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A genetic algorithm-based optimization model for pool boiling heat transfer on horizontal rod heaters at isolated bubble regime

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Abstract

A new optimized model which can predict the heat transfer in the nucleate boiling at isolated bubble regime is proposed for pool boiling on a horizontal rod heater. This model is developed based on the results of direct observations of the physical boiling phenomena. Boiling heat flux, wall temperature, bubble departing diameter, bubble generation frequency and bubble nucleation site density have been experimentally measured. Water and ethanol have been used as two different boiling fluids. Heating surface was made by several metals and various degrees of roughness. The mentioned model considers various mechanisms such as latent heat transfer due to micro-layer evaporation, transient conduction due to thermal boundary layer reformation, natural convection, heat transfer due to the sliding bubbles and bubble super-heating. The fractional contributions of individual mentioned heat transfer mechanisms have been calculated by genetic algorithm. The results show that at wall temperature difference more that about 3 K, bubble sliding transient conduction, non-sliding transient conduction, micro-layer evaporation, natural convection, radial forced convection and bubble super-heating have higher to lower fractional contributions respectively. The performance of the new optimized model has been verified by comparison of the existing experimental data.

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Abbreviations

A :

Area (m\(^2\))

\(a_1\) :

The specific area occupied by these bubbles per unit heater surface

\(a_2\) :

The specific area occupied by the sliding bubbles per unit heater surface area

\(a_3\) :

The specific area over which transient heat conduction takes

\(C_p\) :

Heat capacity at constant pressure (J kg\(^{-1}\) K\(^{-1}\))

\(c_1\) :

Constant, see Eq. (9) (K m\(^{-2}\))

\(c_2\) :

Constant, see Eq. (9) (K m\(^{-1}\))

\(c_3\) :

Constant, see Eq. (9) (K)

d :

Bubble departing diameter (m)

E :

Relative error

f :

Bubble departing frequency (Hz)

G :

The chromosome vector

\(G_0\) :

The ratio of bubble waiting period to total period of bubble generation cycle

\(G_1\) :

The ratio of area of influence to projected area of bubble at departure

\(G_2\) :

The ratio of average bubble stem area to the maximum project area

\(G_3\) :

The ratio of actual sliding length to maximum theoretical distance between most compact arrangement of nucleation site densities

\(G_4\) :

The ratio of area of radially forced convection influence to projected area of bubble at departure

\(G_5\) :

The ratio of sliding nucleation site density to actual nucleation site density

H :

An auxiliary parameter, see Eq. (41)

\(h_{fg}\) :

Specific heat of vaporization (J kg\(^{-1}\))

I :

Electrical current (A)

k :

Thermal conductivity (W m\(^{-1}\) K\(^{-1}\))

\(l_s\) :

Sliding length (m)

L :

Heater length (m)

N :

Nucleation site

Nu :

Nusselt number

OD :

Outside diameter of the heater (m)

Pr :

Prandtl number

q :

Heat (W)

r :

Radius of rod heater (m)

R :

Radius (m)

Re :

Reynolds number

Ro :

Roughness (m)

T :

Temperature (K)

t :

Time (s)

u :

Velocity (m s\(^{-1}\))

V :

Electrical voltage (V)

x :

Characteristic length (m) or distance

\(\upalpha \) :

Heat transfer coefficient (W m\(^{-2}\) K\(^{-1}\))

\(\widehat{\upalpha }\) :

Thermal diffusivity (m\(^{2}\) s\(^{-1}\))

\(\updelta \) :

Heat penetration depth (m)

\(\upnu \) :

Viscosity (Pa s)

\(\uprho \) :

Density (kg m\(^{-3}\))

\(\uptau \) :

Bubble cycle period (s)

\(\upvarphi \) :

Phase difference between voltage and electrical current

b :

Bulk

bsh :

Bubble super-heating

g :

Growing

l :

Liquid

me :

Micro-layer evaporation

nc :

Natural convection

OD :

Outside diameter

rfc :

Radial forced convection

s :

Sliding

stc :

Sliding transient conduction

th :

Thermocouple location

tc :

Transient conduction

v :

Vapor

w :

Wall or waiting

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Acknowledgements

The author is thankful to Department of Chemical Engineering, College of Chemistry and Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran for financial support.

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Authors and Affiliations

  1. Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran

    S. Ali Alavi Fazel

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Alavi Fazel, S.A. A genetic algorithm-based optimization model for pool boiling heat transfer on horizontal rod heaters at isolated bubble regime. Heat Mass Transfer 53, 2731–2744 (2017). https://doi.org/10.1007/s00231-017-2013-8

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