Advertisement

Optimization of Pin Fin Profiles

  • Viorel Badescu
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 93)

Abstract

Direct and indirect optimal control methods are used. Two different objective functions are considered. First, the transferred heat flux is maximized and the resulting optimal pin fin shape is a cylinder. Second, the pin volume is minimized for given value of the heat flux. Then, the optimum pin fin profile consists of two regions. In the first region, close to the basis, the pin thickness decreases linearly. In the second region the pin thickness is constant or may decrease, depending on thermal loads and operation. The optimal control solution is usually singular but may be very well approximated by a bang-bang solution. The technology and design constraints have important effects on pin fin profile.

Keywords

Heat Flux Optimal Control Problem Biot Number Optimal Control Method Cylinder Volume 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Azarkish, H., Sarvari, S.M.H., Behzadmehr, A.: Optimum geometry design of a longitudinal fin with volumetric heat generation under the influences of natural convection and radiation. Energy Convers. Manag. 51, 1938–1946 (2010)CrossRefGoogle Scholar
  2. Badescu, V.: Optimal profile of heat transfer pin fins under technological constraints. Energy 93, Part 2, 2292–2298 (2015)Google Scholar
  3. Betts, J.T.: Practical Methods For Optimal Control Using Nonlinear Programming Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2001)Google Scholar
  4. Bonnans, F., Giorgi, D., Grelard, V., Maindrault, S., Martinon, P., (2014). BOCOP—The Optimal Control Solver, User Guide. 8 Apr 2014 http://bocop.org
  5. Chung, B.T.F., Talbot, D.J., Van Dyke, J.M.: A new look at the optimum dimensions of convective splines. AIChE Heat Transfer 84, 108–113 (1988)Google Scholar
  6. Das, S., Razelos, P.: Optimization of convective trapezoidal profile circular pin fins. Int. Comm. Heat Mass Transfer 24, 533–541 (1997)CrossRefGoogle Scholar
  7. Georgiou, E.N.: Analysis and optimization of convective pin fins with trapezoidal profile having internal heat generation density. J. Franklin Inst. 335B, 179–197 (1998)CrossRefGoogle Scholar
  8. Hajabdollahi, F., Rafsanjani, H.H., Hajabdollahi, Z., Hamidi, Y.: Multi-objective optimization of pin fin to determine the optimal fin geometry using genetic algorithm. Appl. Math. Model. 36, 244–254 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  9. Hanin, L.: A new optimum pin fin beyond the “length-of-arc” assumption. Heat Transfer Eng. 29, 608–614 (2008)CrossRefGoogle Scholar
  10. Hanin, L., Campo, A.: A new minimum volume straight cooling fin taking into account the “length of arc”. Int. J. Heat Mass Transf. 46, 5145–5152 (2003)CrossRefzbMATHGoogle Scholar
  11. Hollands, K.G.T., Stedman, B.A.: Optimization of an absorber plate fin having a step-change in local thickness. Sol. Energy 49, 493–495 (1992)CrossRefGoogle Scholar
  12. Kobus, C.J., Cavanaugh, R.B.: A theoretical investigation into the optimal longitudinal profile of a horizontal pin fin of least material under the influence of pure forced and pure natural convection with a diameter-variable convective heat transfer coefficient. J. Heat Transfer 128, 843–846 (2006)CrossRefGoogle Scholar
  13. Kovarik, M.: Optimal solar energy collector systems. Sol. Energy 17, 91–94 (1975)CrossRefGoogle Scholar
  14. Kundu, B.: Performance and optimization analysis of SRC profile fins subject to simultaneous heat and mass transfer. Int. J. Heat Mass Transf. 50, 1545–1558 (2007)CrossRefzbMATHGoogle Scholar
  15. Kundu, B., Lee, K.-S.: Shape optimization for the minimum volume of pin fins in simultaneous heat and mass transfer environments. Heat Mass Transfer 48, 1333–1343 (2012a)CrossRefGoogle Scholar
  16. Kundu, B., Lee, K.-S.: A novel analysis for calculating the smallest envelope shape of wet fins with a nonlinear mode of surface transport. Energy 44, 527–543 (2012b)CrossRefGoogle Scholar
  17. Kundu, B., Lee, K.-S.: Analytic solution for heat transfer of wet fins on account of all nonlinearity effects. Energy 41, 354–367 (2012c)CrossRefGoogle Scholar
