, 2006, 49(23–24): 4552–4557
Lorenzini G, Moretti S. Numerical analysis of heat removal enhancement with extended surfaces. Int J Heat Mass Transfer, 2007, 50(3–4): 746–755
Biserni C, Rocha L A O, Stanescu G, et al. Constructal H-shaped cavities according to Bejan’s theory. Int J Heat Mass Transfer, 2007, 50(11–12): 2132–2138
Lorenzini G, Moretti S. A CFD application to optimize T-shaped fins: comparisons to the constructal theory’s results. Trans ASME J Electron Packag, 2007, 129(3): 324–327
Lorenzini G, Moretti S. Numerical analysis on heat removal from Y-shaped fins: Efficiency and volume occupied for a new approach to performance optimization. Int J Thermal Sci, 2007, 46(6): 573–579
Lorenzini G, Moretti S. Numerical heat transfer optimization in modular systems of Y-shaped fins. Trans ASME J Heat Transfer, 2008, 130(8): 081801
Lorenzini G, Moretti S. Numerical performance analysis of constructal | and Y finned heat exchanging modules. Trans ASME J Electron Packag, 2009, 131(3): 031012
Lorenzini G, Moretti S. A Bejan’s constructal theory approach to the overall optimization of heat exchanging finned modules with air in forced convection and laminar flow condition. Trans ASME J Heat Transfer, 2009, 131(8): 081801
Sharqawy M H, Zubair S M. Performance and optimum geometry of spines with simultaneous heat and mass transfer. Int J Thermal Sci, 2009, 48(11): 2130–2138
Lorenzini G, Rocha L A O. Constructal design of T-Y assembly of fins for an optimized heat removal. Int J Heat Mass Transfer, 2009, 52(5–6): 1458–1463
Lorenzini G, Rocha L A O. Geometric optimization of T-Y-shaped cavity according to Constructal design. Int J Heat Mass Transfer, 2009, 52(21–22): 4683–4688
Xie Z H, Chen L G, Sun F R. Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective. Sci China Ser E-Tech Sci, 2009, 52(12): 3504–3513
Xie Z H, Chen L G, Sun F R. Constructal optimization on T-shaped cavity based on entransy dissipation minimization. Chin Sci Bull, 2009, 54(23): 4418–4427
Xie Z H, Chen L G, Sun F R. Constructal optimization of twice level Y-shaped assemblies of fins by taking maximum thermal resistance minimization as objective. Sci China Tech Sci, 2010, 53(10): 2756–2764
Han G Z, Guo Z Y. Physical mechanism of heat conduction ability dissipation and its analytical expression (in Chinese). Proc CSEE, 2007, 27(17): 98–102
Zhu H Y, Chen Z J, Guo Z Y. Electricity and thermal analogous experimental study for entransy dissipation extreme principle (in Chinese). Prog Natural Sci, 2007, 17(12): 1692–1698
Wei S H, Chen L G, Sun F R. “Volume-point” heat conduction constructal optimization with entransy dissipation minimization objective based on rectangular element. Sci China Ser E-Tech Sci, 2008, 51(8): 1283–1295
Wei S H, Chen L G, Sun F R. Constructal multidisciplinary optimization of electromagnet based on entransy dissipation minimization. Sci China Ser E-Tech Sci, 2009, 52(10): 2981–2989
Wei S H. Constructal Entransy Dissipation Rate Minimization for Heat Conduction. Dissertation of Doctoral Degree. Wuhan: Naval University of Engineering, 2009
Cheng X T, Xu X H, Liang X G. Homogenization of temperature field and temperature gradient field. Sci China Ser E-Tech Sci, 2009, 52(10): 2937–2942
Chen Q, Wang M, Pan N, et al. Irreversibility of heat conduction in complex multiphase systems and its application to the effective thermal conductivity of porous media. Int J Nonlinear Sci, 2009,10(1): 57–66
Cheng X T, Xu X H, Liang X G. Homogenization of temperature field for the thermal radiator in space (in Chinese). J Eng Thermophys, 2010, 31(6): 1031–1033
