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Heat and Mass Transfer

, Volume 55, Issue 1, pp 151–164 | Cite as

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

  • Nusrat Parveen
  • Sadaf ZaidiEmail author
  • Mohammad Danish
Original
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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.

Nomenclature

Bo

Boiling number

C

Cost function

Co

Convective number

Cp

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

hlg

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

Q2ext

Leave-one-out cross validation for the test set

Q2Loo

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

yi

Output vector

Subscripts

l

Liquid phase

nb

Nucleate boiling

sat

Saturated

tp

Two-phase

v

Vapor phase

w

Wall

Greek symbols

Γ

Surface development parameter

σ

Width parameter of RBF kernel

ε

Loss function

γ

Regularization parameter

λ and λ*

Lagrange multipliers

ϕ(xi)

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

Abbreviations

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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Notes

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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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemical Engineering, Z.H. College of Engineering and TechnologyAligarh Muslim UniversityAligarhIndia

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