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


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.



Boiling number


Cost function


Convective number


Specific heat, J/kg.K


Hydraulic diameter, m

f (x)

Regression function


Mass flux, kg/m2.s


Heat transfer coefficient, kW/m2.K


Enthalpy of vaporization, J/kg


Thermal conductivity, W/m.K


Kernel function


Dual form of the Lagrangian function


Fluid pressure, kPa


Peclet number


Prandtl number


Leave-one-out cross validation for the test set


Leave-one-out cross validation for the training set


Correlation coefficient


Reynolds number


Suppression factor


temperature, K


heat flux density, W/m2


Input vector


Lockhart-Martinelli parameter


Output vector



Liquid phase


Nucleate boiling






Vapor phase



Greek symbols


Surface development parameter


Width parameter of RBF kernel


Loss function


Regularization parameter

λ and λ*

Lagrange multipliers


High dimensional mapping feature function for input vector x


Thermal conductivity, W/m.K


Kinematic viscosity, kg/m.s


Density, kg/m3


Surface tension, N/m



Average absolute relative error


Artificial neural network


Mean relative error


Radial basis function


Support vector machines


Support vector regression


Structural risk minimization


Root mean square error


Standard deviation



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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Copyright information

© 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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