Wei S H, Chen L G, Sun F R. Constructal entransy dissipation minimization for “volume-point” heat conduction without the premise of optimized last-order construct. Int J Exergy, 2010, 7(5): 627–639
Wei S H, Chen L G, Sun F R. Constructal optimization of discrete and continuous variable cross-section conducting path based on entransy dissipation rate minimization. Sci China Tech Sci, 2010, 53(6): 1666–1677
Xiao Q H, Chen L G, Sun F R. Constructal entransy dissipation rate minimization for “disc-point” heat conduction. Chin Sci Bull, 2010, doi: 10.1007/s11434-010-4081-8
Wei S H, Chen L G, Sun F R. Constructal entransy dissipation minimization for “volume-point” heat conduction based on triangular element. Thermal Sci, 2010, 14(4): 1075–1088
Meng J A, Chen Z J, Li Z X, et al. Field-coordination analysis and numerical study on turbulent convective heat transfer enhancement. J Enhanced Heat Transfer, 2005, 12(1): 73–84
Liu X B, Meng J A, Guo Z Y. Entropy generation extremum and entransy dissipation extremum for heat exchanger optimization. Chin Sci Bull, 2009, 54(6): 943–947
Chen Q, Ren J X. Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation. Chin Sci Bull, 2008, 53(23): 3753–3761
Xia S J, Chen L G, Sun F R. Optimization for entransy dissipation minimization in heat exchanger. Chin Sci Bull, 2009, 54(19): 3587–3595
Guo J F, Cheng L, Xu M T. Entransy dissipation number and its application to heat exchanger performance evaluation. Chin Sci Bull, 2009, 54(15): 2708–2713
Liu X B, Guo Z Y. A novel method for heat exchanger analysis (in Chinese). Acta Phys Sin, 2009, 58(7): 4766–4771
Xu M T, Cheng L, Guo J F. Application of entransy dissipation theory in heat exchanger design (in Chinese). J Eng Thermophys, 2009, 30(12): 2090–2092
Chen Q, Wang M, Pan N, et al. Optimization principles for convective heat transfer. Energy, 2009, 34(9): 1199–1206
Guo J, Xu M, Cheng L. Principle of equipartition of entransy dissipation for heat exchanger design. Sci China Tech Sci, 2010, 53(5): 1309–1314
Xiao Q H, Chen L G, Sun F R. Constructal entransy dissipation rate and flow-resistance minimization for cooling channels. Sci China Tech Sci, 2010, 53(9): 2458–2468
Xiao Q H, Chen L G, Sun F R. Constructal entransy dissipation rate minimization for umbrella-shaped assembly of cylindrical fins. Sci China Tech Sci, 2011, 54(1): 211–219
Chen L G, Wei S H, Sun F R. Constructal entransy dissipation rate minimization of a disc. Int J Heat Mass Transfer, 2011, 54(1–3): 210–216
Chen Q, Ren J X, Guo Z Y. The extremum principle of mass entransy dissipation and its application to decontamination ventilation designs in space station cabins. Chin Sci Bull, 2009, 54(16): 2862–2870
Xia S J, Chen L G, Sun F R. Entransy dissipation minimization for liquid-solid phase processes. Sci China Tech Sci, 2010, 53(4): 960–968
Wu J, Liang X G. Application of entransy dissipation extremum principle in radiative heat transfer optimization. Sci China Ser E-Tech Sci, 2008, 51(8): 1306–1314
Xia S J, Chen L G, Sun F R. Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law. Appl Math Model, 2010, 34(8): 2242–2255
Wang S P, Chen Q L, Zhang B J. An equation of entransy and its application. Chin Sci Bull, 2009, 54(19): 3572–3578
Bejan A. Street network theory of organization in nature. J Advanced Transport, 1996, 30(2): 85–107
Zhou S B, Chen L G, Sun F R. Optimization of constructal economics for volume to point transport. Appl Energy, 2007, 84(5): 505–511
