Abstract
The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For a heat transfer model of a rectangular solid wall with an open T-shaped cavity, a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective, and constructal optimization for the model is carried out when the system volume, the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed. Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle. The formulation of dimensionless global (maximum) thermal resistance presented in a literature is modified; some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective. Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different. The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective, so that the performance of heat transfer for the total system can be improved. The more freedom the cavity has, the better the total system performance is. The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.
Similar content being viewed by others
References
Guo Z Y, Li D Y, Wang B X. A novel concept for convective heat transfer enhancement. In J Heat Mass Transfer, 1998, 41: 2221–2225
Guo Z Y. Mechanism and control of convective heat transfer-coordination of velocity and heat flow fields. Chinese Sci Bull, 2001, 46: 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: 111–114
Bejan A. Entropy Generation Minimization. New York: Wiley, 1996
Bejan A. Entropy generation minimization: the new thermodynamics of finite-size devices and finite-time processes. J Appl Phys, 1996, 79: 1191–1218
Chen L, Wu C, Sun F. Finite time thermodynamic optimization or entropy generation minimization of energy systems. J Non-Equibri Thermodyn, 1999, 24: 327–359
Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. Trans ASME J Heat Transfer, 1997, 40: 799–816
Bejan A, Almogbel M. Constructal T-shaped fins. Int J Heat Mass Transfer, 2000, 43: 2101–2115
Bejan A, Rocha L A O, Lorente S. Thermodynamic optimization of geometry: T and Y-shaped constructs of fluid streams. Int J Thermal Sci, 2000, 39:949–960
Bejan A, Lorente S. Design with Constructal Theory. New Jersey: Wiley, 2008
Wang A H, Liang X G, Ren J X. Constructal enhancement of heat conduction with phase change. Int J Thermophy, 2006, 27: 126–138
Yu B, Li B. Fractal-like tree networks reducing the thermal conductivity. Phys Rev E, 2006, 73: 066302
Wu W, Chen L, Sun F. On the “area to point” flow problem based on constructal theory. Energy Convers Mgmt, 2007, 48: 101–105
Zhou S, Chen L, Sun F. Optimization of constructal volume-point conduction with variable cross-section conducting path. Energy Convers Mgmt, 2007, 48: 106–111
Xu X, Liang X, Ren J. Optimization of heat conduction using combinatorial optimization algorithms. Int J Heat Mass Transfer, 2007, 50: 1675–1682
Wu W, Chen L, Sun F. Improvement of tree-like network constructal method for heat conduction optimization. Sci China Ser E: Technolo Sci, 2006, 49: 332–341
Zhou S, Chen L, Sun F. Constructal optimization for solid-gas reactors based on triangular element. Sci China Ser E: Technolo Sci, 2008, 51: 1554–1562
Bejan A. Advanced Engineering Thermodynamics. New York: Wiley, 1997
Shah R K, Skiepko T. Entropy generation extrema and their relationship with heat exchanger effectiveness-Number of transfer unit behavior for complex flow arrangements. Trans ASME J Heat Transfer, 2004, 126: 994–1002
Guo Z Y, Zhu H Y, Liang X G. Entransy—A physical quantity describing heat transfer ability. Int J Heat Mass Transfer, 2007, 50: 2545–2556
Guo Z Y. New physical quantities in heat (in Chinese). J Engineer Thermophy, 2008, 29: 112–114
Guo Z X, Cheng X G, Xia Z Z. Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization. Chinese Sci Bull, 2003, 48: 406–410
Cheng X, Li Z, Guo Z. The construction of high conductivity channel based on bionic optimization. Sci China Ser E: Technolo Sci, 2003, 33: 251–256
Han G Z, Guo Z Y. Two different thermal optimization objective functions: dissipation of heat transport potential capacity and entropy production(in Chinese). J Engineer Thermophy, 2007, 27: 811–813
Cheng X G, Meng J A, Guo Z Y. Potential capacity dissipation minimization and entropy generation minimization in heat conduction optimization (in Chinese). J Engineer Thermophy, 2005, 26: 1034–1036
Chen Q, Ren J X. Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation. Chinese Sci Bull, 2008, 53: 3753–3761
Han G Z, Guo Z Y. Physical mechanism of heat conduction ability dissipation and its analytical expression(in Chinese). Proc CSEE, 2007, 27: 98–102
Zhu H Y, Chen J Z, Guo Zeng Y. Electricity and thermal analogous experimental study for entransy dissipation extreme principle (in Chinese). Prog Nat Sci, 2007, 17: 1692–1698.
Liu X B, Guo Z Y, Meng J A. Analyses for entransy dissipation and heat resistance in heat exchangers (in Chinese). Prog Nat Sci, 2008, 18: 1186–1190
Song W M, Meng J A, Liang X G, et al. Demonstration of uniformity principle of temperature difference field for one-dimensional heat exchangers (in Chinese). J Chem Indu Eng, 2008, 59: 2460–2464.
Liu X, Meng J, Guo Z. Entropy generation extremum and entransy dissipation extremum for heat exchanger optimization. Chinese Sci Bull, 2009, 54: 943–947
Wu J, Liang X G. Application of entransy dissipation extremum principle in radiative heat transfer optimization. Sci China Ser E: Technolo Sci, 2008, 51: 1306–1314
Wei S, Chen L, Sun F. “Volume-point” heat conduction constructal optimization with entransy dissipation minimization objective based on rectangular element. Sci China Ser E: Technolo Sci, 2008, 51: 1283–1295
Wei S, Chen L, Sun F. Constructal multidisciplinary optimization of electromagnet based on entransy dissipation minimization. Sci China Ser E: Technolo Sci, in 2009, 52, doi: 10.1007/s11431-009-0153-x
Xia S, Chen L, Sun F. Optimization for entransy dissipation minimization in heat exchanger. Chinese Sci Bull, 2009, 54, doi: 10.1007/s11434-009-0202-7
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: 2577–2583
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Program for New Century Excellent Talents in Universities of China (Grant No. 20041006) and Foundation for the Authors of National Excellent Doctoral Dissertation of China (Grant No. 200136)
About this article
Cite this article
Xie, Z., Chen, L. & Sun, F. Constructal optimization on T-shaped cavity based on entransy dissipation minimization. Chin. Sci. Bull. 54, 4418–4427 (2009). https://doi.org/10.1007/s11434-009-0507-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-009-0507-6