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

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Abstract

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.

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Abbreviations

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

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)

Pr :

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

\( \alpha \) :

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)

\( \rho \) :

Density

\( \lambda \) :

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

f :

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

\( {\text{sub}} \) :

Subcooled

\( \sup \) :

Superheat

\( w \) :

Related to the jet width

\( \infty \) :

Free stream-related value

′:

First derivative

″:

Second derivative

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  1. Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

    M. R. Mohaghegh & Asghar B. Rahimi

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  1. M. R. Mohaghegh
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Correspondence to Asghar B. Rahimi.

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Mohaghegh, M.R., Rahimi, A.B. Single- and two-phase water jet impingement heat transfer on a hot moving surface. J Therm Anal Calorim 137, 1401–1411 (2019). https://doi.org/10.1007/s10973-019-08072-4

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