Bejan A, Lorente S. Design with Constructal Theory. New Jersey: Wiley, 2008
Miguel A F. Constructal theory of pedestrian dynamics. Phys Lett A, 2009, 373: 1734–1738
Bejan A, Lorente S. The constructal law of design and evolution in nature. Phil Trans R Soc B: Biological Sci, 2010, 365(3): 1335–1347
Reis A H, Gama C. Sand size versus beachface slope-An explanation based on the constructal law. Geomorphology, 2010, 114(3): 276–283
Bai C, Wang L Q. Constructal structure of nanofluids. J Appl Phys, 2010, 108(7): 074317
Wu W J, Chen L G, Sun F R. Improvement of tree-like network constructal method for heat conduction optimization. Sci China Ser E-Tech Sic, 2006, 49(3): 332–341
Zhou S B, Chen L G, Sun F R. Constructal theory in designing photovoltaic cell (in Chinese). Prog Natl Sci, 2006, 16(11): 1500–1505
Yu B M, Li B. Fractal-like tree networks reducing the thermal conductivity. Phys Rev E, 2006, 73(6): 066302
Zhou S B, Chen L G, Sun F R. Optimization of constructal volume-point conduction with variable cross-section conducting path. Energy Convers Mgmt, 2007, 48(1): 106–111
Wu W J, Chen L G, Sun F R. On the “area to point” flow problem based on constructal theory. Energy Convers Mgmt, 2007, 48(1): 101–105
Luo L A, Fan Y L, Zhang W W, et al. Integration of constructal distributors to a mini crossflow heat exchanger and their assembly configuration optimization. Chem Engng Sci, 2007, 62(13): 3605–3619
Zhou S B, Chen L G, Sun F G. Constructal optimization for solid-gas reactors based on triangular element. Sci China Ser E-Tech Sci, 2008, 51(9): 1554–1562
Deng Q H. Fluid flow and heat transfer characteristics of natural convection in square cavities due to discrete source-sink pairs. Int J Heat Mass Transfer, 2008, 51(25–26): 5949–5957
Wei S H, Chen L G, Sun F R. The volume-point constructal optimization for discrete variable cross-section conducting path. Appl Energy, 2009, 86(7–8): 1111–1118
Bai C, Wang L Q. Constructal allocation of nanoparticles in nanofluids. Tans ASME J Heat Transfer, 2010, 132(5): 052404
Wei S H, Chen L G, Sun F R. Constructal complex-objective optimization of electromagnet based on magnetic induction and maximum temperature difference. Rev Mexi Fis, 2010, 56(3): 245–250
Xie Z H, Chen L G, Sun F R. Constructal optimization of a vertical insulating wall based on a complex-objective combining heat flow and strength. Sci China Tech Sci, 2010, 53(8): 2278–2290
Liu H, Li P, Lew J V. CFD study on flow distribution uniformity in fuel distributors having multiple structural bifurcations of flow channels. Int J Hydrogen Energy, 2010, 35(17): 9186–9198
Chen Y, Zhang C, Shi M, et al. Thermal and hydrodynamic characteristics of constructal tree-shaped minichannel heat sink. AIChE J, 2010, 56(8): 2018–2029
Xie Z H, Chen L G, Sun F R. Multi-objective constructal optimization of rectangular cavities based on complex function combining thermal resistances. In: Proceedings of Chinese Society of Engineering Thermophysics on Engineering Thermophysics and Energy Utilization. Nanjing: Chinese Society of Engineering Thermophysics, 2010. Paper No. 101033
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xie, Z., Chen, L. & Sun, F. Comparative study on constructal optimizations of T-shaped fin based on entransy dissipation rate minimization and maximum thermal resistance minimization. Sci. China Technol. Sci. 54, 1249–1258 (2011). https://doi.org/10.1007/s11431-011-4317-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-011-4317-0