Skip to main content

Geometric optimization of T-shaped constructs coupled with a heat generating basement: A numerical approach motivated by Bejan’s constructal theory

Abstract

This work relies on constructal design to perform the geometric optimization of morphing T-shaped fins that remove a constant heat generation rate from a rectangular basement. The fins are bathed by a steady stream with constant ambient temperature and convective heat transfer. The body that serves as a basement for the T-shaped construct generates heat uniformly and it is perfectly insulated on the outer perimeter. It is shown numerically that the global dimensionless thermal resistance of the T-shaped construct can be minimized by geometric optimization subjected to constraints, namely, the basement area constraint, the T-shaped fins area fraction constraint and the auxiliary area fraction constraint, i.e., the ratio between the area that circumscribes the T-shaped fin and the basement area. The optimal design proved to be dependent on the degrees of freedom (L1/L0, t1/t0, H/L): first achieved results indicate that when the geometry is free to morph then the thermal performance is improved according to the constructal principle named by Bejan “optimal distribution of imperfections.”

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Torabi, M., Aziz, A., and Zhang, K., A Comparative Study of Longitudinal Fins of Rectangular, Trapezoidal and Concave Parabolic Profiles withMultiple Nonlinearities, Energy, 2013, vol. 51, pp. 243–256.

    Google Scholar 

  2. 2.

    Hazarika, S.A., Bhanja, D., Nath, S., and Kundu, B., Analytical Solution to Predict Performance and Optimum Design Parameters of a Constructal T-Shaped Fin with Simultaneous Heat and Mass Transfer, Energy, 2015, vol. 84, pp. 303–316

    Article  Google Scholar 

  3. 3.

    Bejan, A., Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume, Int. J. Heat Mass Transfer, 1997, vol. 40, pp. 799–816

    Article  MATH  Google Scholar 

  4. 4.

    Bejan, A., Advanced Engineering Thermodynamics, 2nd ed., New York: Wiley, 1997.

    Google Scholar 

  5. 5.

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

    Book  Google Scholar 

  6. 6.

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

    MathSciNet  Article  Google Scholar 

  7. 7.

    Miguel, A.F., Constructal Pattern Formation in Stony Corals, Bacterial Colonies and Plant Roots under Different Hydrodynamics Conditions, Theor. Biol., 2006, vol. 242, pp. 954–961.

    Google Scholar 

  8. 8.

    Quéré, S., Constructal Theory of Plate Tectonics, Int. J. Des. Nat. Ecodyn., 2010, vol. 5, pp. 242–253.

    Article  Google Scholar 

  9. 9.

    Bejan, A. and Lorente, S., Constructal Theory of Generation of Configuration in Nature and Engineering, J. Appl. Phys., 2006, vol. 100, p. 041301.

    ADS  Article  Google Scholar 

  10. 10.

    Bejan, A., Badescu, V., and De Vos, A., Constructal Theory of Economics Structure Generation in Space and Time, Energy Convers. Manag., 2000, vol. 41, pp. 1429–1451.

    Article  Google Scholar 

  11. 11.

    Bejan, A., Badescu, V., and De Vos, A., Constructal Theory of Economics, Appl. Energy, 2000, vol. 67, pp. 37–60.

    Article  Google Scholar 

  12. 12.

    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 

  13. 13.

    Miguel, A.F., The Emergence of Design in Pedestrian Dynamics: Locomotion, Self-Organization, Walking Paths and Constructal Law, Phys. Life Rev., 2013, vol. 10, pp. 168–190.

    Google Scholar 

  14. 14.

    Bejan, A., WhyUniversityRankingsDo Not Change: Education as a NaturalHierarchicalFlowArchitecture, Int. J. Des. Nat. Ecodyn., 2007, vol. 2, pp. 319–327.

    Google Scholar 

  15. 15.

    Bejan, A., Two Hierarchies in Science: The Free Flow of Ideas and the Academy, Int. J. Des. Nat. Ecodyn., 2009, vol. 4, pp. 386–394.

    Article  Google Scholar 

  16. 16.

    Bejan, A., Constructal Thermodynamics: Life and Evolution as Physics, Proc. Constructal Lawand Second Law Conf., 2015, Parma, Italy, pp. 19–37.

    Google Scholar 

  17. 17.

    Bello-Ochende, T., Liebenberg, L., and Meyer, J.P., Constructal Cooling Channels for Micro-Channel Heat Sinks, Int. J. HeatMass Transfer, 2007, vol. 50, pp. 4141–4150.

    Article  MATH  Google Scholar 

  18. 18.

    Bello-Ochende, T., Meyer, J.P., and Bejan, A., Constructal Ducts with Wrinkled Entrances, Int. J. Heat Mass Transfer, 2009, vol. 52, pp. 3628–3633.

    Article  MATH  Google Scholar 

  19. 19.

    Olakoyejo, O.T., Bello-Ochende, T., andMeyer, J.P., Mathematical Optimization of Laminar ForcedConvection Heat Transfer through a Vascularized Solid with Square Channels, Int. J. Heat Mass Transfer, 2012, vol. 55, pp. 2402–2411.

    Article  Google Scholar 

  20. 20.

    Olakoyejo, O.T., Bello-Ochende, T., and Meyer, J.P., Constructal Conjugate Cooling Channels with Internal Heat Generation, Int. J. Heat Mass Transfer, 2012, vol. 55, pp. 4385–4396.

    Article  Google Scholar 

  21. 21.

    Lee, J., Kim, Y., Lorente, S., and Bejan, A., Constructal Design of a Comb-Like Channel Network for Self-Heating and Self-Cooling, Int. J. Heat Mass Transfer, 2013, vol. 66, pp. 898–905.

    Article  Google Scholar 

  22. 22.

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

    Article  MATH  Google Scholar 

  23. 23.

    MATLAB, User’s Guide, Vers. 6.0.088, Mathworks, 2000.

  24. 24.

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

    Article  MATH  Google Scholar 

  25. 25.

    Bejan, A. and Lorente, S., The Constructal Law Origin of the Logistic S Curve, J. Appl. Phys., 2011, 110:024901.

    ADS  Article  Google Scholar 

  26. 26.

    Bejan, A. and Marden, J.H., The Constructal Unification of Biological and Geophysical Design, Phys. Life Rev., 2009, vol. 6, pp. 85–102.

    ADS  Article  Google Scholar 

  27. 27.

    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 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to G. Lorenzini.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lorenzini, G., Biserni, C., Dalpiaz, F.L. et al. Geometric optimization of T-shaped constructs coupled with a heat generating basement: A numerical approach motivated by Bejan’s constructal theory. J. Engin. Thermophys. 26, 485–497 (2017). https://doi.org/10.1134/S1810232817040051

Download citation