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Modeling of flow boiling heat transfer coefficient of R11 in mini-channels using support vector machines and its comparative analysis with the existing correlations

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Abstract

In recent years, extensive research efforts have been devoted to flow boiling heat transfer mechanisms in macro and mini-channels. However, it is still difficult to predict the flow boiling heat transfer coefficient with satisfactory accuracy. In this study, support vector regression (SVR) models have been constructed using a respectable experimental database (767 samples) from the literature to predict the heat transfer coefficient of R11 in mini-channels for subcooled (324 samples) and saturated (443 samples) boiling regions. The prediction performance of the SVR-based models have been evaluated based on the statistical parameters. SVR-based models have been found to exhibit an average absolute relative error (AARE) of 1.7% and correlation coefficient (R) of 0.9996 for subcooled boiling, while for saturated boiling the values of AARE and R are 1.6% and 0.9993, respectively. Also, the developed SVR-based models have been compared with the well-known existing correlations. The superior prediction performance of SVR-based models has been observed with the lowest value of AARE and the highest value of correlation coefficient (R). Furthermore, parametric effects of mass flux, vapor quality, heat flux and pressure on the flow boiling heat transfer coefficient have also been investigated and the SVR-based models have been found to agree well with the experimental results.

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Abbreviations

Bo:

Boiling number

C :

Cost function

Co :

Convective number

C p :

Specific heat, J/kg.K

Dh :

Hydraulic diameter, m

f (x):

Regression function

G :

Mass flux, kg/m2.s

h :

Heat transfer coefficient, kW/m2.K

h lg :

Enthalpy of vaporization, J/kg

k:

Thermal conductivity, W/m.K

K(xi,xj):

Kernel function

L :

Dual form of the Lagrangian function

P :

Fluid pressure, kPa

Pe:

Peclet number

Pr:

Prandtl number

Q2 ext :

Leave-one-out cross validation for the test set

Q2 Loo :

Leave-one-out cross validation for the training set

R:

Correlation coefficient

Re:

Reynolds number

S:

Suppression factor

T:

temperature, K

q :

heat flux density, W/m2

xi :

Input vector

Xtt :

Lockhart-Martinelli parameter

y i :

Output vector

l:

Liquid phase

nb:

Nucleate boiling

sat:

Saturated

tp:

Two-phase

v:

Vapor phase

w:

Wall

Γ:

Surface development parameter

σ:

Width parameter of RBF kernel

ε:

Loss function

γ:

Regularization parameter

λ and λ*:

Lagrange multipliers

ϕ(x i):

High dimensional mapping feature function for input vector x

K :

Thermal conductivity, W/m.K

μ:

Kinematic viscosity, kg/m.s

ρ:

Density, kg/m3

σ:

Surface tension, N/m

AARE:

Average absolute relative error

ANN:

Artificial neural network

MRE:

Mean relative error

RBF:

Radial basis function

SVM:

Support vector machines

SVR:

Support vector regression

SRM:

Structural risk minimization

RMSE:

Root mean square error

SD:

Standard deviation

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Acknowledgments

Authors sincerely extend their thanks and gratitude to Messrs. Z.Y. Bao, D.F. Fletcher and B.S. Haynes for the availability of their published work from which the flow boiling heat transfer data has been retrieved for model formulation and validation. Authors also want to acknowledge Messrs. N.O. Olayiwola and S.M. Ghiaassiaan from whom we got the motivation for carrying out the present research.

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  1. Department of Chemical Engineering, Z.H. College of Engineering and Technology, Aligarh Muslim University, Aligarh, UP, 202002, India

    Nusrat Parveen, Sadaf Zaidi & Mohammad Danish

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  1. Nusrat Parveen
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Correspondence to Sadaf Zaidi.

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Parveen, N., Zaidi, S. & Danish, M. Modeling of flow boiling heat transfer coefficient of R11 in mini-channels using support vector machines and its comparative analysis with the existing correlations. Heat Mass Transfer 55, 151–164 (2019). https://doi.org/10.1007/s00231-018-2459-3

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