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Thermal and hydraulic characteristics of TiO2/water nanofluid flow in tubes possessing internal trapezoidal and triangular rib shapes

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Abstract

Configuration improvements are greatly important in heat transfer enhancement. In this study, TiO2/water nanofluid was used in combination with ribbed tubes for this purpose. Namely, this article presents a numerical investigation on the effect of rib geometries (trapezoidal and triangular rib shapes), number of ribs (4, 6, and 8 ribs) on heat transfer using TiO2 nanofluid in turbulent flow with Reynolds numbers of 5000–40,000. The thermal and hydraulic behavior of nanofluids was simulated utilizing single-phase approach with the assumption that the fluid properties are constant with temperature, and the flow is under uniform heat flux. The average size of the nanoparticles used in this work was 50 nm, and the nanofluid was considered at concentrations of 0.25–1.0%. The investigations were performed with the aim of establishing the impact of rib numbers and shapes on friction factor and heat transfer employing TiO2/water nanofluid as the working fluid. The results show that the helical-ribbed tube significantly improves heat transfer compared to the plain tube taking into account the shape and number of ribs. Further, by means of performance evaluation criteria, the tubes with trapezoidal ribs provide better thermal performance followed by the ones with triangular ribs compared to the plain tubes. Ultimately, the nonlinear models of Nusselt number and friction factor in the foregoing configurations were proposed with maximum deviations of ± 7.0% and ± 5.0%, respectively.

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Abbreviations

\(b\) :

Rib average width (m)

\(C\) :

Specific heat (J kg−1 K−1)

\(C_{1}\), \(C_{2}\), \(C_{\mu }\) :

Constants in Eqs. (8) and (9)

\(d\) :

Diameter (m)

\(E\) :

Energy (J)

\(e\) :

Rib’s height (m)

\(f\) :

Friction factor (\(=\Delta pd_{\text{h}} /2L\rho u^{2}\))

\(G_{\text{k}}\) :

Generated turbulent kinetic energy (J)

\(g\) :

Tube wall thickness (m)

\(h\) :

Heat transfer coefficient (W m−2 K−1)

\(k\) :

Thermal conductivity (W m−1 K−1)

\(L\) :

Tube length (m)

\(N\) :

Number of ribs

\({\text{Nu}}\) :

Nusselt number (\(= hd_{\text{h}} /k\))

\(P\) :

Pitch (m)

\({ \Pr }\) :

Prandtl number (\(= \mu C /k\))

\({\text{PEC}}\) :

Performance evaluation criteria

\(p\) :

Pressure (Pa)

\(q\) :

Heat flux (W m−2)

\({\text{Re}}\) :

Reynolds number (\(= \rho ud_{\text{h}} /\mu\))

\(T\) :

Temperature (°C or K)

Trap:

Trapezoidal ribbed tube

Tri:

Triangular ribbed tube

\(u\) :

Velocity (m s−1)

\(x\) :

Axial direction (m)

y + :

Dimensionless wall distance (\(= \rho yu_{\tau } /\mu\))

\(\alpha_{\text{k}} , \alpha_{\varepsilon }\) :

Constants in Eqs. (8) and (9)

\(\beta\) :

Helix angle (°)

\(\delta_{\text{ij}}\) :

Kronecker delta function

\(\varepsilon\) :

Turbulent kinetic energy dissipation rate (m2 s−3)

\(\eta\) :

Variable in Eq. (4)

\(\kappa\) :

Thermal conductivity ratio

\(\mu\) :

Viscosity (kg m−1 s−1)

\(\rho\) :

Density (kg m−3)

\(\phi\) :

Volume fraction (concentration)

eff:

Effective

f :

Fluid

h :

Hydraulic

i :

Internal

in:

Inlet

min:

Minimal

nf:

Nanofluid

o :

Reference value (plain tube)

p :

Nanoparticle

t :

Turbulent

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Acknowledgements

The authors of this work would like to thank Tikrit University for providing facilities and technical support.

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Authors and Affiliations

  1. Mechanical Engineering Department, Tikrit University, Tikrit, Iraq

    Aadel A. R. Alkumait, Thamir K. Ibrahim, Maki H. Zaidan & Ahmed T. Al-Sammarraie

  2. Department of Mechanical Engineering, University of California, Riverside, CA, 92521, USA

    Ahmed T. Al-Sammarraie

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Alkumait, A.A.R., Ibrahim, T.K., Zaidan, M.H. et al. Thermal and hydraulic characteristics of TiO2/water nanofluid flow in tubes possessing internal trapezoidal and triangular rib shapes. J Therm Anal Calorim 147, 379–392 (2022). https://doi.org/10.1007/s10973-020-10289-7

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