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Local heat flow and temperature fluctuations in wall and fluid in nucleate boiling systems

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Abstract

Recent numerical and experimental investigations to improve the understanding of the nucleate boiling heat transfer process mainly concentrate on the description or measurement of local transport phenomena. It is known from these investigations that the interaction between microscale evaporation and macroscale transient heat flow in the wall and the thermal boundary layer is a key aspect for our physical understanding of boiling processes. However reliable quantitative data on the local and transient heat distribution and storage in the heater wall and thermal boundary layer is rare. In this paper we summarize recent developments and present new numerical and experimental results in this specific field of research. A fully transient numerical model has been developed based on a previous quasi stationary model of Kern and Stephan (ASME J Heat Transf 125,1106–1115). It allows describing the transient heat and fluid flow during the entire periodic cycle of a growing, detaching and rising bubble including the waiting time between two successive bubbles from a single nucleation site. It contains a multiscale approach ranging from the nanometer to the millimeter scale for the detailed description of the relevant local phenomena. The detailed analysis of the computed transient temperature profiles in wall and fluid gives accurate information about the heat supply, temporal energy storage and evaporation. It is shown that during the bubble growth and detachment period more heat is consumed by evaporation than heat supplied to the overall system. Thus the wall and liquid thermal boundary layer cool down. After detachment, during the bubble rise period and waiting time, the evaporative heat flow decreases. In this period more heat is supplied to the overall system than consumed by evaporation, thus the wall and liquid thermal boundary layer heat up again. Experimental investigations with high resolution wall temperature measurements underneath a vapor bubble were performed in a micro-g environment and qualitatively confirm these numerical observations.

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Abbreviations

c :

specific heat capacity (J/(kg K))

g :

acceleration of gravity (m/s2)

\(\dot{m}\) :

mass flux (kg/s)

N b :

bubble site density (1/m2)

p :

pressure (N/m2)

p * :

reduced pressure (p/p c ) (–)

p c :

critical pressure (N/m2)

\(\dot{Q}\) :

heat flow (W)

\(\dot{q}\) :

heat flux (W/m2)

\(\dot{q}_{m}\) :

time- and area-averaged heat flux (W/m2)

R 1 :

radius of curvature (m)

R 2 :

radius of curvature (m)

r :

radius (m)

T :

temperature (K)

ΔT iso :

temperature difference between isotherms (K)

λ:

thermal conductivity (W/(mK))

ν:

kinematic viscosity (m2/s)

ξ:

radial co-ordinate parallel to the wall (m)

ρ:

density (kg/m3)

Θ:

angle (°)

t :

time (s)

t b :

time period of one bubble cycle (s)

u :

velocity (m/s)

x L,1 :

liquid mole fraction of the more volatile component (–)

α m :

time- and area-averaged heat transfer coefficient (W/(m2 K))

β:

coefficient of thermal expansion (1/K)

δ:

liquid film thickness (m)

δ l :

thickness of liquid boundary layer (m)

δ w :

wall thickness (m)

η:

co-ordinate normal to the wall (m)

φapp :

apparent contact angle (°)

ads :

adsorbed film

evap :

evaporation

η:

vertical direction

l :

liquid

m :

mean

mesh :

mesh

mic :

micro region

out :

outer surface of the wall

ref :

reference property in bulk

sat :

saturation

sub :

subsystem

w :

wall

ξ:

radial direction

1−7:

interface numbers radial direction interfaces

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Acknowledgments

The authors are indebted to Deutsche Forschungsgemeinschaft, Bonn, for their financial support in the frame of the gradute school GRK 91–4 and the project STE 994/4. We also thank the European Space Agency ESA for supporting the micro-g investigations during the 41st ESA Parabolic Flight Campaign.

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Authors and Affiliations

  1. Chair of Technical Thermodynamics, University of Technology Darmstadt, 64287, Darmstadt, Germany

    P. Stephan & T. Fuchs

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  1. P. Stephan
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  2. T. Fuchs
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Correspondence to P. Stephan.

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Stephan, P., Fuchs, T. Local heat flow and temperature fluctuations in wall and fluid in nucleate boiling systems. Heat Mass Transfer 45, 919–928 (2009). https://doi.org/10.1007/s00231-007-0320-1

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