Single- and two-phase water jet impingement heat transfer on a hot moving surface

  • M. R. Mohaghegh
  • Asghar B. RahimiEmail author


In this study, the laminar flow and heat transfer of water jet impingement on a hot moving plate is investigated. A similarity solution is applied to momentum and energy equations formulating the single-phase forced convection in order to determine the flow velocity and heat transfer. The heat flux in flow boiling regime is predicted by a superposition approach which is based on the combination of the single-phase and nucleate pool boiling components. The effects of surface motion and arbitrary surface temperature distribution on important forced convection and nucleate boiling heat transfer parameters for both stationary and moving plates are examined in the stagnation line and its nearby region. The results show that surface motion does not affect the rate of heat transfer in stagnation region when surface temperature is constant, while this motion is found to decrease heat transfer for a non-uniform surface temperature distribution state. However, it is observed that in fully developed nucleate boiling regime, the parameters including the surface velocity, the surface temperature gradient and the local distance from the stagnation line have negligible effect on the rate of heat transfer from the surface.


Jet impingement Stagnation region Moving surface Surface temperature gradient Similarity solution Nucleate boiling 

List of symbols

\( c_{\text{p}} \)

Specific heat (J kg−1 k−1)

\( C \)

Free-stream velocity gradient in stagnation region

\( \overline{C} \)

Dimensionless velocity gradient

\( f \)

Dimensionless function related to flow velocity

\( g \)

Gravity acceleration (m s−2)

\( h \)

Heat transfer coefficient (W m−2 K−1)

\( h_{\text{fg}} \)

Latent heat of vaporization (J kg−1)

\( I \)

Dimensionless function related to flow velocity due to plate motion

\( k \)

Thermal conductivity (W m−1 K−1)

\( Nu_{\text{w}} \)

Local Nusselt number \( = {{hw_{\text{j}} } \mathord{\left/ {\vphantom {{hw_{\text{j}} } k}} \right. \kern-0pt} k} \)

\( Nu^{ * } \)

Ratio of local Nusselt number for moving plate to local Nusselt number for stationary plate

\( p \)

Pressure (N m−2)


Prandtl number

\( q^{\prime\prime} \)

Heat flux (W m−2)

\( Re_{\text{w}} \)

Jet Reynolds number \( = {{V_{\text{j}} w_{\text{j}} } \mathord{\left/ {\vphantom {{V_{\text{j}} w_{\text{j}} } \nu }} \right. \kern-0pt} \nu } \)

\( S \)

Suppression factor defined in Eq. (23)

\( T \)

Temperature (°C or K)

\( T_{{{\text{s}}_{0} }} \)

Temperature of impingement surface at stagnation line

\( \Delta T \)

Temperature difference (°C or K)

\( u \)

Velocity component in x direction (m s−1)

\( U_{\infty } \)

Free-stream velocity (m s−1)

\( \overline{U}_{\infty } \)

Dimensionless free-stream velocity \( {{ = U_{\infty } } \mathord{\left/ {\vphantom {{ = U_{\infty } } {V_{\text{j}} }}} \right. \kern-0pt} {V_{\text{j}} }} \)

\( v \)

Velocity component in y direction (m s−1)

\( V_{\text{j}} \)

Jet velocity (m s−1)

\( V_{\text{p}} \)

Surface velocity (m s−1)

\( \overline{V}_{\text{p}} \)

Dimensionless surface velocity \( {{ = V_{\text{p}} } \mathord{\left/ {\vphantom {{ = V_{\text{p}} } {V_{\text{j}} }}} \right. \kern-0pt} {V_{\text{j}} }} \)

\( w_{\text{j}} \)

Jet width (m)

\( x \)

Horizontal distance from stagnation line

\( \overline{X} \)

Dimensionless horizontal distance \( {{ = x} \mathord{\left/ {\vphantom {{ = x} {w_{\text{j}} }}} \right. \kern-0pt} {w_{\text{j}} }} \)

\( y \)

Vertical distance above impingement surface

Greek symbols

\( \alpha \)

Molecular thermal diffusivity (m2 s−1)

\( \beta \)

Surface temperature gradient

\( \nu \)

Molecular kinematic diffusivity (m2 s−1)

\( \mu \)

Molecular dynamic diffusivity (kg m−1 s−1)

\( \rho \)


\( \lambda \)

Parameter defined in Eq. (22)

\( \sigma \)

Surface tension (N m−1)

\( \eta \)

Dimensionless distance from surface

\( \theta \)

