Experimental investigation and optimization of pool boiling heat transfer enhancement over graphene-coated copper surface


The current study presents an artificial neural network model used to predict the boiling heat transfer coefficient of different coating thicknesses of a graphene-coated copper surface in the pool boiling experimental setup for deionized water. The surface characterization has been carried out to study the structure, morphology and surface behavior. The investigations are carried out to evaluate the boiling heat transfer coefficient, heat flux and wall superheat for various thicknesses of nano-coated surfaces experimentally, and the obtained results are compared with those of the reported studies and existing empirical correlations. After that, these results are compared with the outputs such as current, heat flux, wall superheat and boiling heat transfer coefficient obtained using a MATLAB-based artificial neural network model with coating thickness, surface roughness and voltage as input variables. The admirable accuracies are obtained with the predicted optimal model outputs with experimental observation in each test case.

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Heat transfer coefficient (h) (kW m−2 K−1)


Critical heat flux (W m−2)

Tn, To, Tp :

Temperature of copper heating block (°C)

Tq, Tr, Ts :

Calculated temperature of sample at different sections (°C)

T l :

Temperature of base fluid (°C)

T s :

Surface temperature of specimen (°C)

T :

Wall superheat (°C)

Qpq, Qqr, Qrs :

Heat flux at various sections (W m−2)

Kpq, Kqr, Krs :

Thermal conductivity of copper material at various sections (W m−1 K−1)

Apq, Aqr, Ars :

Cross-sectional area at various sections (m2)

xpq, ∆xrs, ∆xrs :

Thickness of surface at various sections (m)

k :

Thermal conductivity of the working fluid (W m−1 K−1)

Pr :

Prandtl number \(\left( {\frac{{\mu C_{\text{p}} }}{K}} \right)\)

C p :

Specific heat of the working fluid (kJ kg−1 K−1)

h fg :

Latent heat of vaporization of the working fluid (kJ kg−1)

q :

Pool boiling heat transfer (W m−2)

I :

Current (A)


Artificial intelligence


Artificial neural networks


Gene expression programming


Support vector regression


In-vessel retention through extend reaction vessel cooling


Carbon nanotubes


Polyethylene glycol




X-ray diffraction


Atomic force microscopy


Scanning electron microscopy



d :

Interplanar spacing

h, k, l :

Miller indices

a, c :

Lattice constants

g :

Acceleration due to gravity (m s−2)


Multilayer perceptron


Levenberg–Marquardt backpropagation


Scaled conjugate gradient backpropagation


BFGS quasi-Newton backpropagation


Gradient descent with adaptive learning rate backpropagation


Hyperbolic tangent sigmoid transfer function




Matrix laboratory


Mean square error

R :

Regression coefficient


Mean absolute percentage error

n :

Total number of output data

µ :

Viscosity (N s m−2)

σ :

Surface tension (N m−2)

ρ :

Density (kg m−3)

λ :

Wavelength (m)








Experimental values


Predicted values


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Correspondence to Sameer S. Gajghate.

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Gajghate, S.S., Barathula, S., Das, S. et al. Experimental investigation and optimization of pool boiling heat transfer enhancement over graphene-coated copper surface. J Therm Anal Calorim 140, 1393–1411 (2020). https://doi.org/10.1007/s10973-019-08740-5

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  • Nucleate pool boiling heat transfer
  • Heat transfer coefficient
  • Critical heat flux
  • Graphene
  • Dip coating
  • Artificial neural network