Heat and Mass Transfer

, Volume 53, Issue 9, pp 2853–2866 | Cite as

Experimental estimation of convective heat transfer coefficient from pulsating semi-confined impingement air slot jet by using inverse method

  • Somayeh Davoodabadi FarahaniEmail author
  • Farshad Kowsary


An experimental study on pulsating impingement semi-confined slot jet has been performed. The effect of pulsations frequency was examined for various Reynolds numbers and Nozzle to plate distances. Convective heat transfer coefficient is estimated using the measured temperatures in the target plate and conjugate gradient method with adjoint equation. Heat transfer coefficient in Re < 3000 tended to increase with increasing frequency. The pulsations enhance mixing, which results in an enhancement of mean flow velocity. In case of turbulent jet (Re > 3000), heat transfer coefficient is affected by the pulsation from particular frequency. In this study, the threshold Strouhal number (St) is 0.11. No significant heat transfer enhancement was obtained for St < 0.11. The thermal resistance is smaller each time due to the newly forming thermal boundary layers. Heat transfer coefficient increases due to decrease thermal resistance. This study shows that maximum enhancement in heat transfer due to pulsations occurs in St = 0.169. Results show the configuration geometry has an important effect on the heat transfer performances in pulsed impinging jet. Heat transfer enhancement can be described to reflect flow by the confinement plate.


Heat Transfer Heat Transfer Coefficient Nusselt Number Stagnation Point Conjugate Gradient Method 
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.

List of symbols


Vector of unity matrices


Mass diffusivity (m2/s)


Plate thickness (m)


Frequency (Hz)


Heat transfer coefficient (W/m2 K)


Nozzle-target plate distance (m)


Thermal conductivity (W/m K)


Plate length (m)


Time index


Number of discrete measurements


Nusselt number


Nusselt number at stagnation point


Number of unknown parameters


Number of sensors


Prandtl number (Pr = υ/α)


Heat flux (W/m2)


Sum of squares (K2)


Schmidt number (Sc = υ/D)


Sherwood number (Sh = κDh/D)


Strouhal number \(\left( {St = \frac{{fD_{h} }}{v}} \right)\)


Vector of calculated temperatures (K)


x-Velocity (m/s)


y-Velocity (m/s)


Slot width (m)

x, y

Space coordinates (m)


Measured temperatures (K)

Greek symbols


Kinematic viscosity (m2/s)


Thermal diffusivity (m2/s)


Stefan–Boltzmann coefficient, 5.67 × 10−8 (W/m2/K4)


Search step size


Surface emissivity coefficient


Conjugate coefficient


Convective mass transfer film coefficient (m/s)