Dimensionless temperature

\( \theta_{\text{s}} \)

Dimensionless surface temperature



Film temperature

\( {\text{FDB}} \)

Fully developed boiling

\( j \)

Jet related value

\( {\text{nb}} \)

Nucleate boiling

\( {\text{onb}} \)

Onset of nucleate boiling

\( s \)

Surface (wall, plate)

\( {\text{sp}} \)

Single phase

\( {\text{sub}} \)


\( \sup \)


\( w \)

Related to the jet width

\( \infty \)

Free stream-related value


First derivative

Second derivative



  1. 1.
    Inada S, Miyasaka Y, Izumi R. A study on the laminar-flow heat transfer between a two-dimensional water jet and a flat surface with constant heat flux. Bull JSME. 1981;24(196):1803–10. Scholar
  2. 2.
    Wang B, Guo X, Xie Q, Wang Z, Wang G. Heat transfer characteristic research during jet impinging on top/bottom hot steel plate. Int J Heat Mass Transf. 2016;101:844–51.CrossRefGoogle Scholar
  3. 3.
    Dagtekin I, Oztop HF. Heat transfer due to double laminar slot jets impingement onto an isothermal wall within one side closed long duct. Int Commun Heat Mass Transf. 2008;35(1):65–75.CrossRefGoogle Scholar
  4. 4.
    Ellahi R, Alamri SZ, Basit A, Majeed A. Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation. J Taibah Univ Sci. 2018;12(4):476–82. Scholar
  5. 5.
    Majeed A, Zeeshan A, Alamri SZ, Ellahi R. Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction. Neural Comput Appl. 2018;30(6):1947–55. Scholar
  6. 6.
    Mahian O, Pop I, Sahin AZ, Oztop HF, Wongwises S. Irreversibility analysis of a vertical annulus using TiO2/water nanofluid with MHD flow effects. Int J Heat Mass Transf. 2013;64:671–9. Scholar
  7. 7.
    Mahian O, Oztop H, Pop I, Mahmud S, Wongwises S. Entropy generation between two vertical cylinders in the presence of MHD flow subjected to constant wall temperature. Int Commun Heat Mass Transf. 2013;44:87–92. Scholar
  8. 8.
    Selimefendigil F, Öztop HF. Analysis of MHD mixed convection in a flexible walled and nanofluids filled lid-driven cavity with volumetric heat generation. Int J Mech Sci. 2016;118:113–24. Scholar
  9. 9.
    Hassan M, Marin M, Alsharif A, Ellahi R. Convective heat transfer flow of nanofluid in a porous medium over wavy surface. Phys Lett A. 2018;382(38):2749–53. Scholar
  10. 10.
    Miyasaka Y, Inada S. The effect of pure forced convection on the boiling heat transfer between a two-dimensional subcooled water jet and a heated surface. J Chem Eng Jpn. 1980;13(1):22–8. Scholar
  11. 11.
    Robidou H, Auracher H, Gardin P, Lebouché M. Controlled cooling of a hot plate with a water jet. Exp Thermal Fluid Sci. 2002;26(2):123–9.CrossRefGoogle Scholar
  12. 12.
    Karwa N, Gambaryan-Roisman T, Stephan P, Tropea C. Experimental investigation of circular free-surface jet impingement quenching: transient hydrodynamics and heat transfer. Exp Thermal Fluid Sci. 2011;35(7):1435–43.CrossRefGoogle Scholar
  13. 13.
    Modak M, Nirgude V, Sharma AK, Sahu SK. Experimental study on heat transfer characteristics of circular jet impingement boiling on the variety of structured copper surfaces in stagnation zone. 2016(50053):V005T15A48.
  14. 14.
    Nobari AH, Prodanovic V, Militzer M. Heat transfer of a stationary steel plate during water jet impingement cooling. Int J Heat Mass Transf. 2016;101:1138–50.CrossRefGoogle Scholar
  15. 15.
    de Brún C, Jenkins R, Lupton TL, Lupoi R, Kempers R, Robinson AJ. Confined jet array impingement boiling. Exp Therm Fluid Sci. 2017;86(Supplement C):224–34. Scholar
  16. 16.
    Agrawal C, Kumar R, Gupta A, Chatterjee B. Determination of rewetting velocity during jet impingement cooling of hot vertical rod. J Therm Anal Calorim. 2016;123(1):861–71. Scholar
  17. 17.
    Wolf D, Incropera F, Viskanta R. Jet impingement boiling. Adv Heat Transf. 1993;23:1–132.CrossRefGoogle Scholar
