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Development and validation of a mathematical model to predict the thermal behaviour of nanofluids

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Abstract

With a single-phase approach, a 3D mathematical model was developed through Computational Fluid Dynamics (CFD) techniques, coupling the momentum and heat transfer balances for the study of the thermal behaviour of nanofluids. The local heat transfer coefficient and thermal boundary layer thickness of CuO/water, Fe2O3/water and Al2O3/water nanofluids, have been predicted and compared with those experimentally determined at three volume concentration of nanoparticles (ϕ=0.01%, 0.03% and 0.05%), at T = 25 °C and T = 55 °C for laminar and turbulent flow conditions, using a newly developed sophisticated noninvasive heat transfer coefficient probe that is flush mounted on the inner wall of the test section. Such conditions have been used for the mathematical model, considering the effects of the nanoparticle materials and volume concentrations through effective thermophysical properties. The predicted results from the mathematical model show a good agreement with the trend and the experimental observations. The enhancement of the heat transfer coefficient and reduction of the thermal boundary layer when increasing the volume concentration of the nanofluids and when increasing the flow rates have been properly predicted by the mathematical model results, showing average absolute relative errors between 1.7% and 8.4%. The model exhibits an enhancement in the agreement between the experimental measurements and the predicted results when comparing with other models found in literature.

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Abbreviations

CFD :

Computational Fluid Dynamics

C p :

Heat capacity \( \left[\frac{J}{kgK.}\right] \)

g :

Gravity acceleration \( \left[\frac{m}{s^2}\right] \)

h :

Local heat transfer coefficient \( \left[\frac{W}{m^2K}\right] \)

H :

Enthalpy of the fluid [J]

I :

Identity matrix

k :

Turbulent kinetic energy

K :

Thermal conductivity \( \left[\frac{W}{mK}\right] \)

n :

Normal vector

P :

Absolute pressure [Pa]

q :

Heat flux \( \left[\frac{W}{m^2}\right] \)

\( \dot{Q} \) :

Flow rate \( \left[\frac{l}{\mathit{\min}}\right] \)

T :

Temperature [K]

v :

Fluid velocity \( \left[\frac{m}{s}\right] \)

δ :

Thermal boundary layer [mm]

ε :

Turbulent dissipation rate

ϕ :

Volume concentration

μ :

Dynamic viscosity [Pa s]

ρ :

Density \( \left[\frac{kg}{m^3}\right] \)

0:

Initial conditions

B :

Bulk

nf :

nanofluid

np :

Nanoparticle

s :

surface

w :

Water

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors

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Authors and Affiliations

  1. Chemical and Biochemical Engineering Department, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Sebastián Uribe & Muthanna Al-Dahhan

  2. Chemical Engineering Department, Jazan University, Jazan, Saudi Arabia

    Nasser Zouli

  3. Universidad Popular Autónoma del Estado de Puebla (UPAEP), Escuela de Ingeniería Química, PUE 72410, Puebla, Mexico

    Mario E. Cordero

  4. Mining and Nuclear Engineering Department, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Muthanna Al-Dahhan

Authors
  1. Sebastián Uribe
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  2. Nasser Zouli
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  3. Mario E. Cordero
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  4. Muthanna Al-Dahhan
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Correspondence to Muthanna Al-Dahhan.

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Highlights

- A single-phase approach mathematical model was developed for nanofluids

- The effect of nanoparticles was incorporated through effective properties

- Prediction of heat transfer coefficients in good agreement with experiments

- High predictive quality of the enhancement of the heat transfer coefficient

- Improvement in the predictive quality in comparison with other literature models

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Uribe, S., Zouli, N., Cordero, M.E. et al. Development and validation of a mathematical model to predict the thermal behaviour of nanofluids. Heat Mass Transfer 57, 93–110 (2021). https://doi.org/10.1007/s00231-020-02927-5

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  • DOI: https://doi.org/10.1007/s00231-020-02927-5

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