INVESTIGATIONS ON THE INTERNAL SHAPE OF CONSTRUCTAL CAVITIES INTRUDING A HEAT GENERATING BODY

Abstract

This paper deals with the influence that the internal shape of open ‘cavities' exerts on the Constructal design of a heat generating body. Several shapes of cavity are studied; triangular, elliptical, trapezoidal and Y-shaped cavities intruding into a trapezoidal shaped solid with uniform heat generation. The trapezoidal solid is commonly used in round electronic devices. The geometric aspect ratios of the cavities and the solid are free to vary while the total volume occupied by the solid and the cavity are fixed. The objective is minimizing the peak (hot spot) temperature with respect to the geometrical parameters of the system. Finite element method is employed to calculate the peak temperature of the solid. With respect to the Constructal thermal design, the numerical results prove that, utilizing the triangular and Y-Shaped cavities can result more reliable and effective rather than other studied cavities.

Keywords

Dates

  • Submission Date2012-04-27
  • Revision Date2012-09-01
  • Acceptance Date2012-09-24

DOI Reference

10.2298/TSCI120427164P

References

  1. Bejan, A. , Lorente, S., Design with Constructal Theory, John Wiley and Sons Inc., New Jersey, USA, 2008
  2. Wechsatol, W., Lorente, S., Bejan, A., Optimal Tree-shaped networks for fluid flow in a disc- shaped body, Int J Heat Mass Transfer, 45 (2002), pp. 4911-4924
  3. Zhou, S., Chen, L., Sun, F., Optimization of constructal volume-point conduction with variable cross section conducting path, Energy Conversion and Management, 48 (2007), 1, pp. 106-111
  4. Zimparov, V.D., Silva, A.K.D., Bejan, A., Thermodynamic optimization of tree-shaped flow geometries with constant channel wall temperature, Int J Heat Mass Ttransfer, 49 (2006), pp. 4839-4849
  5. Alebrahim, A., Bejan, A., Constructal trees of circular fins for conductive and convective heat transfer, Int J Heat Mass Transfer, 42 (1999), pp. 3585-3597
  6. Almogbel, M., Bejan., A., Cylindrical trees of pin fins, Int J Heat Mass Transfer, 43 (2000), pp. 4285-4297
  7. Bejan, A., Almogbel, M., T-shaped fins, Int J Heat Mass Transfer, 43 (2000), pp. 2101-2115
  8. Lorenzini, G., Rocha, L. ,Constructal design of Y-shaped assembly of fins, Int J Heat Mass Transfer, 49 (2006) ,pp. 4552-4557
  9. Lorenzini, G., Rocha, L.A.O., Constructal design of T-Y assembly of fins for an optimized heat removal, Int J Heat Mass Transfer, 52 (2009), 5-6, pp. 1458 - 1463
  10. Lorenzini, G., Moretti, S., Numerical performance analysis of Constructal I and Y finned heat exchanging modules, ASME Journal of Electronic Packaging, 131 (2009), 3, pp. 031012-1 - 031012-10
  11. 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, ASME Journal of Heat Transfer, 131 (2009), 8, pp. 081801-1 - 081801-18
  12. Lorenzini, G., Moretti, S., Thermofluid dynamic performances numerical-constructal analysis of heat exchangers with standard and optimized profiles, Int J Heat Technology, 27 (2009), 1, pp. 145 - 149
  13. Kundu, B., Bhanja, D., Performance and optimization analysis of a Constructal T-shaped fin subject to variable thermal conductivity and convective heat transfer coefficient, Int J Heat Mass Transfer, 53 (2010), pp. 254-267
  14. Zhang, X., Liu, D., Optimum geometric arrangement of vertical rectangular fin arrays in natural convection, Energy Conversion and Management, 51 (2010), pp. 2449-2456
  15. Lorenzini, G., Moretti, S., Bejan's Constructal theory analysis of gas-liquid cooled finned modules, ASME Journal of Heat Transfer, 133 (2011), 7, pp. 071801-1 - 071801-10
  16. Lorenzini, G., Lima Correa, , R., Domingues dos Santos, E., Rocha, L.A.O., Constructal design of complex assembly of fins, ASME Journal of Heat Transfer, 133 (2011), 8, pp. 081902-1- 081902-7
  17. Biserni, C., Lorenzini, G., Orlandelli, C.M., Frequency Analysis of the Vapotron Effect in Forced Convection: a Challenge for Numerical Description of Multiphase Flows, in: Int. Conf. Computational Methods in Multiphase Flow, WIT Press, Orlando, 2001, pp. 173-182
  18. Bejan, A., Shape and Structure from Engineering to Nature, Cambridge University Press, Cambridge UK, 2000
  19. Rocha, L., Lorenzini, E., Biserni, C., Geometric optimization of shapes on the basis of Bejan's Constructal theory, Int Com in Heat Mass Transfer, 32 (2005), pp. 1281-1288
  20. Rocha, L., Montanari, G.C., Dos Santos, E.D., Rocha, A.D., Constructal design applied to the study of cavities, Engeoharia Tennica (thermal Engineering), 6 (2007), pp. 41-47
  21. Biserni, C., Constructal H-Shaped cavities according to Bejan's theory, Int J Heat Mass Transfer, 50 (2007), pp. 2132-2138
  22. Lorenzini, G., Biserni, C., Isoldi, L. A., Domingues dos Santos, E., Rocha, L.A.O., Constructaldesign applied to the geometric optimization of Y-shaped cavities embedded in a conducting medium, ASME Journal of Electronic Packaging, 133 (2011), 4, pp. 041008-041016
  23. Lorenzini, G., Biserni, C., Rocha, L.A.O., Geometric optimization of isothermal cavities according to Bejan's theory, Int J Heat Mass Transfer, 54 (2001), 17-18, pp. 3868 - 3873
  24. Lorenzini, G., Rocha, L., Geometric optimization of T-Y-shaped cavity according to Constructal design, Int J Heat Mass Transfer, 52 (2009), pp. 4683-4688
  25. Lorenzini, G., Garcia, F.L., Dos Santos, E.D., Biserni, C., Constructal design applied to the optimization of complex geometries: T-Y-shaped cavities with two additional lateral intrusions cooled by convection, Int J Heat Mass Transfer, 55 (2012), pp. 1505-1512
  26. Rocha, L.A.O., Lorenzini, G., Biserni, C., Cho, Y., Constructal Design Of A Cavity Cooled By Convection, Int. J. of Design & Nature and Ecodynamic, 5 (2010), pp. 212-220
  27. Xie, Z., Chen, L., Sun, F., Geometry optimization of T-shaped cavities according to Constructal theory, Mathematical and computer modeling, 52 (2010), pp. 1538-1546
  28. Lorenzini, G., Biserni, C., Garcia, F. L., Isoldi, L. A., Domingues dos Santos, E., Rocha, L.A.O., Constructal design of cavities inserted into a cylindrical solid body, ASME Journal of Heat Transfer, 134 (2012), 7, pp. 071301-1 - 071301-6
  29. MATLAB, User's Guide, Version 6.0.088, Release 12, 2000, The Mathworks Inc.
  30. FIDAP Manual, Fluid Dynamics International, Inc., 1998, Evanston, IL.