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Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle

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Abstract

Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.

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References

  1. Bejan A. Shape and Structure, from Engineering to Nature. Cambridge: Cambridge University Press, 2000

    MATH  Google Scholar 

  2. Bejan A, Lorente S. Thermodynamic optimization of flow geometry in mechanical and civil engineering. J Non-Equilib Thermodyn, 2001, 26(4): 305–354

    Article  Google Scholar 

  3. Bejan A, Lorente S. Constructal multi-scale and multi-objective structures. Int J Energy Res, 2005, 29(7): 689–710

    Article  Google Scholar 

  4. Bejan A, Marden J H. Unifying constructal theory for scale effects in running, swimming and flying. J Exp Biol, 2006, 209(2): 238–248

    Article  Google Scholar 

  5. Bejan A, Merkx G W. Constructal Theory of Social Dynamics. New York: Springer, 2007

    Google Scholar 

  6. Bejan A, Lorente S. Design with Constructal Theory. New Jersey: Wiley, 2008

    Book  Google Scholar 

  7. Bejan A, Lorente S, Miguel A F, et al. Constructal Human Dynamics, Security & Sustainability. Amsterdam: IOS Press, 2009

    Google Scholar 

  8. Bejan A. The constructal-law origin of the wheel, size, and skeleton in animal design. Am J Phys, 2010, 78(7): 692–699

    Article  Google Scholar 

  9. Bejan A, Lorente S. The constructal law and the evolution of design in nature. Phys Life Rev, 2011, 8(3): 209–240

    Article  Google Scholar 

  10. Chen L. Progress in study on constructal theory and its applications. Sci China Tech Sci, 2012, 55(3): 802–820

    Article  Google Scholar 

  11. Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. Int J Heat Mass transfer, 1997, 40(4): 799–816

    Article  MATH  Google Scholar 

  12. Ledezma G, Bejan A, Errera M. Constructal tree networks for heat transfer. J Appl Phys, 1997, 82(1): 89–100

    Article  Google Scholar 

  13. Neagu M, Bejan A. Constructal-theory tree networks of ‘constant’ thermal resistance. J Appl Phys, 1999, 86(2): 1136–1144

    Article  Google Scholar 

  14. Ghodoossi L, Egrican N. Exact solution for cooling of electronics using constructal theory. J Appl Phys, 2003, 93(8), 4922–4929

    Article  Google Scholar 

  15. Wu W, Chen L, Sun F. Improvement of tree-like network constructal method for heat conduction optimization. Sci China Ser-E: Tech Sci, 2006, 49(3): 332–341

    Article  Google Scholar 

  16. Zhou S, Chen L, Sun F. Optimization of constructal volume-point conduction with variable cross-section conducting path. Energy Convers Mgmt, 2007, 48(1): 106–111

    Article  MathSciNet  Google Scholar 

  17. Wei S, Chen L, Sun F. The area-point constructal optimization for discrete variable cross-section conducting path. Appl Energy, 2009, 86(7/8): 1111–1118

    Article  Google Scholar 

  18. Xiao Q, Chen L, Sun F. Constructal optimization for “disc-to-point” heat conduction without the premise of optimized last-order construct. Int J Therm Sci, 2011, 50(6): 1031–1036

    Article  Google Scholar 

  19. Xia Z, Guo Z. Simulation of heat conduction optimization by using biological evolution process (in Chinese). Prog Natural Sci, 2001, 8, 845–852

    Google Scholar 

  20. Cheng X, Li Z, Guo Z. Constructs of highly effective heat transport paths by bionic optimization. Sci China: Ser E-Tech Sci, 2003, 46(3): 296–302

    Article  Google Scholar 

  21. Xia Z, Cheng X, Li Z, et al. Bionic optimization of heat transport paths for heat conduction problems. J Enhanced Heat Transfer, 2004, 11(2): 119–131

    Article  Google Scholar 

  22. Gersborg-Hansen A, Bendsoe M P, Sigmund O. Topology optimization of heat conduction problems using the finite volume method. Struct Multidisc Optim, 2006, 31(2): 251–259

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu S, Zhang Y. Design of conducting paths based on topology optimization. Heat Mass Transfer, 2008, 44(10): 1217–1227

    Article  Google Scholar 

  24. Mathieu-Potvin F, Gosselin L. Optimal conduction pathways for cooling a heat-generating body: A comparison exercise. Int J Heat Mass Transfer, 2007, 50(15–16): 2996–3006

