Heat and Mass Transfer

, Volume 40, Issue 5, pp 377–382 | Cite as

The critical radius of insulation in thermal radiation environment

  • Ahmet Z. Sahin
  • Muammer Kalyon


Critical radius of insulation for a circular tube subjected to radiative and convective heat transfer has been studied analytically. It is assumed that condensation or evaporation takes place inside the circular tube such that the bulk fluid temperature inside the tube remains constant. As the fluid is transported from one end to the other, either an increase or decrease of heat transfer is desired depending on the application. The variation of the rate of heat transfer with respect to the variation of insulation thickness is studied. It is found that an critical insulation thickness may exist such that the heat transfer between the fluid and the radiative environment becomes a maximum. For certain special cases, explicit solutions to the critical insulation thickness are obtained.


Heat Transfer Heat Transfer Coefficient Radiation Heat Transfer Heat Transfer Enhancement Radiation Parameter 
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The authors acknowledge the support of the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for this work.


  1. 1.
    Bejan A (1993) How to distribute a finite amount of insulation on a wall with nonuniform temperature. Int J Heat Mass Transfer 36(1): 49–56Google Scholar
  2. 2.
    Bejan A (1993) Heat transfer, Wiley, New YorkGoogle Scholar
  3. 3.
    Bejan A (2000) Shape and structure, from Engineering to Nature. Cambridge University Press, Cambridge, UKGoogle Scholar
  4. 4.
    Bejan A; Tsatsaronis G; Moran M (1996) Thermal design and optimization. John Wiley and Sons, New YorkGoogle Scholar
  5. 5.
    Ito K; Akagi S; Nishikawa M (1982) A multi-objective optimization approach to design problem of heat insulation for thermal distribution piping network systems. ASME Paper 82-DET-57Google Scholar
  6. 6.
    Boehm RF (1987) Design analysis of thermal systems. John Wiley and Sons, New YorkGoogle Scholar
  7. 7.
    Westerberg A (1981) Optimization in computer aided design. In: Mah R, Seider W (eds) Foundations of computer-aided chemical process design, vol. 1. Engineering Foundation, New York, pp 149–183Google Scholar
  8. 8.
    Arpaci VS; Kao SH; Selamet A (1999) Introduction to heat transfer. Prentice Hall, New JerseyGoogle Scholar
  9. 9.
    Aziz A (1997) The critical thickness of insulation. Heat Transfer Eng 18(2): 61–91Google Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

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