Constructal structures for self-cooling: microvascular wavy and straight channels

Abstract

This paper shows that a conductive domain which is subjected to heating from its bottom can be cooled with embedded microvascular cooling channels in it. The volume of the domain and the coolant are fixed. The actively cooled domain is mimicked from the human skin (which regulates temperature with microvascular blood vessels). The effect of the shape of cooling channels (sinusoidal or straight) and their locations in the direction perpendicular to the bottom surface on the peak and average temperatures are studied. In addition, the effect of pressure difference in between the inlet and outlet is varied. The pressure drop in the sinusoidal channel configurations is greater than the straight channel configurations for a fixed cooling channel volume. The peak and average temperatures are the smallest with straight cooling channels located at y = 0.7 mm. Furthermore, how the cooling channel configuration should change when the heat is generated throughout the volume is studied. The peak and average temperatures are smaller with straight channels than the sinusoidal ones when the pressure drop is less than 420 Pa, and they become smaller with sinusoidal channel configurations when the pressure drop is greater than 420 Pa. In addition, the peak and average temperatures are the smallest with sinusoidal channels for a fixed flow rate. Furthermore, the peak temperatures for multiple cooling channels is documented, and the multiple channel configurations promise to the smallest peak temperature for a fixed pressure drop value. This paper uncovers that there is no optimal cooling channel design for any condition, but there is one for specific objectives and conditions

Keywords

• Constructal; Vascular; Self-cooling; Bio-mimicry; Heat generation

Constructal structures for self-cooling: microvascular wavy and straight channels

Abstract

Keywords

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References

1. Hamilton, A.R., Sottos, N.R., White, S.R., 2010. Self- healing of internal damage in synthetic vacular materials, Adv. Mat., 22, 5159-5163.
2. Kessler, M.R., Sottos, N.R., White, S.R., 2003. Self- healing structural composite materials, Composites Part A: Appl. Science Manufacturing, 34, pp. 743-753.
3. Cetkin, E., Lorente, S., Bejan, A., 2011. Hybrid grid and tree structures for cooling and mechanical strength, J. Appl. Phys., 110, 064910.
4. Bejan A, Lorente S. Design with Constructal Theory, 2008, Wiley, Hoboken.
5. Bejan, A., Lorente, S., 2013. Constructal law of design and evolution: Physics, biology, technology and society, J. Appl. Phys., 113, 151301.
6. Bejan, A., Zane, J.P., 2012. Design in Nature: How the constructal law governs evolution in biology, physics, technology and social organization, Doubleday, New York.
7. Beyene, A., Peffley, J., 2009. Constructal theory, adaptive motion, and their theoretical application to low-speed turbine design, J. Energy Eng., 135, pp. 112-118.
8. Cetkin, E., Lorente, S., Bejan, A., 2010. Natural constructal emergence of vascular design with turbulent flow, J. Appl. Phys., 107, 114901.

9. da Silva, A.K., Bejan A., 2005. Constructal multi-scale structure for maximal heat transfer density in natural convection, Int. J. Heat Fluid Flow, 26, pp. 34-44.
10. Miguel, A.F., 2006. Constructal pattern formation in stony corals, bacterial colonies and plant roots under different hydrodynamics conditions, J. Theoretical Biol., 242, pp. 954-961.
11. Reis, A.H., 2006. Constructal theory: from engineering to physics, and how flow systems develop shape and structure, Appl. Mec. Rev., 59, pp. 269-282.
12. Reis, A.H., Miguel, A.F., Aydin, M., 2004. Constructal theory of flow architecture of lungs, Med. Phys., 31, pp. 1135-1140.
13. Reis, A.H., 2006. Constructal view of scaling laws of river basins, Geomorphology, 78, pp. 201-206.
14. Bejan, A., Merkx, G.W., 2007. Constructal theory of social dynamics, Springer, New York.
15. White, S.R., Sottos, N.R., Geubelle, P.H., Moore, J.S., Kessler, M.R., Sriram, S.R., Brown, E.N.,Viswanathan, S., 2001. Autonomic healing of polymer composites, Nature, 409, pp. 794–797.
16. Therriault, D., White, S.R., Lewis, J.A., 2003.Chaotic mixing in three-dimensional microvascular networks fabricated by direct-write assembly, Nature Materials, 2, pp. 265-271.
17. Odom, S.A., Tyler, T.P., Caruso, M.M., Ritchey, J.A., Schulmerich, M.V., Robinson, S.J., Bhargava, R., Sottos, N.R., White, S.R., Hersam, M.C., Moore, J.S., 2012. Autonomic Restoration of Electrical Conductivity using Polymer-stabilized Carbon Nanotube and Graphene Microcapsules, Appl. Phys. Lett., 101, 043106.
18. Bejan, A.,Lorente, S., 2008. Vascularized multi-functional materials and structures, Advanced Materials Research, 47- 50, pp. 511-514.
19. Kim, S., Lorente, S., Bejan, A., 2009. Design with constructal theory: vascularized composites for volumetric cooling, Proceedings of ASME IMECE 2008, 8, pp. 437- 444.
20. Wang, K.-M., Lorente, S., Bejan, A., 2010. Vascular structures for volumetric cooling and mechanical strength, J. Appl. Phys., Vol. 107, 044901.
21. Cetkin, E., Lorente, S., Bejan, A., 2014. Vascularization for cooling and reduced thermal stresses (accepted for publication in Int. J. Heat Mass Transfer).
22. Soghrati, S.,Thakre, P.R., White, S.R., Sottos, N.R., Geubelle, P.H., 2012. Computational modelling and design of actively-cooled microvascular materials, Int. J. Heat Mass Transfer, 55, pp. 5309-5321.
23. Xie, G., Asadi, M., Sunden, B., Zheng, S., 2014. Constructal theory based geometric optimization of wavy channels in the low Reynolds number regime, J. Electron. Packag., 136 (3) 031013.
24. Hao, X., Peng, B., Xie, G., Chen, Y., 2014. Thermal analysis and experimental validation of laminar heat transfer and pressure drop in serpentine channel heat sinks for electronic cooling, J. Electron. Packag., 136 (3) 031009.
25. See www.comsol.com for information about COMSOL Multiphysics.