    Article  MATH  Google Scholar 

  25. Xu X, Liang X, Ren J. Optimization of heat conduction using combinatorial optimization algorithms. Int J Heat Mass Transfer, 2007, 50(9–10): 1675–1682

    Article  MATH  Google Scholar 

  26. Boichot R, Luo L. Heat transfer intensification using a cellular automation. Proc 5th Int Confer Heat Transfer, Fluid Mechanics, Thermodyn, July 1–4, 2007, Sun City, South Africa

  27. Bejan A. How to distribute a finite amount of insulation on a wall with nonuniform temperature. Int J Heat Mass Transfer, 1993, 36(1): 49–56

    Article  Google Scholar 

  28. Kalyon M, Sahin A Z. Application of optimal control theory in pipe insulation. Numer Heat Transfer, Part A, 2002, 41(4): 391–402

    Article  Google Scholar 

  29. Sahin A Z. Optimal insulation of ducts in extraterrestrial applications. Int J Energy Res, 2004, 28(3): 195–203

    Article  Google Scholar 

  30. Sahin A Z, Kalyon M. Maintaining uniform surface temperature along pipes by insulation. Energy, 2005, 30(5): 637–647

    Article  Google Scholar 

  31. Ozel M, Pihtili K. Optimum location and distribution of insulation layers on building walls with various orientations. Building Environ, 2007, 42(8): 3051–3059

    Article  Google Scholar 

  32. Yu J, Yang C, Tian L, et al. A study on optimum insulation thicknesses of external walls in hot summer and cold winter zone of China. Appl Energy, 2009, 86(11): 2520–2529

    Article  Google Scholar 

  33. Xie Z, Chen L, Sun F. 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

    Article  MATH  Google Scholar 

  34. Kang D H, Lorente S, Bejan A. Constructal distribution of multi-layer insulation. Int J Energy Res, doi: 10.1002/er.1895

  35. Guo Z, Zhu H, Liang X. Entransy — A physical quantity describing heat transfer ability. Int J Heat Mass Transfer, 2007, 50(13/14): 2545–2556

    Article  MATH  Google Scholar 

  36. Li Z, Guo Z. Field Synergy Principle of Heat Convection Optimization. Beijing: Science Press, 2010

    Google Scholar 

  37. Guo Z, Cheng X, Xia Z. Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization. Chin Sci Bull, 2003, 48(4): 406–410

    Google Scholar 

  38. Han G, Zhu H, Cheng X, et al. Transfer similarity among heat conduction, elastic motion and electric conduction (in Chinese). J Eng Thermophys, 2005, 26(6): 1022–1024

    Google Scholar 

  39. Han G, Guo Z. Physical mechanism of heat conduction ability dissipation and its analytical expression (in Chinese). Proc CSEE, 2007, 27(17): 98–102

    Google Scholar 

  40. Zhu H, Chen J, Guo Z. Electricity and thermal analogous experimental study for entransy dissipation extreme principle (in Chinese). Prog Natural Sci, 2007, 17(12): 1692–1698

    Google Scholar 

  41. Chen Q, Ren J. Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation. Chin Sci Bull, 2008, 53(23): 3753–3761

    Article  Google Scholar 

  42. Liu X, Meng J, Guo Z. Entropy generation extremum and entransy dissipation extremum for heat exchanger optimization. Chin Sci Bull, 2009, 54(6): 943–947

    Article  Google Scholar 

  43. Xia S, Chen L, Sun F. Optimization for entransy dissipation minimization in heat exchanger. Chin Sci Bull, 2009, 54(19): 3587–3595

    Article  Google Scholar 

  44. Wang S, Chen Q, Zhang B. An equation of entransy and its application. Chin Sci Bull, 2009, 54(19): 3572–3578

    Article  Google Scholar 

  45. Guo J, Cheng L, Xu M. Entransy dissipation number and its application to heat exchanger performance evaluation. Chin Sci Bull, 2009, 54(15): 2708–2713

    Article  Google Scholar 

  46. Wu J, Liang X. Application of entransy dissipation extremum principle in radiative heat transfer optimization. Sci China Ser E-Tech Sci, 2008, (51)8: 1306–1314

    Article  MathSciNet  Google Scholar 

  47. Cheng X, Xu X, Liang X. Homogenization of temperature field and temperature gradient field. Sci China Ser E-Tech Sci, 2009, 52(10): 2937–2942

