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Thermal exchange diffusivity in nucleate boiling

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Summary

The phase conversion occurring in nucleate boiling is investigated by referring to the vapor-liquid exchange concept and making use of the boiling enthalpy ratio (liquid excess enthalpy ρL C L ΔT/vapor excess enthalpy ρυ λ). The ratio serves as a criterion to distinguish two fundamentally different kinds of boiling equations: first, thermodynamically oriented correlations which do not account for the exchange effect; and secondly, rate process equations describing the exchange as a function of governing system parameters. Taking advantage of the first possibility allows the correlation of the metastable liquid superheat as a function of reduced thermodynamic coordinates.

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Abbreviations

a :

thermal diffusivity

a*:

boiling exchange diffusivity

C L :

liquid heat capacity

c :

constant

E kin :

kinetic energy of liquid

f :

dimensionless temperature difference (T−T s )/(T w −T s )

F :

function of T r , equation (17)

g :

acceleration due to gravity

h :

thickness of supersaturated liquid layer

H :

thickness of thermal boundary layer

J :

integral, equation (5)

k :

liquid thermal conductivity

L :

reference length

M :

boiling exchange number ρL C L ΔT/λ ρυ

\(\left. \begin{gathered} m \hfill \\ n \hfill \\ \end{gathered} \right\}\) :

exponents

Nu L :

Nusselt number qL/ΔTk (containing reference length L)

p :

pressure

\(\bar \Delta\) p :

effective pressure difference

Pr :

Prandtl number

q :

heat flux

r :

radius

R :

bubble radius (R* maximum value, R 0 nucleus radius)

t :

time (t* value at R*)

T :

temperature (T s saturation value, T L bulk liquid temperature, T w wall temperature, T c critical temperature)

T r :

ratio T/T c

ΔT :

\(\bar T\) w −T s

(ΔT)max :

maximum metastable liquid excess temperature

v :

velocity

y :

wall distance

β*:

growth parameter

ε :

degree of metastability, equation (15)

ε vdW :

nominal metastability value evaluated from van der Waals' equation

ζ :

density ratio (ρ L −ρ v )/ρ L

η :

ratio y/H

Θ L :

parameter (T w −T L )/(T w −T s )

λ :

heat of vaporization

ρ L :

saturated liquid density

ρ v :

density of saturated vapor

σ :

surface tension

τ b :

bubble period

p :

peak value

r :

reduced quantity (e.g. T r =T/T c )

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  1. Department of Engineering, University of California, Los Angeles, USA

    T. H. K. Frederking

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Frederking, T.H.K. Thermal exchange diffusivity in nucleate boiling. Appl. sci. Res. 13, 371–388 (1964). https://doi.org/10.1007/BF00382063

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