  18. Kundu, B., Lee, K.-S.: The effect of arc length on the least-volume fin under sensible and latent heat loads. Int. J. Heat Mass Transf. 63, 414–424 (2013)CrossRefGoogle Scholar
  19. Lawson, S.A., Thrift, A.A., Thole, K.A., Kohli, A.: Heat transfer from multiple row arrays of low aspect ratio pin fins. Int. J. Heat Mass Transf. 54, 4099–4109 (2011)CrossRefGoogle Scholar
  20. Li, C.H.: Optimum cylindrical pin fin. AIChE J. 29, 1043–1044 (1983)CrossRefGoogle Scholar
  21. Maday, C.J.: The minimum weight one-dimensional straight fin. ASME J. Engng. Ind. 96, 161 (1974)CrossRefGoogle Scholar
  22. Natarajan, U., Shenoy, U.V.: Optimum shapes of convective pin fins with variable heat transfer coefficient. J. Franklin Inst. 327, 965–982 (1990)CrossRefGoogle Scholar
  23. Nocedal, J., Wright, S.J.: Numerical optimization. Springer, New York (1999)CrossRefzbMATHGoogle Scholar
  24. Nwosu, N.P.: Employing exergy-optimized pin fins in the design of an absorber in a solar air heater. Energy 35, 571–575 (2010)CrossRefGoogle Scholar
  25. H.J. Oberle, W. Grimm, 2001. BNDSCO, A program for the Numerical Solution of Optimal Control Problems, Report No. 515 der DFVLR, [Deutsche Forschungs-und Versuchsanstalt fur Luft-und Raumfahrt e.V. 1989, Reihe B, Bericht 36], Oct 2001, (http://www.math.uni-hamburg.de/home/oberle/software.html)
  26. Panda, S., Bhowmik, A., Das, R., Repaka, R., Martha, S.C.: Application of homotopy analysis method and inverse solution of a rectangular wet fin. Energy Convers. Manag. 80, 305–318 (2014)CrossRefzbMATHGoogle Scholar
  27. Piskunov, N.: Differential and integral calculus. MIR Publishers, Moscow (1969)zbMATHGoogle Scholar
  28. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: Mathematical theory of optimal processes. Wiley, New York (1962)Google Scholar
  29. Razelos, P., Georgiou, E.: Two-dimensional effects and design criteria for convective extended surfaces. Heat Transfer Eng. 13, 38–48 (1992)CrossRefGoogle Scholar
  30. Razelos, P., Imre, K.: Minimum mass convective fins with variable heat transfer coefficients. J. Franklin Inst. 315, 269 (1983)CrossRefGoogle Scholar
  31. Rong-Hua, Y.: Errors in one-dimensional fin optimization problem for convective heat transfer, Int. J. Heat Mass Transfer 39, 3075–3078 ( 1996)Google Scholar
  32. Rong-Hua, Y.: An analytical study of the optimum dimensions of rectangular fins and cylindrical pin fins. Int. J. Heat Mass Transf. 40, 3607–3615 (1997)CrossRefzbMATHGoogle Scholar
  33. Schmidt, E.: Die Wlrmeubertragung durch Rippen. Z. Verein. Deutsch Ing. 70, 885 (1926)Google Scholar
  34. Sertkaya, A.A., Bilir, S., Kargıcı, S.: Experimental investigation of the effects of orientation angle on heat transfer performance of pin-finned surfaces in natural convection. Energy 36, 1513–1517 (2011)CrossRefGoogle Scholar
  35. Shuja, S.Z.: Optimal fin geometry based on exergoeconomic analysis for a pin-fin array with application to electronics cooling. Exergy 2, 248–258 (2002)CrossRefGoogle Scholar
  36. Sonn, A., Bar-Cohen, A.: Optimum cylindrical pin fin, ASME. J. Heat Transfer 103, 814–815 (1981)CrossRefGoogle Scholar
  37. Tiris, C., Tiris, M., Ture, I.E.: Effects of fin design on collector efficiency. Energy 20, 1021–1026 (1995)CrossRefGoogle Scholar
  38. Tolle, H.: Optimization methods. Springer, New York (1975)CrossRefzbMATHGoogle Scholar
  39. Torabi, M., Aziz, A., Zhang, K.: A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities. Energy 51, 243–256 (2013)CrossRefGoogle Scholar
  40. Wachter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program 106, 25–57 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  41. Walther, A., Griewank, A.: Getting started with ADOL-C. In: Naumann, U., Schenk, O. (eds.) Combinatorial Scientific Computing, Chapman-Hall CRC, Computational Science (2012)Google Scholar
  42. Yovanovich, M.M.: On the effect of shape, aspect ratio and orientation upon natural convection from isothermal bodies of complex shape. ASME HTD 82, 121–129 (1987)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Candida Oancea InstitutePolytechnic University of BucharestBucharestRomania

Personalised recommendations