    Article  MATH  Google Scholar 

  48. Wang S, Chen Q, Zhang B, et al. A general theoretical principle for single-phase convective heat transfer enhancement. Sci China Ser-E: Tech Sci, 2009, 52(12): 3521–3526

    Article  MathSciNet  MATH  Google Scholar 

  49. Guo Z, Liu X, Tao W, et al. Effectiveness-thermal resistance method for heat exchanger design and analysis. Int J Heat Mass Transfer, 2010, 53(13/14): 2877–2884

    Article  MATH  Google Scholar 

  50. Chen Q, Yang K, Wang M, et al. A new approach to analysis and optimization of evaporative cooling system I: Theory. Energy, 2010, 35(6): 2448–2454

    Article  Google Scholar 

  51. Xia S, Chen L, Sun F. Entransy dissipation minimization for liquid-solid phase processes. Sci China Tech Sci, 2010, 53(4): 960–968

    Article  MATH  Google Scholar 

  52. 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

    Article  MATH  Google Scholar 

  53. Guo J, Xu M, Cheng L. The entransy dissipation minimization principle under given heat duty and heat transfer area conditions. Chin Sci Bull, 2011, 56(19): 2071–2076

    Article  Google Scholar 

  54. Cheng X, Xu X, Liang X. Application of entransy to optimization design of parallel thermal network of thermal control system in spacecraft. Sci China Tech Sci, 2011, 54(4): 964–971

    Article  MATH  Google Scholar 

  55. Chen Q, Wu J, Wang M, et al. A comparison of optimization theories for energy conservation in heat exchanger groups. Chin Sci Bull, 2011, 56(4–5): 449–454

    Article  Google Scholar 

  56. Cheng X, Liang X, Guo Z. Entransy decrease principle of heat transfer in an isolated system. Chin Sci Bull, 2011, 56(9): 847–854

    Article  Google Scholar 

  57. Li X, Guo J, Xu M, et al. Entransy dissipation minimization for optimization of heat exchanger design. Chin Sci Bull, 2011, 56(20): 2174–2178

    Article  Google Scholar 

  58. Hu G, Cao B, Guo Z. Entransy and entropy revisited. Chin Sci Bull, 2011, 56(27): 2974–2977

    Article  Google Scholar 

  59. Xia S, Chen L, Sun F. Entransy dissipation minimization for a class of one-way isothermal mass transfer processes. Sci China Tech Sci, 2011, 54(2): 352–361

    Article  MATH  Google Scholar 

  60. Liu W, Liu Z, Jia H, et al. Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process. Int J Heat Transfer, 2011, 54(13–14): 3049–3059

    Article  MATH  Google Scholar 

  61. Chen Q, Pan N, Guo Z. A new approach to analysis and optimization of evaporative cooling system II: Applications. Energy, 2011, 36(5): 2890–2898

    Article  Google Scholar 

  62. Xu M. The thermodynamic basis of entransy and entransy dissipation. Energy, 2011, 36(7): 4272–4277

    Article  Google Scholar 

  63. Qian X, Li Z, Li Z. Entransy-dissipation-based thermal resistance analysis of heat exchanger networks. Chin Sci Bull, 2011, 56(31): 3289–3295

    Article  MathSciNet  Google Scholar 

  64. Guo J, Xu M, Cheng L. The influence of viscous heating on the entransy in two-fluid heat exchangers. Sci China Tech Sci, 2011, 54(5): 1267–1274

    Article  MATH  Google Scholar 

  65. Li Q, Chen Q. Application of entransy theory in the heat transfer optimization of flat-plate solar collectors. Chin Sci Bull, 2012, 57(2–3): 299–306

    Article  Google Scholar 

  66. Li Z, Guo Z. Optimization Principles for Heat Convection. In: Wang L Q, ed. Advances in Transport Phenomena. Berlin: Springer, 2011. 1–91

    Chapter  Google Scholar 

  67. Cheng X, Xu X, Liang X. Principles of potential entransy in generalized flow (in Chinese). Acta Phys Sin, 2011, 60(11): 118103

    Google Scholar 

  68. Cheng X, Dong Y, Liang X. Potential entransy and potential entransy decrease principle (in Chinese). Acta Phys Sin, 2011, 60(11): 114402

