International Scientific Journal


This paper documents two reliable methods to cope with the rising temperature in an array of heated segments with a known overall heat load and exposed to forced convective boundary layer flow. Minimization of the hot spots (peak temperatures) in the array of heated segments constitutes the primary goal that sets the platform to develop the methods. The two proposed methods consist of: 1) Designing an array of unequal heaters so that each heater has a different size and generates heat at different rates, and 2) Distancing the unequal heaters from each other using an insulated spacing. Multi-scale design based on constructal theory is applied to estimate the optimal insulated spacing, heaters size and heat generation rates, such that the minimum hot spots temperature is achieved when subject to space constraint and fixed overall heat load. It is demonstrated that the two methods can considerably reduce the hot spot temperatures and consequently, both can be utilized with confidence in industry to achieve optimized heat transfer.
PAPER REVISED: 2013-09-30
PAPER ACCEPTED: 2013-11-25
CITATION EXPORT: view in browser or download as text file
  1. Luo, L., Tondeur, D., Gall, H.L., Corbel, S., Constructal approach and multi-scale components, Applied Thermal Engineering, 27 (2007), pp. 1708-1714.
  2. Bejan, A., Lorente, S., Design with Constructal Theory, Wiley, Hoboken, NJ, 2008.
  3. A. Bejan, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge, England, UK, 2000.
  4. Bejan, A., Convection Heat Transfer, 3rd ed., Wiley, Hoboken, NJ, 2004.
  5. Tso, C.P., Xu, G.P., Tou, K.W., An experimental study on forced convection heat transfer from flush-mounted discrete heat sources, J. Heat Transfer, 121 (1999), pp. 326-332.
  6. Bhowmik, H., Tso, C.P., Tou, K.W., Tan, F.L., Convection heat transfer from discrete heat sources in a liquid cooled rectangular channel, Applied Thermal Engineering, 25 (2005), pp. 2532-2542.
  7. Chen, L., Tian, H., Li, Y., Zhang, D., Experimental study on natural convective heat transfer from a vertical plate with discrete heat sources mounted on the back, Energy Conversion and Management, 47 (2006), pp. 3447-3455
  8. Dogan, A., Sivrioglu, M., Baskaya, S., Experimental investigation of mixed convection heat transfer in a rectangular channel with discrete heat sources at the top and at the bottom, Int. Comm. Heat Mass Transfer, 32 (2005), pp. 1244-1252
  9. Chen, S., Liu, Y., Chan, S.F., Leung, C.W., Chan, T.L., Experimental study of optimum spacing problem in the cooling of simulated electronics package, Int. J. Heat Mass Transfer, 37 (2001), pp. 251-257.
  10. Wang, H.Y., Penot, F., Saulnier, J.B., Numerical study of a buoyancy-induced flow along a vertical plate with discretely heated integrated circuit packages, Int. J. Heat Mass Transfer, 40 (1997), pp. 1509-1520
  11. Tou, S.K.W., Zhang, X.F., Three-dimensional numerical simulation of natural convection in an inclined liquid-filled enclosure with an array of discrete heaters, Int. J. Heat Mass Transfer, 46 (2003), pp.127-138.
  12. Deng, Q.H. , Tang, G.F., Li, Y.G., Ha, M.Y., Interaction between discrete heat sources in horizontal natural convection enclosures, Int. J. Heat Mass Transfer, 45 (2002), pp. 5117-5132.
  13. Sezai, I., Mohamad, A.A., Natural convection from a discrete heat source on the bottom of a horizontal enclosure, Int. J. Heat Mass Transfer, 43 (2000), pp. 2257-2266.
  14. Liu, Y., Phan-Thien,N., An optimum spacing problem for three chips mounted on a vertical substrate in an enclosure, Num. Heat Transfer, 37 (2000), pp. 613-630.
  15. Muftuoglu, A., Bilgen, E., Natural convection in an open square cavity with discrete heaters at their optimized positions, Int. J. Thermal Sciences, 47 (2008), pp. 369-377.
  16. Sudhakar, T.V.V., Balaji, C., Venkateshan, S.P., Optimal configuration of discrete heat sources in a vertical duct under conjugate mixed convection using artificial neural networks, Int. J. Thermal Sciences, 48 (2009), pp. 881-890.
  17. Hajmohammadi, M. R., Poozesh, S., Rahmani, M., Campo, A., Heat transfer improvement due to the imposition of non-uniform wall heating for in-tube laminar forced convection, Applied Thermal Engineering, 61 (2013), pp. 268-277
  18. Dias, T., Milanez, L.F., Optimal location of heat sources on a vertical wall with natural convection through genetic algorithms, Int. J. Heat Mass Transfer, 49 (2006), pp. 2090-2096.
  19. da Silva, A.K., Lorenzini, G., Bejan, A., Placement of heat sources in vertical open channels with natural convection, Int. J. Heat Mass Transfer, 48 (2005), pp. 1462-1469
  20. Hajmohammadi, M. R., Nourazar, S. S., Campo, A., Poozesh, S., Optimal discrete distribution of heat flux elements for in-tube laminar forced convection, Int. J. Heat Fluid Flow, 40 (2013), pp. 89-96.
  21. Hajmohammadi, M.R., Shirani, E., Salimpour, M. R., Campo, A., Constructal placement of unequal heat sources on a plate cooled by laminar forced convection, Int. J. Thermal Sciences, 60 (2012), pp. 13-22.
  22. da Silva, A.K., Lorente, S., Bejan, A., Optimal distribution of discrete heat sources on a wall with natural convection, Int. J. Heat Mass Transfer, 47 (2004), pp. 203-214.
  23. da Silva, A.K., Lorente, S., Bejan, A., Optimal distribution of discrete heat sources on a plate with laminar forced convection, Int. J. Heat Mass Transfer, 47, (2004), pp. 2139-2148.

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence