Advertisement

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
  • 23 Downloads

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

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.

References

  1. 1.
    Rao M, Khandekar S (2009) Simultaneously Developing Flows Under Conjugated Conditions in a Mini-Channel Array: Liquid Crystal Thermography and Computational. Heat Transf Eng 30:751–761.  https://doi.org/10.1080/01457630802678573. CrossRefGoogle Scholar
  2. 2.
    Thakkar K, Kumar K, Trivedi H (2014) Thermal & Hydraulic Characteristics of Single phase flow in Mini-channel for Electronic cooling – Review. Int J Innov Res Sci Eng Technol 3:9726–9733Google Scholar
  3. 3.
    Kandlikar SG (2002) Fundamental issues related to flow boiling in minichannels and microchannels. Exp Thermal Fluid Sci 26:389–407.  https://doi.org/10.1016/S0894-1777(02)00150-4 CrossRefGoogle Scholar
  4. 4.
    Joshi LC, Singh S, Kumar SR (2014) A review on enhancement of heat transfer in microchannel heat exchanger. Int J Innov Sci Eng Technol 1:529–535Google Scholar
  5. 5.
    Qu W, Mudawar I (2003) Flow boiling heat transfer in two-phase micro-channel heat sinks -I. Experimental investigation and assessment of correlation methods. Int J Heat Mass Transf 46:2755–2771.  https://doi.org/10.1016/S0017-9310(03)00041-3 CrossRefGoogle Scholar
  6. 6.
    Copetti JB, Zinani F, Ayres FGB, Schaefer F (2015) Boiling heat transfer in Mini Tube: A discussion of two phase heat transfer coefficient behaviour, flow patterns and heat transfer correlations for two refrigerants, IV Journeys Multiph. Flows (JEM 2015), 1–9Google Scholar
  7. 7.
    Li W, Wu Z (2010) A general criterion for evaporative heat transfer in micro/mini-channels. Int J Heat Mass Transf 53:1967–1976.  https://doi.org/10.1016/j.ijheatmasstransfer.2009.12.059 CrossRefGoogle Scholar
  8. 8.
    Xiande F, Rongrong S, Zhanru Z (2011) Correlations of Flow Boiling Heat Transfer of R-134a in Minichannels : Comparative study. Energy Sci Technol 1:1–15Google Scholar
  9. 9.
    Piasecka M (2014) Application of heat transfer correlations for FC-72 flow boiling heat transfer in minichannels with various orientations. MATEC Web Conf 18:1–8CrossRefGoogle Scholar
  10. 10.
    Mahmoud MM, Karayiannis TG (2013) Heat transfer correlation for flow boiling in small to micro tubes. Int J Heat Mass Transf 66:553–574CrossRefGoogle Scholar
  11. 11.
    Basu S, Ndao S, Michna GJ, Jensen MK (2011) Flow Boiling of R134a in Circular Microtubes -Part I: Study of Heat. J Heat Transf 133:051502–051509.  https://doi.org/10.1115/1.4003159. CrossRefGoogle Scholar
  12. 12.
    Olayiwola NO (2005) Boiling in Mini and Micro-Channels. M. S. Thesis, School of mechanical Engineering, Georgia Institute of Technology, AtlantaGoogle Scholar
  13. 13.
    Olayiwola NO, Ghiaasiaan SM (2006) Assessment of flow boiling heat transfer correlations for application to mini-channels. In: 2006 ASME Int. Mech. Eng. Congr. Expo., ASME, Chicago, pp. 1–16Google Scholar
  14. 14.
    Bao ZY, Fletcher DF, Haynes BS (2000) Flow boiling heat transfer of Freon R11 and HCFC123 in narrow passages. Int J Heat Mass Transf 43:3347–3358.  https://doi.org/10.1016/S0017-9310(99)00379-8 CrossRefGoogle Scholar
  15. 15.
    Baird JR, Bao ZY, Fletcher DF, Haynes BS (2000) Local flow boiling heat transfer coefficients in narrow conduits. Multiph Sci Technol 12:129–144.  https://doi.org/10.1615/MultScienTechn.v12.i3-4.80 CrossRefGoogle Scholar
  16. 16.
    Yan Y-Y, Lin T-F (1998) Evaporation heat transfer and pressure drop of refrigerant R-134a in a small pipe. Int J Heat Mass Transf 41:4183–4194CrossRefGoogle Scholar
  17. 17.
    Peng H, Ling X (2015) Predicting thermal-hydraulic performances in compact heat exchangers by support vector regression. Int J Heat Mass Transf 84:203–213.  https://doi.org/10.1016/j.ijheatmasstransfer.2015.01.017. CrossRefGoogle Scholar
  18. 18.
    Zaidi S (2012) Development of support vector regression (SVR)-based model for prediction of circulation rate in a vertical tube thermosiphon reboiler. Chem Eng Sci 69:514–521.  https://doi.org/10.1016/j.ces.2011.11.005. CrossRefGoogle Scholar
  19. 19.
    Shabri A, Suhartono (2012) Streamflow forecasting using least-squares support vector machines. Hydrol Sci J 57:1275–1293.  https://doi.org/10.1080/02626667.2012.714468 CrossRefGoogle Scholar
  20. 20.
    Bui Tien D, Pham BT, Nguyen QP, Hoang N-D (2016) Spatial prediction of rainfall-induced shallow landslides using hybrid integration approach of Least-Squares Support Vector Machines and differential evolution optimization: a case study in Central Vietnam. Int J Digit Earth 9:1077–1097.  https://doi.org/10.1080/17538947.2016.1169561 CrossRefGoogle Scholar
  21. 21.
    Thissen U, Van Brakel R, De WP, Melssen WJ, Buydens LMC (2003) Using support vector machines for time series prediction. Chemom Intell Lab Syst 69:35–49.  https://doi.org/10.1016/S0169-7439(03)00111-4 CrossRefGoogle Scholar
  22. 22.
    Burbidge R, Trotter M, Buxton B, Holden S (2001) Drug design by machine learning : support vector machines for pharmaceutical data analysis. Comput Chem 26:5–14CrossRefGoogle Scholar
  23. 23.
    Parveen N, Zaidi S, Danish M (2016) Support vector regression model for predicting the sorption capacity of lead (II). Perspect Sci 8:629–631CrossRefGoogle Scholar
  24. 24.
    Parveen N, Zaidi S, Danish M (2017) Support Vector Regression Prediction and Analysis of the Copper (II) Biosorption Efficiency. Indian Chem Eng 59:295–311.  https://doi.org/10.1080/00194506.2016.1270778 CrossRefGoogle Scholar
  25. 25.
    Vapnik V, Golowich SE, Smola A (1996) Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing. Adv Neural Inf Proces Syst 9:281–287Google Scholar
  26. 26.
    Gunn S (1997) Support Vector Machines for Classification and Regression, ISIS Technical Report. University of Southampton, Southampton, pp 1–42Google Scholar
  27. 27.
    Zaidi S (2015) Novel application of Support Vector Machines to model the two phase-boiling heat transfer coefficient in a vertical tube thermosiphon reboiler. Chem Eng Res Des 98:44–58.  https://doi.org/10.1016/j.saa.2011.10.074. CrossRefGoogle Scholar
  28. 28.
    Parveen N, Zaidi S, Danish M (2017) Development of SVR-based model and comparative analysis with MLR and ANN models for predicting the sorption capacity of Cr(VI). Process Saf Environ Prot 107:428–437.  https://doi.org/10.1016/j.psep.2017.03.007. CrossRefGoogle Scholar
  29. 29.
    Vapnik VN (1995) The Nature of Statistical Learning Theory. Springer, New YorkCrossRefzbMATHGoogle Scholar
  30. 30.
    Pan Y, Jiang J, Wang R, Cao H, Cui Y (2009) Predicting the auto-ignition temperatures of organic compounds from molecular structure using support vector machine. J Hazard Mater 164:1242–1249.  https://doi.org/10.1016/j.jhazmat.2008.09.031. CrossRefGoogle Scholar
  31. 31.
    Sriraam A, Sekar S K, Samui P (2012) Support Vector Machine Modelling for the Compressive Strength of Concrete, In: B.H.V. Topping (Ed.), Proc. Eighth Int. Conf. Eng. Comput. Technol., Civil-Comp Press, Scotland, pp. 1–15Google Scholar
  32. 32.
    Nachev A, Stoyanov B (2012) Product quality analysis using support vector machines. Int J Inf Model Anal 1:179–192Google Scholar
  33. 33.
    Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222.  https://doi.org/10.1023/B:STCO.0000035301.49549.88 MathSciNetCrossRefGoogle Scholar
  34. 34.
    Chen JC (1966) Correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Process Des Dev 5:322–329CrossRefGoogle Scholar
  35. 35.
    Gungor KE, Winterton RHS (1987) Simplified general correlation for saturated flow boiling and comparison with data. Chem Eng Res Des 65:148–156Google Scholar
  36. 36.
    Kandlikar S G, (1990) Flow boiling maps for water, R-22 and R-134a in the saturated region. In: Int. Heat Transf. Conf., Jerusalem, pp. 1–6Google Scholar
  37. 37.
    Lazarek GM, Black SH (1982) Evaporative heat transfer, pressure drop and critical heat flux in a small vertical tube with R-113. Int J Heat Mass Transf 25:945–960CrossRefGoogle Scholar
  38. 38.
    Lee J, Mudawar I (2005) Two-phase flow in high-heat-flux micro-channel heat sink for refrigeration cooling applications: Part II — heat transfer characteristics. Int J Heat Mass Transf 48:941–955.  https://doi.org/10.1016/j.ijheatmasstransfer.2004.09.019 CrossRefGoogle Scholar
  39. 39.
    Liu Z, Winterton RHS (1991) A general correlation for saturated and subcooled flow boiling in tubes and annuli , based on a nucleate pool boiling equation. Int J Heat Mass Transf 34:2759–2766CrossRefGoogle Scholar
  40. 40.
    Mohammad PE, Shah M (1982) Chart correlation for saturated boiling heat transfer : Equations and further study. ASHRAE Trans 88:185–196Google Scholar
  41. 41.
    Warrier GR, Dhir VK, Momoda LA (2002) Heat transfer and pressure drop in narrow rectangular channels. Exp Thermal Fluid Sci 26:53–64CrossRefGoogle Scholar
  42. 42.
    Piasecka M (2015) Correlation for flow boiling heat transfer in minichannels with various orientations. Int J Heat Mass Transf 81:114–121CrossRefGoogle Scholar
  43. 43.
    Shi XZ, Zhou J, Wu BB, Huang D, Wei W (2012) Support vector machines approach to mean particle size of rock fragmentation due to bench blasting prediction. Trans Nonferrous Metals Soc China 22:432–441.  https://doi.org/10.1016/S1003-6326(11)61195-3 CrossRefGoogle Scholar
  44. 44.
    Lee C-Y, Chern S-G (2013) Application of a Support Vector Machine for Liquefaction Assessment. J Mar Sci Technol 21:318–324.  https://doi.org/10.6119/JMST-012-0518-3. Google Scholar
  45. 45.
    Chang C-C, Lin C-J (2011) A Library for Support Vector Machines, ACM Trans. Interlligent Syst. Technology 2:1–27.  https://doi.org/10.1145/1961189.1961199 Google Scholar
  46. 46.
    Jung Y (2018) Multiple predicting K -fold cross-validation for model selection. J Nonparametr Stat 30:197–215.  https://doi.org/10.1080/10485252.2017.1404598 MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Chang Q, Chen Q, Wang X (2005) Scaling Gaussian RBF kernel width to improve SVM classification. In: Int. Conf. Neural Networks Brain, 2005 ICNN, BeijingGoogle Scholar
  48. 48.
    Bertsch SS, Groll EA, Garimella SV (2009) Effects of heat flux, mass flux, vapor quality, and saturation temperature on flow boiling heat transfer in microchannels. Int J Multiphase Flow 35:142–154.  https://doi.org/10.1016/j.ijmultiphaseflow.2008.10.004 CrossRefGoogle Scholar
  49. 49.
    Yan J, Bi Q, Liu Z, Zhu G, Cai L (2015) Subcooled flow boiling heat transfer of water in a circular tube under high heat fluxes and high mass fluxes. Fusion Eng Des 100:406–418.  https://doi.org/10.1016/j.fusengdes.2015.07.007. CrossRefGoogle Scholar

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

Personalised recommendations