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Layout Design of Conductive Heat Channel by Emulating Natural Branch Systems

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Abstract

To design effective and easy-to-manufacture conductive heat channels, a heuristic method by emulating the natural branch systems is suggested. The design process of the method is divided into two steps, which are the principal channel design and the lateral channel design. During the process, the width of each channel is controlled by the bifurcation law, and the end point of the channel is located at the point with the maximum temperature while the start points of the principal channel and the lateral channel are respectively determined by the location of the heat sink and the law of the minimum thermal resistance. Four design examples with different boundary conditions are studied by the suggested method, and the design results are compared with that of the traditional structural topology optimization method. Not only lower maximum temperature and relatively uniform distribution of temperature are obtained by the suggested method, but also straight channels are achieved without gray element, which is easy to manufacture. The suggested method inspired by the natural branch systems can provide an effective solution for heat channel design in the heat dissipation structures.

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References

  1. Guo K, Qi W Z, Liu B T, Liu C J, Huang Z Q, Zhu G M. Optimization of an “area to point” heat conduction problem. Applied Thermal Engineering, 2016, 93, 61–71.

    Article  Google Scholar 

  2. Hannemann R J. Thermal control of electronics: Perspectives and prospects. Proceedings of Rohsenow Symposium, Massachusetts, USA, 2003, 1–6.

    Google Scholar 

  3. Zhang X F, Chen X. Radiating technology of power electronics. Electronics & Packaging, 2007, 7, 35–39.

    Google Scholar 

  4. Zhang Y, Liu S. Design of conducting paths based on topology optimization. Heat & Mass Transfer, 2008, 44, 1217–1227.

    Article  Google Scholar 

  5. Shabany Y. Heat Transfer: Thermal Management of Electronics, China Machine Press, Beijing, China, 2013. (in Chinese)

    Google Scholar 

  6. LI Q Y, Wang W, Zhou G Y. Status of techniques on heat dissipation in electronic components. Journal of Electron Devices, 2005, 28, 937–941.

    Google Scholar 

  7. Guo K, Qi W Z, Liu B T, Liu C J, Huang Z Q, Zhu G M. Optimization of an “area to point” heat conduction problem. Applied Thermal Engineering, 2016, 93, 61–71.

    Article  Google Scholar 

  8. Hannemann R J. Thermal control of electronics: Perspectives and prospects. Proceedings of Rohsenow Symposium, Massachusetts, USA, 2003, 1–6.

    Google Scholar 

  9. Zhang X F, Chen X. Radiating technology of power electronics. Electronics & Packaging, 2007, 7, 35–39.

    Google Scholar 

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

    Article  Google Scholar 

  11. Shabany Y. Heat Transfer: Thermal Management of Electronics, China Machine Press, Beijing, China, 2013. (in Chinese)

    Google Scholar 

  12. LI Q Y, Wang W, Zhou G Y. Status of techniques on heat dissipation in electronic components. Journal of Electron Devices, 2005, 28, 937–941.

    Google Scholar 

  13. Dbouk T. A review about the engineering design of optimal heat transfer systems using topology optimization. Applied Thermal Engineering, 2016, 112, 841–854.

    Article  Google Scholar 

  14. Bejan A. Shape and structure, from engineering to nature. Entropy, 2001, 3, 293–294.

    Article  Google Scholar 

  15. Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. International Journal of Heat & Mass Transfer, 1997, 40, 799–811.

    Article  MATH  Google Scholar 

  16. Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics & Engineering, 1988, 71, 197–224.

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhuang C G, Xiong Z H, Ding H. A level set method for topology optimization of heat conduction problem under multiple load cases. Computer Methods in Applied Mechanics & Engineering, 2007, 196, 1074–1084.

    Article  MathSciNet  MATH  Google Scholar 

  18. Xie Y M, Huang X D, Zuo Z H, Tang J W, Rong J H. Recent advances in evolutionary structural optimization (ESO) and bi-directional evolutionary structural optimization (BESO). Advances in Mechanics, 2011, 41, 462–471. (in Chinese)

    Google Scholar 

  19. Zhao L, Chen W Y, Ma J F, Yang Y B. Structural bionic design and experimental verification of a machine tool column. Journal of Bionic Engineering, 2008, 5, 46–52.

    Article  Google Scholar 

  20. Ding X H, Yamazaki K. Adaptive growth technique of stiffener layout pattern for plate and shell structures to achieve minimum compliance. Engineering Optimization, 2005, 37, 259–276.

