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Numerical analysis of a nanofluid behavior in an expanded curved duct using the two-phase Buongiorno model

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Abstract

In various industrial applications, especially those that focus on heat transfer, curved ducts present an interesting equipment. The flow behavior inside curved ducts is more complex compared to straight ducts, particularly in the presence of nanofluids. Hence, the present paper reports a numerical investigation of a nanofluid two-phase flow according to the Buongiorno model in a curved duct with abruptly expanded cross section. It deals with a toroidal duct with a circular cross-section abruptly expanded through which an Alumina-water nanofluid flows. The nanofluid penetrates the duct with a constant initial velocity at a cold constant temperature. Moreover, the lateral surface of the expanded part of the duct is maintained at a hot temperature, however, the rest of the duct boundaries are assumed to be adiabatic. The aim of the present study is to visualize the impact of the phenomenon of inertia (10 ⩽ Re ⩽ 200), mass diffusion (0.1 ⩽ Le ⩽ 100) and alumina nanoparticles concentration (0 ⩽ φ0 ⩽ 0.1)  on the hydrodynamic, thermal and mass behavior of the nanofluid inside the expanded curved ducts under Brownian and thermophoretic diffusions. The nanofluid flow is governed by the mathematical model of Buongiorno including the mass, momentum, energy and nanoparticles equations and solved by the Galerkin finite element method. The numerical results have indicated that, in addition to the presence of Dean’s vortices, the enlarged configuration of the current duct leads to the emergence of vortices resulting from flow reattachment. Moreover, the heat transfer rate increases with higher Reynolds numbers. Furthermore, the addition of alumina nanoparticles enhances the heat transfer with a percentage of 15% compared to pure water. Additionally, there is a relative decrease in the heat transfer rate due to nanoparticles’ thermophoretic migration. On the other hand, the increase in the Lewis number does not significantly influence this heat transfer rate, although it does promote a more homogeneous distribution of nanoparticles.

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Abbreviations

a 1 :

Radius of restricted duct/m

a 2 :

Radius of expanded duct/m

Cp:

Specific heat/J kg−1 K−1

D :

Diameter of restricted duct/m

D B :

Brownian motion coefficient/m2 s−1

De:

Dean number/–

d p :

Nanoparticles diameter/m

D T :

Thermophoresis coefficient/m2 s−1

k :

Thermal conductivity/W m−1 K−1

K B :

Boltzmann coefficient/J K−1

Le:

Lewis number/–

N B :

Brownian motion parameter/–

N T :

Thermophoresis parameter/–

Nu:

Nusselt number/–

P :

Dimensionless pressure/–

p :

Pressure/Pa

Pr:

Prandtl number/–

q w :

Heat flux/W/m−2 K−1

R :

Dimensionless radial coordinate/–

R c :

Average curvature radius/m

Re:

Reynolds number/–

Ri:

Richardson number/–

S :

Lateral area of expanded duct/m2

t :

Time/s

T :

Temperature/K

u 0 :

Inlet velocity/m s−1

u r :

Radial velocity/ m s−1

U R :

Dimensionless radial velocity/–

u z :

Vertical velocity/ m s−1

U Z :

Dimensionless vertical velocity/–

u θ :

Axial velocity/m s−1

U θ :

Dimensionless axial velocity/–

V :

Magnitude velocity/m s−1

x :

x-Cartesian coordinate/m

y :

y-Cartesian coordinate/m

Z :

Dimensionless vertical coordinate/–

z :

Vertical coordinate/m

α :

Thermal diffusivity/m2 s−1

β :

Thermal expansion coefficient/K−1

Θ:

Dimensionless temperature/–

θ :

Axial coordinate/rd

μ :

Viscosity/Pa s

ρ :

Density/kg m−3

τ :

Dimensionless time/–

φ :

Volume fraction or concentration/–

φ 0 :

Mean concentration/–

Φ:

Dimensionless concentration/–

ϕ :

Cross section angle coordinate/rd

Ω:

Computational domain

f:

Base fluid

p:

Nanoparticles

nf:

Nanofluid

h:

Hot

c:

Cold

ave:

Average

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Authors and Affiliations

  1. Laboratory of Maritime Sciences and Engineering LSIM, Faculty of Mechanical Engineering, University of Science and Technology of Oran, Mohamed Boudiaf, El Mnaouar, B.P. 1505, 31000, Oran, Algeria

    Djamila Derbal, Mohamed Bouzit & Fayçal Bouzit

  2. Mechanics, Modeling and Experimentation Laboratory L2ME, Faculty of Sciences and Technology, Bechar University, B.P. 417, 08000, Bechar, Algeria

    Abderrahim Mokhefi

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  1. Djamila Derbal
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Contributions

DD performed the simulation and showed the results and interpretation, MB proposed the idea of the paper and helped in the interpretation, AM detailed the mathematical formulation and helped in the analyze of the results, FB contributed in the redaction.

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Correspondence to Djamila Derbal.

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Derbal, D., Bouzit, M., Mokhefi, A. et al. Numerical analysis of a nanofluid behavior in an expanded curved duct using the two-phase Buongiorno model. J Therm Anal Calorim 148, 11131–11154 (2023). https://doi.org/10.1007/s10973-023-12423-7

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