    Google Scholar 

  69. Guo J, Xu M, Chen L. The influence of viscous heating on the entransy in two-fluid heat exchangers. Sci China Tech Sci, 2011, 54(5): 1267–1274

    Article  MATH  Google Scholar 

  70. Cheng X, Xu X, Liang X. Radiative entransy flux in enclosures with non-isothermal or no-grey, opaque, diffuse surfaces and its application. Sci China Tech Sci, 2011, 54(9): 2446–2456

    Article  Google Scholar 

  71. Chen Q, Xu Y. An entransy dissipation-based optimization principle for building central chilled water systems. Energy, 2012, 37(1): 571–579

    Article  Google Scholar 

  72. Yuan F, Chen Q. Optimization criteria for the performance of heat and mass transfer in indirect evaporative cooling systems. Chin Sci Bull, 2012, 57(6): 687–693

    Article  Google Scholar 

  73. 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-Tech Sci, 2008, 51(8): 1283–1295

    Article  MATH  Google Scholar 

  74. Wei S, Chen L, Sun F. Constructal multidisciplinary optimization of electromagnet based on entransy dissipation minimization. Sci China Ser E-Tech Sci, 2009, 52(10): 2981–2989

    Article  MATH  Google Scholar 

  75. Xie Z, Chen L, Sun F. Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective. Sci China Ser E-Tech Sci, 2009, 52(12): 3504–3513

    Article  MATH  Google Scholar 

  76. Xie Z, Chen L, Sun F. Constructal optimization on T-shaped cavity based on entransy dissipation minimization. Chin Sci Bull, 2009, 54(23): 4418–4427

    Article  Google Scholar 

  77. Wei S, Chen L, Sun F. 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

    Article  MATH  Google Scholar 

  78. Xiao Q Chen L, Sun F. Constructal entransy dissipation rate minimization for “disc-to-point” heat conduction. Chin Sci Bull, 2011, 56(1): 102–112

    Article  Google Scholar 

  79. Xiao Q, Chen L, Sun F. Constructal entransy dissipation rate mini mization for umbrella-shaped assembly of cylindrical fins. Sci China Tech Sci, 2011, 54(1): 211–219

    Article  MATH  Google Scholar 

  80. Xiao Q, Chen L, Sun F. Constructal entransy dissipation rate and flow-resistance minimizations for cooling channels. Sci China Tech Sci, 2010, 53(9): 2458–2468

    Article  MATH  Google Scholar 

  81. Wei S, Chen L, Sun F. Constructal entransy dissipation rate minimization of round tube heat exchanger cross-section. Int J Therm Sci, 2011, 50(7): 1285–1292

    Article  Google Scholar 

  82. Chen L, Wei S, Sun F. Constructal entransy dissipation rate minimization of a disc. Int J Heat Mass Transfer, 2011, 54(1–3): 210–216

    Article  MATH  Google Scholar 

  83. 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 Tech Sci, 2011, 41(7): 962–970

    Google Scholar 

  84. Xiao Q, Chen L, Sun F. Constructal design for a steam generator based on entransy dissipation extremum principle. Sci China Tech Sci, 2011, 54(6): 1462–1468

    Article  MATH  Google Scholar 

  85. Xiao Q, Chen L, Sun F. Constructal entransy dissipation rate minimization for a heat generating volume cooled by forced convection. Chin Sci Bull, 2011, 56(27): 2966–2973

    Article  Google Scholar 

  86. Feng H, Chen L, Sun F. “Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements at micro and nanoscales. Sci China Tech Sci, 2012, 55(3): 779–794

    Article  Google Scholar 

  87. Feng H, Chen L, Sun F. Constructal entransy dissipation rate minimization for leaf-like fins. Sci China Tech Sci, 2012, 55(2): 515–526

    Article  Google Scholar 

  88. Chen L. Progress in entransy theory and its applications. Chin Sci Bull, 2012, doi: 10.1007/s11434-012-5477-4

  89. Bejan A. Heat Transfer. New York: Wiley, 1993

    Google Scholar 

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  1. College of Power Engineering, Naval University of Engineering, Wuhan, 430033, China

    HuiJun Feng, LinGen Chen, ZhiHui Xie & FengRui Sun

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  1. HuiJun Feng
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Correspondence to LinGen Chen.

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Feng, H., Chen, L., Xie, Z. et al. Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle. Sci. China Technol. Sci. 55, 3322–3333 (2012). https://doi.org/10.1007/s11431-012-5046-8

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