Initial state


Position index






Average data


  1. 1.
    Martin H (1977) Heat and mass transfer between impinging gas jets and solid surfaces. Adv Heat Transf 13:1–60. doi: 10.1016/S0065-2717(08)70221-1 CrossRefGoogle Scholar
  2. 2.
    Maurel S, Solliec C (2001) A turbulent plane jet impinging nearby and far from a flat plate. Exp Fluids 31:687–696. doi: 10.1007/s003480100327 CrossRefGoogle Scholar
  3. 3.
    Kayansayan N, Kucuka S (2001) Impingement cooling of a semi-cylindrical concave channel by confined slot-air-jet. Exp Therm Fluid Sci 25:383–396. doi: 10.1016/S0894-1777(01)00094-2 CrossRefGoogle Scholar
  4. 4.
    Zuckerman N, Lior N (2006) Impingement heat transfer: correlations and numerical modeling. Adv Heat Transf 39:565–631. doi: 10.1016/S0065-2717(06)39006-5 CrossRefGoogle Scholar
  5. 5.
    Choo KS, Kim SJ (2010) Comparison of thermal characteristics of confined and unconfined impinging jets. Int J Heat Mass Transf 53:3366–3371. doi: 10.1016/j.ijheatmasstransfer.2010.02.023 CrossRefGoogle Scholar
  6. 6.
    Sparrow EM, Wong TC (1975) Impingement transfer coefficients due to initially laminar slot jets. Int J Heat Mass Transf 18:597–605. doi: 10.1016/0017-9310(75)90271-9 CrossRefGoogle Scholar
  7. 7.
    Koseoglu MF, Baskaya S (2010) The role of jet inlet geometry in impinging jet heat transfer: modeling and experiments. Int J Therm Sci 49:1417–1426. doi: 10.1016/j.ijthermalsci.2010.02.009 CrossRefGoogle Scholar
  8. 8.
    Na-pompet K, Boonsupthip W (2011) Effect of a narrow channel on heat transfer enhancement of a slot-jet impingement system. J Food Eng 103:366–376. doi: 10.1016/j.jfoodeng.2010.11.006 CrossRefGoogle Scholar
  9. 9.
    San JY, Chen JJ (2014) Effects of jet-to-jet spacing and jet height on heat transfer characteristics of an impinging jet array. Int J Heat Mass Transf 71:8–17. doi: 10.1016/j.ijheatmasstransfer.2013.11.079 CrossRefGoogle Scholar
  10. 10.
    Zumbrunnen DA, Aziz M (1993) Convective heat transfer enhancement due to intermittency in an impinging jet. J Heat Transf 115(91):91–98. doi: 10.1115/1.2910675 CrossRefGoogle Scholar
  11. 11.
    Sheriff HS, Zumbrunnen DA (1994) Effect of flow pulsations on the cooling effectiveness of an impinging jet. J Heat Transf 116:886–895. doi: 10.1115/1.2911463 CrossRefGoogle Scholar
  12. 12.
    Mladin EC, Zumbrunnen DA (1995) Dependence of heat transfer to a pulsating stagnation flow on pulse characteristics. J Thermo Phys Heat Transf 9(1):181–192. doi: 10.2514/3.645 CrossRefGoogle Scholar
  13. 13.
    Mladin EC, Zumbrunnen DA (1994) Nonlinear dynamics of laminar boundary layers in pulsatile stagnation flows. J Thermo Phys Heat Transf 8(3):514–523. doi: 10.2514/3.573 CrossRefGoogle Scholar
  14. 14.
    Mladin EC, Zumbrunnen DA (1996) Local convective heat transfer to submerged pulsating jets. Int J Heat Mass Transf 40(14):3305–3321. doi: 10.1016/S0017-9310(96)00380-8 CrossRefGoogle Scholar
  15. 15.
    Mladin EC, Zumbrunnen DA (2000) Alterations to coherent flow structures and heat transfer due to pulsations in an impinging air-jet. Int J Therm Sci 39:236–248. doi: 10.1016/S1290-0729(00)00242-8 CrossRefGoogle Scholar
  16. 16.
    Sailor DJ, Rohli DJ, Fu Q (1999) Effect of variable duty cycle flow pulsations on heat transfer enhancement for an impinging air jet. Int J Heat Fluid Flow 20(6):574–580. doi: 10.1016/S0142-727X(99)00055-7 CrossRefGoogle Scholar
  17. 17.
    Fallen M (1982) Wärmeübergang im Rohr mit überlagerter Strömungspulsation. Wärme Stoffübertrag 16:89–99. doi: 10.1007/BF01459765 CrossRefGoogle Scholar
  18. 18.
    Hofmann HM, Movileanu DL, Kind M, Martin H (2007) Influence of a pulsation on heat transfer and flow structure in submerged impinging jets. Int J Heat Mass Transf 50:3638–3648. doi: 10.1016/j.ijheatmasstransfer.2007.02.001 CrossRefGoogle Scholar
  19. 19.
    Woodbury KA, Beck JV (2013) Estimation metrics and optimal regularization in a Tikhonov digital filter for the inverse heat conduction problem. Int J Heat Mass Transf 62:31–39. doi: 10.1016/j.ijheatmasstransfer.2013.02.052 CrossRefGoogle Scholar
  20. 20.
    Ozisik MN, Orlande HRB (2000) Inverse heat transfer fundamentals and applications. Taylor and Francis, LondonGoogle Scholar
  21. 21.
    Kowsary F, Farahani SD (2010) the smoothing of temperature data using the mollification method in heat flux estimating. Numer Heat Transf Part A 58:227–246. doi: 10.1080/10407782.2010.490447 CrossRefzbMATHGoogle Scholar
  22. 22.
    Farahani SD, Kowsary F (2012) Estimation local convective boiling heat transfer coefficient in mini channel. Int Commun Heat Mass Transf 39(2):304–310. doi: 10.1016/j.icheatmasstransfer.2011.11.007 CrossRefGoogle Scholar
  23. 23.
    Kline SJ, McClintock FA (1953) Describing experimental uncertainties in single sample experiment. Mech Eng 75(1):3–8. doi: Scholar
  24. 24.
    Scholtz MT, Trass O (1970) Mass transfer in a non-uniform impinging jet. AIChE J 16:82–90. doi: 10.1002/aic.690160117 CrossRefGoogle Scholar
  25. 25.
    Farahani SD, Kowsary F (2014) Inverse experiment design for estimation of convective heat transfer coefficient impinging slot jet. Sharif Univ Technol J 30(3):31–38Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Somayeh Davoodabadi Farahani
    • 1
    Email author
  • Farshad Kowsary
    • 2
  1. 1.Mechanical Engineering DepartmentArak University of TechnologyArākIran
  2. 2.School of Mechanical EngineeringUniversity of TehranTehranIran

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