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Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

Abstract

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA1/2/k)1/2. The structure of the T-shaped cavity has four degrees of freedom: L0/L1 (ratio between the lengths of the stem and bifurcated branches), H1/L1 (ratio between the thickness and length of the bifurcated branches), H0/L0 (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L1/L0) ○○ and (H0/L0), the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.

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References

  1. 1.

    Bejan, A. and Lorente, S., The Constructal Law and the Evolution of Design in Nature, Phys Life Rev., 2011, vol. 8, pp. 209–240.

    ADS  Article  Google Scholar 

  2. 2.

    Bejan, A. and Lorente, S., Constructal Law of Design and Evolution: Physics, Biology, Technology, and Society, J. Appl. Phys., 2013, vol. 113, p. 151301.

    ADS  Article  Google Scholar 

  3. 3.

    Bejan, A. and Zane, J.P., Design in Nature, New York: Doubleday, 2012.

    Google Scholar 

  4. 4.

    Bejan, A. and Lorente, S., Design with Constructal Theory, Hoboken: Wiley, 2008.

    Book  Google Scholar 

  5. 5.

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

    MATH  Google Scholar 

  6. 6.

    Bejan, A., Lorente. S., and Lee, J., Unifying Constructal Theory of Tree Roots, Canopies and Forests, J. Theor. Biol., 2008, vol. 254, pp. 529–540.

    MathSciNet  Article  Google Scholar 

  7. 7.

    Reis, A.H. and Bejan, A., Constructal Theory ofGlobal Circulation and Climate, Int. J. HeatMass Transfer, 2006, vol. 49, pp. 1857–1875.

    Article  MATH  Google Scholar 

  8. 8.

    Miguel, A.F., The Emergence of Design in Pedestrian Dynamics: Locomotion, Self-Organization, Walking Paths and Constructal Law, Phys Life Rev., 2013, http://dx.doi.org/10.1016/j.plrev.2013.03.007.

    Google Scholar 

  9. 9.

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

    Google Scholar 

  10. 10.

    Constructal Law and the Unifying Principle of Design, Rocha, L.A.O., Lorente, S., and Bejan, A., Eds., Springer-Verlag, 2013.

    Google Scholar 

  11. 11.

    Beyene, A. and Peffley, J., Constructal Theory, Adaptive Motion, and Their Theoretical Application to Low-Speed Turbine Design, J. Energ. Eng-ASCE, 2009, vol. 135, no. 4, pp. 112–118.

    Article  Google Scholar 

  12. 12.

    Chen, L., Progress in Study on Constructal Theory and Its Applications, Sci. China Tech. Sci., 2012, vol. 55, no. 3, pp. 802–820.

    Article  Google Scholar 

  13. 13.

    Kim, Y., Lorente, S., and Bejan, A., Steam Generator Structure: Continuous Model and Constructal Design, Int. J. Energy Res., 2011, vol. 35, pp. 336–345.

    Article  Google Scholar 

  14. 14.

    Azad, A.V. and Amidpour, M., Economic Optimization of Shell and Tube Heat Exchanger Based on Constructal Theory, Energy, 2011, vol. 36, pp. 1087–1096.

    Article  Google Scholar 

  15. 15.

    Kraus, A.D., Developments in the Analysis of Finned Arrays, Int. J. Transp. Phenom., 1999, vol. 1, pp. 141–164.

    Google Scholar 

  16. 16.

    Aziz, A., Optimum Dimensions of Extended Surfaces Operating in a Convective Environment, Appl. Mech. Rev., 1992, vol. 45, no. 5, pp. 155–173.

    ADS  Article  Google Scholar 

  17. 17.

    Bello-Ochende, T., Mejer, J.P., and Bejan, A., Constructal Multi-Scale Pin Fins, Int. J. Heat Mass Transfer, 2010, vol. 53, pp. 2773–2779.

    Article  MATH  Google Scholar 

  18. 18.

    Biserni, C., Rocha, L.A.O., and Bejan, A., Inverted Fins: Geometric Optimization of the Intrusion into a Conducting Wall, Int. J. Heat Mass Transfer, 2004, vol. 47, pp. 2577–2586.

    Article  MATH  Google Scholar 

  19. 19.

    Rocha, L.A.O., Lorenzini, G., Biserni, C., and Cho, Y., Constructal Design of a Cavity Cooled by Convection, Int. J. Design Nat. Ecodyn., 2010, vol. 5, pp. 212–220.

    Article  Google Scholar 

  20. 20.

    Rocha, L.A.O., Lorenzini, E., and Biserni, C., Geometric Optimization of Shapes on the Basis of Bejan’s Constructal Theory, Int. Comm. Heat Mass Transfer, 2005, vol. 32, pp. 1281–1288.

    Article  Google Scholar 

  21. 21.

    Lorenzini, G., Biserni, C., Garcia, F.L., and Rocha, L.A.O., Geometric Optimization of a Convective T-Shaped Cavity on the Basis of Constructal Theory, Int. J. Heat Mass Transfer, 2012, vol. 55, pp. 6951–6958.

    Article  Google Scholar 

  22. 22.

    Lorenzini, G. and Rocha, L.A.O., Geometric Optimization of T-Y-Shaped Cavity According to Constructal Design, Int. J. Heat Mass Transfer, 2009, vol. 52, pp. 4683–4688.

    Article  MATH  Google Scholar 

  23. 23.

    Lorenzini, G., Garcia, F.L., dos Santos, E.D., Biserni, C., and Rocha, L.A.O., 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, 2012, vol. 55, pp. 1505–1512.

    Article  MATH  Google Scholar 

  24. 24.

    Biserni, C., Rocha, L.A.O., Stanescu, G., et al., Constructal H-Shaped Cavities According to Bejan’s Theory, Int. J. Heat Mass Transfer, 2007, vol. 50, pp. 2132–2138.

    Article  MATH  Google Scholar 

  25. 25.

    Xie, Z., Chen, L., and Sun, F., Geometry Optimization of T-Shaped Cavities According to Constructal Theory, Math. Comp. Model., 2010, vol. 52, nos. 9/10, pp. 1538–1546.

    Article  Google Scholar 

  26. 26.

    Lorenzini, G., Biserni, C., Isoldi, L.A., dos Santos, E.D., and Rocha, L.A.O., Constructal Design Applied to the Geometric Optimization of Y-Shaped Cavities Embedded in a Conducting Medium, J. Electron. Packaging, 2011, vol. 133, pp. 041008-1–041008-8.

    Article  Google Scholar 

  27. 27.

    Hajmohammadi, M.R., Poozesh, S., Campo, A., and Nourazar, S.S., Valuable Reconsideration in the Constructal Design of Cavities, Energy Conv. Manag., 2013, vol. 66, pp. 33–40.

    Article  Google Scholar 

  28. 28.

    Bejan, A. and Almogbel, M., Constructal T-Shaped Fins, Int. J. Heat Mass Transfer, 2000, vol. 43, pp. 2101–2115.

    Article  MATH  Google Scholar 

  29. 29.

    MATLAB, User’s Guide, vers. 6.0.088, rel. 12, The Mathworks, 2000.

    Google Scholar 

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Correspondence to G. Lorenzini.

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Lorenzini, G., Biserni, C., Link, F.B. et al. Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces. J. Engin. Thermophys. 22, 309–321 (2013). https://doi.org/10.1134/S1810232813040048

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Keywords

  • Heat Mass Transfer
  • Cavity Surface
  • Constructal Theory
  • Engineer THERMOPHYSICS
  • Geometric Optimization