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A review on correlations of bubble growth mechanisms and bubble dynamics parameters in nucleate boiling

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Abstract

The benefits of nucleate pool boiling phenomena and their potential applications on thermal management of various microelectronic devices have triggered the development of new approaches that augment the magnitude of heat transfer rate. To implement these approaches, an accurate estimation of the boiling heat transfer coefficient between the fluid and the heated surface is often required. The acquisition of the boiling heat transfer coefficient must follow a better understanding of the bubble ebullition cycle because of its inherent coupling with heat transfer mechanisms involved in this cycle. Bubble ebullition occurs by periodic bubble nucleation on a boiling surface, bubble growth, and subsequent bubble departure from the surface. Different parameters related to the dynamics of the bubble ebullition cycle, including bubble departure diameter, bubble waiting period, active nucleation site density, bubble growth period, bubble departure frequency, and bubble growth rate govern the heat transfer rate in the nucleate pool boiling. Thus, numerous empirical correlations that determine the boiling heat transfer coefficient have been proposed by many researchers according to different bubble dynamics parameters. To accurately predict the boiling heat transfer coefficient and boiling heat flux based on the bubble ebullition cycle, understanding bubble growth mechanisms and associated dominant parameters is crucial. In this review, different bubble growth mechanisms during nucleate pool boiling are thoroughly reviewed. Then, bubble dynamics parameters used in different correlations for determining the boiling heat transfer coefficient are discussed. Semi-empirical and empirical correlations for determining these parameters are also extensively provided. Additionally, a detailed review of factors affecting bubble dynamics parameters is provided. Next, different applications of nucleate boiling in cooling systems are reviewed. Overall, this review includes various correlations from experimental and numerical data, which can be used to better predict the heat transfer during nucleate boiling.

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Abbreviations

A :

Area of heated surface (m2)

C p :

Specific heat (kJ kg−1 °C−1)

C D :

Drag coefficient

D d :

Bubble departure diameter (m)

D :

Bubble diameter (m)

D c :

Cavity diameter (μm)

dD/dt :

Bubble growth rate

f :

Bubble departure frequency (1 s− 1)

g :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient (W m−2K−1)

h lv :

Latent heat of vaporization (J kg− 1)

Ja :

Jakob number (\(\rho_{\text{l}} C_{\text{pl}} (T_{\text{w}} - T_{\text{sat}} )/\rho_{\text{v}} h_{\text{lv}}\))

k :

Thermal conductivity (W/m− 1K− 1)

Nu :

Nusselt number (hD k− 1)

N :

Number of nucleation sites

n s :

Active nucleation site density (sites m− 2)

\(\overline{n}_{a}\) :

Average cavity density (sites m−2)

P :

Pressure (MPa)

Pr :

Prandtl number (\(\mu_{l} C_{pl} /k_{l}\))

R a :

Surface roughness (μm)

R c :

Cavity radius (μm)

\(R_{c}^{ + }\) :

Non-dimensional critical cavity radius

r :

Bubble radius (m)

r b :

Radius of the liquid microlayer under bubble (m)

\(r^{ + }\) :

Non-dimensional bubble radius

T :

Temperature (K)

t :

Time (s)

t w :

Bubble waiting period (s)

t g :

Bubble growth period (s)

\(t^{ + }\) :

Non-dimensional time

V :

Volume (m3)

V d :

Bubble departure volume

\(\theta\) :

Contact angle (°)

\(\rho\) :

Density (kg m−3)

\(\Delta\) :

Difference

\(\phi\) :

Dimensionless surface roughness parameter

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\beta\) :

Half cone angle (°)

\(\overline{\beta }\) :

Mean half cone angle (°)

\(\nu\) :

Kinematic viscosity (m2 s− 1)

\(\sigma\) :

Surface tension (N m− 1)

\(\delta\) :

Thermal boundary layer thickness (m)

\(\alpha\) :

Thermal diffusivity (\(k_{\text l} /\rho {}_{\text l}C_{\text {pl}}\))(m2 s− 1)

\(\varepsilon\) :

Volumetric expansion coefficient (K− 1)

 + :

Non-dimensional

C :

Cavity

L :

Liquid phase

Max :

Maximum

Min :

Minimum

Nc :

Natural convection

B :

Boiling

Sat :

Saturation condition

Tc :

Transient conduction

S :

Heating surface

\(\nu\) :

Vapor phase

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Acknowledgements

This work has been partially supported by the National Science Foundation (Grant #: 1917272).

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  1. Ocean and Mechanical Engineering, Florida Atlantic University, 777 Glades Rd, Boca Raton, FL, 33431, USA

    Mahyar Ghazivini, Mazen Hafez, Abhishek Ratanpara & Myeongsub Kim

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Ghazivini, M., Hafez, M., Ratanpara, A. et al. A review on correlations of bubble growth mechanisms and bubble dynamics parameters in nucleate boiling. J Therm Anal Calorim 147, 6035–6071 (2022). https://doi.org/10.1007/s10973-021-10876-2

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