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Convective heat transfer performance of hybrid nanofluid in a horizontal pipe considering nanoparticles shapes effect

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Abstract

In this paper, the problem of steady forced convection heat transfer and fluid flow characteristics of a hybrid nanofluid flowing through an isothermally heated horizontal tube considering various nanoparticle shapes has been investigated numerically. The three dimensionless cylindrical coordinate equations are discretized using the finite volume method and solved via a FORTRAN program. A numerical parametric investigation is carried out for a tube filled with regular water, (TiO2/water) nanofluid and (Ag–TiO2/water) hybrid nanofluid. Four different types of nanoparticle shapes are considered in this study, spherical, cylindrical, platelets and blades, with different volume fractions ranging from 0 to 8% using water as a base liquid. The influence of nanoparticle shape, nanoparticle concentration and Reynolds number on the local Nusselt number and the friction factor is essentially examined. The results showed that the friction factor of both nanofluid and hybrid nanofluid flow was increased as the nanoparticle volume fraction increased for all kinds of nanoparticle shapes, whereas it decreased as the Reynolds number increased. Nusselt number increased with increase in the nanoparticle concentration and Reynolds number. The highest heat transfer rate was acquired for the maximum nanoparticle volume concentration by using blade nanoparticle shape followed by platelet shape, cylindrical shape and lastly the sphere shape. It was found that the maximum values of the friction factor were registered for platelet-shape nanoparticles.

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Abbreviations

Cp:

Heat capacity (J kg−1 K−1)

D :

Diameter of tube (m)

f :

Friction factor (–)

g :

Gravitational acceleration (m s−2)

h :

Convective heat transfer coefficient (W m−2 K−1)

Gr :

Grashof number \(( = g\beta_{\text{f}} q^{\prime \prime } D^{4} /k_{\text{f}} \nu_{\text{f}}^{2} )\)

k :

Thermal conductivity (W m−1 K−1)

L :

Length (m)

Nu :

Nusselt number (= hD/k)

Pr :

Prandtl number \(( = {\text{Cp}}_{\text{f}} \cdot \mu_{\text{f}} /k_{\text{f}} )\)

P :

Pressure (Pa)

P * :

Dimensionless pressure \(( = P/\rho_{\text{hnf}} v_{0}^{2} )\)

\(q^{\prime \prime }\) :

Uniform heat flux (W m−2)

Re :

Reynolds number \(( = \rho_{\text{f}} v_{0} D/\mu_{\text{f}} )\)

r :

Radial direction (m)

\(r^{*}\) :

Dimensionless radius (= r/D)

T :

Temperature (K)

\(T^{*}\) :

Dimensionless temperature \(( = (T - T_{0} )/(q_{\text{w}} D/k_{\text{nf}} )\)

t :

Time (s)

\(t^{*}\) :

Dimensionless time \(( = v_{0} t/D)\)

u :

Radial velocity component (m s−1)

\(u^{*}\) :

Dimensionless radial velocity (= u/v0)

v :

Axial velocity component (m s−1)

\(v^{*}\) :

Dimensionless axial velocity (= v/v0)

w:

Tangential velocity (m s−1)

\(w^{*}\) :

Dimensionless tangential velocity \(( = w/v_{0} )\)

z:

Axial direction (m)

\(z^{*}\) :

Dimensionless axial direction (= z/D)

\(\beta\) :

Volumetric expansion coefficient (K−1)

θ :

Angular coordinate

\(\phi\) :

Volume fraction

µ :

Dynamic viscosity (kg m−1 s−1)

υ :

Kinematic viscosity (m2 s−1)

b:

Bulk

hnf:

Hybrid nanofluid

nf:

Nanofluid

f:

Base fluid

0:

Inlet condition

*:

Dimensionless parameters

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Acknowledgements

The authors would like to acknowledge the Energy Physics Laboratory (LPE) of Brothers Mentouri University of Constantine (Algeria) and the Algerian Ministry of High Education and Scientific Research (MESRS) for the financial support through FNR Grant.

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Authors and Affiliations

  1. Physics Department, Faculty of Sciences, University of M’Hamed Bougara Boumerdes, 35000, Boumerdes, Algeria

    Mohammed Benkhedda

  2. Energy Physics Laboratory, Physics Department, Faculty of Exact Sciences, Brothers Mentouri University Constantine 1, 25000, Constantine, Algeria

    Mohammed Benkhedda, Toufik Boufendi & Tahar Tayebi

  3. Faculty of Sciences and Technology, Mohamed El Bachir El Ibrahimi University, 34030, Bordj Bou Arreridj, El-Anasser, Algeria

    Tahar Tayebi

  4. Mechanical Engineering Department, Prince Mohammad Endowment for Nanoscience and Technology, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    Ali J. Chamkha

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  1. Mohammed Benkhedda
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Benkhedda, M., Boufendi, T., Tayebi, T. et al. Convective heat transfer performance of hybrid nanofluid in a horizontal pipe considering nanoparticles shapes effect. J Therm Anal Calorim 140, 411–425 (2020). https://doi.org/10.1007/s10973-019-08836-y

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