# Flow boiling heat transfer analysis of Al_{2}O_{3} and TiO_{2} nanofluids in horizontal tube using artificial neural network (ANN)

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## Abstract

A nanofluid is a suspension of nanometer-sized particles in a base fluid. In the last decade, flow boiling of nanofluid has gained much attention. However, only a few correlations on flow boiling are available. In this paper, an experimental study for HTC (heat transfer coefficient) of water-based TiO_{2} and Al_{2}O_{3} nanofluids flowing in an annulus has been carried out at 1 bar. The volumetric concentration of the nanofluid was varied from 0.05 to 0.20%, and heat flux and the mass flux were varied from 6.25 to 143.2 kW m^{−2} and 338 to 1014 kg m^{−2} s^{−1}, respectively. It was observed that HTC for both the nanofluids was greater than that of the base fluid water, and it increased with increase in the concentration of the nanoparticles, the heat flux and the mass flux. The highest HTC was obtained for Al_{2}O_{3} nanofluid at 0.20% concentration for the heat flux of 143.2 kW m^{−2} and mass flux of 1014 kg m^{−2} s^{−1}. It was found that nanofluid made from Al_{2}O_{3} nanoparticles had better HTC than nanofluid made from TiO_{2} nanoparticles. The HTC ratios, i.e., the ratio of HTC of the nanofluid to the HTC of the base fluid, also increased with the increase in concentration, heat flux and mass flux. In the later part of the paper, new correlations were developed for predicting HTC for TiO_{2} and Al_{2}O_{3} nanofluids. Finally, an ANN model was developed to predict the heat transfer coefficient. Experimental values were found to be in good agreement with ANN predictions.

## Keywords

Nanofluids Heat transfer coefficient Mass flux Heat flux Concentration Correlation Artificial neural network## List of symbols

*C*Concentration of nanofluids

*C*_{p}Specific heat at constant pressure (J kg

^{−1}K^{−1})*d*_{h}The hydraulic diameter of the tube m

*F*Two-phase multiplier

*h*Boiling heat transfer coefficient (kW m

^{−2}K^{−1})*h*_{LG}Latent heat of vaporization (J kg

^{−1})*k*Thermal conductivity (Wm

^{−1}K^{−1})- \(\dot{m}\)
Total mass flux of the liquid and vapor flowing (kg m

^{−2}s^{−1})*m*Mass of nanoparticle gm

*M*Number of independent variables

*Nu*Nusselt number

*Pr*Prandtl number

- \(\Delta p_{\text{sat}}\)
\(\left( {p_{\text{wall}} - p_{\text{sat}} } \right)\) (Pa)

*q*Heat flux (kW m

^{−2})- δ
*R* Uncertainties associated with the dependent variables

*Re*Reynolds number

*R*^{2}Correlation coefficient

*S*Nucleate boiling suppression factor

- \(\Delta T_{\text{sat}}\)
\(\left( {T_{\text{wall}} - T_{\text{sat}} } \right)\) (K)

*x*Vapor quality

*X*_{tt}Martinelli parameter

*δX*_{j}Uncertainties associated with the independent variables

## Greek symbols

- \(\alpha\)
Convective heat transfer coefficient (kW m

^{−2}K^{−1})- \(\mu\)
Dynamic viscosity (kg m

^{−1}s^{−1})- \(\rho\)
Density (kg m

^{−3})- \(\sigma\)
Surface tension (Nm

^{−1})- \(\phi\)
Nanoparticles volume concentration

## Subscripts

- bf
Base fluid

- cb
Convective boiling

- FZ
Forster and Zuber

- G
Gas phase

- j
Specific parameter counter

- L
Liquid phase

- LG
Liquid–gas phase

- nb
Nucleate boiling

- np
Nanoparticle

- sat
Saturated

- tp
Two-phase

## Abbreviations

- ANN
Artificial neural network

- CAD
Computer-aided design

- CHF
Critical heat flux (kW m

^{−2})- DAQ
Data acquisition

- DC
Direct current (ampere)

- DI
Deionized

- EPE
Expanded polyethylene

- HDD
Hard disk drive

- HTC
Heat transfer coefficient (kW m

^{−2}K^{−1})- MSE
Mean square error

- ONB
Onset of nucleate boiling

- RAM
Random access memory

- SS
Stainless steel

- UVM
Ultrasonic vibration machine

## Notes

### Acknowledgements

The authors express their gratitude to Malaviya National Institute of Technology, Jaipur and University Teaching Department, Rajasthan Technical University, Kota, for their support in carrying out this work.

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