    Article  MathSciNet  Google Scholar 

  21. Li B T, Yan S N, Lin Q Y. Automated layout design of stiffened container structures based on the morphology of plant ramifications. Journal of Bionic Engineering, 2016, 13, 344–354.

    Article  Google Scholar 

  22. Metzger R J, Klein O D, Martin G R, Krasnow M A. The branching programme of mouse lung development. Nature, 2008, 453, 745–750.

    Article  Google Scholar 

  23. Runions A, Lane B, Prusinkiewicz P. Modeling trees with a space colonization algorithm. Proceedings of Eurographics Workshop on Natural Phenomena, Prague, Czech Republic, 2014, 63–70.

    Google Scholar 

  24. Lynch J P, Kai L N, Davis R D, Jablokow A G. SimRoot: Modelling and visualization of root systems. Plant & Soil, 1997, 188, 139–151.

    Article  Google Scholar 

  25. Runions A, Fuhrer M, Lane B, Federl P, Rollandlagan A, Prusinkiewicz P. Modeling and visualization of leaf venation patterns. ACM Transactions on Graphics, 2005, 24, 702–711.

    Article  Google Scholar 

  26. Camburn B, Otto K, Dan J, Crawford R, Wood K. Designing biologically inspired leaf structures: Computational geometric transport analysis of volume-to-point flow channels. Engineering with Computers, 2015, 31, 361–374.

    Article  Google Scholar 

  27. Peng Y, Liu W Y, Chen W, Wang N L. A conceptual structure for heat transfer imitating the transporting principle of plant leaf. International Journal of Heat & Mass Transfer, 2014, 71, 79–90.

    Article  Google Scholar 

  28. Lohan D J, Dede E M, Allison J T. Topology optimization for heat conduction using generative design algorithms. Structural and Multidisciplinary Optimization, 2017, 55, 1063–1077.

    Article  MathSciNet  Google Scholar 

  29. Xia Z Z, Cheng X G, Li Z X, Guo Z Y. Bionic optimization of heat transport paths for heat conduction problems. Journal of Enhanced Heat Transfer, 2004, 11, 119–132.

    Article  Google Scholar 

  30. Ding X H, Yamazaki K. Constructal design of cooling channel in heat transfer system by utilizing optimality of branch systems in nature. Journal of Heat Transfer, 2007, 129, 245–255.

    Article  Google Scholar 

  31. He J K, Mao M, Li D C, Jin Z M. Characterization of leaf-inspired microfluidic chips for pumpless fluid transport. Journal of Bionic Engineering, 2014, 11, 109–114.

    Article  Google Scholar 

  32. Li B T, Hong J, Liu Z F. Stiffness design of machine tool structures by a biologically inspired topology optimization method. International Journal of Machine Tools & Manufacture, 2014, 84, 33–44.

    Article  Google Scholar 

  33. Bejan A. Constructal Theory of Social Dynamics, Springer, Berlin, Germany, 2007, 71–83.

    Google Scholar 

  34. Murray C D. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proceedings of the National Academy of Sciences of the United States of America, 1926, 12, 207–214.

    Google Scholar 

  35. Duan X B, Li F F, Qin X Q. Topology optimization of incompressible Navier–Stokes problem by level set based adaptive mesh method. Computers & Mathematics with Applications, 2016, 72, 1131–1141.

    Article  MathSciNet  MATH  Google Scholar 

  36. Maruyama S. Heat Transfer. Peking University Press, Beijing, China, 2011, 7.

    Google Scholar 

  37. Sherman T F. On connecting large vessels to small. The meaning of Murray’s law. Journal of General Physiology, 1981, 78, 431–453.

    Article  Google Scholar 

  38. Miguel A F. Fluid flow in a porous tree-shaped network: Optimal design and extension of Hess–Murray’s law. Physica A Statistical Mechanics & Its Applications, 2015, 423, 61–71

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the Chinese National Natural Science Fund (Grant No. 51175347). The support is gratefully acknowledged.

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Correspondence to Xiaohong Ding.

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Ji, Y., Ding, X., Li, H. et al. Layout Design of Conductive Heat Channel by Emulating Natural Branch Systems. J Bionic Eng 15, 567–578 (2018). https://doi.org/10.1007/s42235-018-0047-3

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