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Forced-convection heat transfer over a circular cylinder with Newtonian heating

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Abstract

A mathematical model for the forced convection boundary-layer flow over a circular cylinder is considered when there is Newtonian heating on the surface of the cylinder through which the heat transfer is proportional to the local surface temperature. The dimensionless version of the boundary-layer equations involve two parameters, the Prandtl number σ and γ measuring the strength of the surface heating. The solution near the stagnation point is considered first and this reveals that, to get a physically acceptable solution, γ must be less than some critical value γ c , dependent on σ. Numerical solutions to the full boundary-layer problem are obtained which show that the surface temperature increases as the flow develops from the stagnation point.

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References

  1. Schlichting H, Gersten K (2000) Boundary layer theory, 8th edn. Springer, Berlin

    MATH  Google Scholar 

  2. Rosenhead, L (eds) (1963) Laminar boundary layers. Clarendon Press, Oxford

    MATH  Google Scholar 

  3. Blasius H (1908) Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z Math Phys 56: 1–37

    Google Scholar 

  4. Hiemenz K (1911) Die Grenzschicht an einem in den gleichfömigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers J 326: 321–324

    Google Scholar 

  5. Terrill RM (1960) Laminar boundary-layer flow near separation with and without suction. Philos Trans Roy Soc Lond A 253: 55–100

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Goldstein S (1948) On laminar boundary-layer flow near a position of separation. Q J Mech Appl Math 1: 43–69

    Article  MATH  Google Scholar 

  7. Stewartson K (1958) On the Goldstein theory of laminar separation. Q J Mech Appl Math 11: 399–410

    Article  MATH  MathSciNet  Google Scholar 

  8. Frössling N (1940) Verdungstung Wärmeübergang und Geschwindigkeitsverteilung bei zweidimensionaler und rotations symmetrischer laminarer Grenzschichtströmung. Lunds Univ Arsskr NF Avd 2 36(4)

  9. Koh JCY (1964) Laminar free convection from a horizontal cylinder. In: Paper 76-HT-16 ASME-AIChE heat transfer conference, vol 7, pp 811–813

  10. Saville DA, Churchill SW (1967) Laminar free convection in boundary layers near horizontal cylinders and vertical axisymmetric bodies. J Fluid Mech 29: 391–399

    Article  MATH  ADS  Google Scholar 

  11. Elliott L (1970) Free convection on a two-dimensional or axisymmetric body. Q J Mech Appl Math 23: 153–162

    Article  MATH  Google Scholar 

  12. Wilks G (1972) External natural convection about two-dimensional bodies with constant heat flux. Int J Heat Mass Transf 15: 351–354

    Article  Google Scholar 

  13. Merkin JH, Pop I (1988) A note on the free convection boundary layer on a horizontal circular cylinder with constant heat flux. Wärme-und-Stoffübertragung 22: 79–81

    Article  ADS  Google Scholar 

  14. Merkin JH (1977) Mixed convection from a horizontal circular cylinder. Int J Heat Mass Transf 20: 73–77

    Article  Google Scholar 

  15. Pop I, Sunada JK, Cheng P, Minkowycz WJ (1985) Conjugate free convection from long vertical plate fins embedded in a porous medium. Int J Heat Mass Transf 28: 1629–1636

    Article  Google Scholar 

  16. Pozzi A, Lupo M (1988) The coupling of conduction with laminar natural convection along a flat plate. Int J Heat Mass Transf 31: 1807–1814

    Article  MATH  Google Scholar 

  17. Chaudhary RC, Jain P (2007) An exact solution to the unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating. J Eng Phys Thermophys 80: 954–960

    Article  Google Scholar 

  18. Merkin JH (1994) Natural convection boundary-layer flow on a vertical surface with Newtonian heating. Int J Heat Fluid Flow 15: 392–398

    Article  Google Scholar 

  19. Salleh MZ, Nazar R, Pop I (2009) Forced convection boundary layer flow at a forward stagnation point with Newtonian heating. Chem Eng Commun 196: 987–996

    Article  Google Scholar 

  20. Lesnic D, Ingham DB, Pop I (1999) Free convection boundary layer flow along a vertical surface in a porous medium with Newtonian heating. Int J Heat Mass Transf 42: 2621–2627

    Article  MATH  Google Scholar 

  21. Lesnic D, Ingham DB, Pop I, Storr C (2004) Free convection boundary-layer flow above a nearly horizontal surface in a porous medium with Newtonian heating. Heat Mass Transf 40: 665–672

    Article  ADS  Google Scholar 

  22. Stewartson K (1955) On asymptotic expansions in the theory of boundary layers. J Math Phys 13: 113–122

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Industrial Science & Technology, Universiti Malaysia Pahang (UMP), Lebuhraya Tun Razak, 26300, Kuantan, Pahang, Malaysia

    M. Z. Salleh

  2. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), 43600, Bangi, Selangor, Malaysia

    R. Nazar

  3. Department of Mathematics, Universiti Putra Malaysia (UPM), 43400, Serdang, Selangor, Malaysia

    N. M. Arifin

  4. Faculty of Mathematics, University of Cluj, CP 253, 3400, Cluj, Romania

    I. Pop

  5. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    J. H. Merkin

Authors
  1. M. Z. Salleh
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  2. R. Nazar
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  3. N. M. Arifin
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  4. I. Pop
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  5. J. H. Merkin
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Correspondence to J. H. Merkin.

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Salleh, M.Z., Nazar, R., Arifin, N.M. et al. Forced-convection heat transfer over a circular cylinder with Newtonian heating. J Eng Math 69, 101–110 (2011). https://doi.org/10.1007/s10665-010-9408-6

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  • DOI: https://doi.org/10.1007/s10665-010-9408-6

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