  18. 18.
    Zumbrunnen DA. Convective heat and mass transfer in the stagnation region of a laminar planar jet impinging on a moving surface. J Heat Transf. 1991;113(3):563–70. Scholar
  19. 19.
    Chen J, Wang T, Zumbrunnen DA. Numerical analysis of convective heat transfer from a moving plate cooled by an array of submerged planar jets. Numer Heat Transf Part A Appl. 1994;26(2):141–60. Scholar
  20. 20.
    Chattopadhyay H, Biswas G, Mitra NK. Heat transfer from a moving surface due to impinging slot jets. J Heat Transf. 2002;124(3):433–40. Scholar
  21. 21.
    Chattopadhyay H, Saha SK. Simulation of laminar slot jets impinging on a moving surface. J Heat Transf. 2002;124(6):1049–55. Scholar
  22. 22.
    Ja’fari M, Rahimi AB. Axisymmetric stagnation-point flow and heat transfer of a viscous fluid on a moving plate with time-dependent axial velocity and uniform transpiration. Sci Iran. 2013;20(1):152–61. Scholar
  23. 23.
    Zumbrunnen DA, Incropera FP, Viskanta R. Method and apparatus for measuring heat transfer distributions on moving and stationary plates cooled by a planar liquid jet. Exp Thermal Fluid Sci. 1990;3(2):202–13. Scholar
  24. 24.
    Gradeck M, Kouachi A, Lebouché M, Volle F, Maillet D, Borean JL. Boiling curves in relation to quenching of a high temperature moving surface with liquid jet impingement. Int J Heat Mass Transf. 2009;52(5):1094–104. Scholar
  25. 25.
    Mohaghegh MR, Rahimi AB. Modeling of nucleate boiling heat transfer of a stagnation-point flow impinging on a hot surface. Therm Sci. 2019. Google Scholar
  26. 26.
    Hall DE, Incropera FP, Viskanta R. Jet impingement boiling from a circular free-surface jet during quenching: part 2—two-phase jet. J Heat Transf. 2001;123(5):911–7.CrossRefGoogle Scholar
  27. 27.
    Robidou H, Auracher H, Gardin P, Lebouche M, Bogdanić L. Local heat transfer from a hot plate to a water jet. Heat Mass Transf. 2003;39(10):861–7.CrossRefGoogle Scholar
  28. 28.
    Robidou H, Auracher H, Gardin P, Lebouché M, Bogdanić L. Local heat transfer from a hot plate to a water jet. Heat Mass Transf. 2003;39(10):861–7. Scholar
  29. 29.
    Vader D, Incropera F, Viskanta R. Convective nucleate boiling on a heated surface cooled by an impinging, planar jet of water. J Heat Transf. 1992;114(1):152–60.CrossRefGoogle Scholar
  30. 30.
    Wolf D, Incropera F, Viskanta R. Local jet impingement boiling heat transfer. Int J Heat Mass Transf. 1996;39(7):1395–406.CrossRefGoogle Scholar
  31. 31.
    Omar A, Hamed M, Shoukri M. Modeling of nucleate boiling heat transfer under an impinging free jet. Int J Heat Mass Transf. 2009;52(23):5557–66.CrossRefGoogle Scholar
  32. 32.
    Timm W, Weinzierl K, Leipertz A. Heat transfer in subcooled jet impingement boiling at high wall temperatures. Int J Heat Mass Transf. 2003;46(8):1385–93.CrossRefGoogle Scholar
  33. 33.
    Lienhard V JH. Liquid jet impingement. Ann Rev Heat Transf. 1995;6:199–270.Google Scholar
  34. 34.
    Vader DT, Incropera FP, Viskanta R. Local convective heat transfer from a heated surface to an impinging, planar jet of water. Int J Heat Mass Transf. 1991;34(3):611–23. Scholar
  35. 35.
    Rohsenow W. Heat transfer with evaporation, heat transfer—a symposium held at the University of Michigan during the summer of 1952. Ann Arbor: Univ. of Michigan Press; 1952.Google Scholar
  36. 36.
    Bergles A, Rohsenow W. The determination of forced-convection surface-boiling heat transfer. J Heat Transf. 1964;86(3):365–72.CrossRefGoogle Scholar
  37. 37.
    Gorenflo D, Kenning D. H2 pool boiling. Vdi heat atlas. NewYork: Springer; 2009. p. 757–92.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringFerdowsi University of MashhadMashhadIran

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