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The Superiority of Eulerian Two-Fluid Model for Simulation of Natural Convection of Nanofluids in Comparison with Other Models


Due to special heat transfer characteristics and potential applications in industries, nanofluids have attracted much attention during the past decades. Nanofluids’ behavior in natural convection has been one of the most challenging topics among scientists, and no consensus has been achieved over the suitable method for their simulations. In this regard, the present study examines the laminar natural convection of alumina–water nanofluid inside a square cavity. Four nanoparticle volume fractions, i.e. 0.1%, 0.3%, 1% and 2%, are studied using Eulerian two-fluid model. Moreover, some major interphase interactions, including thermophoresis and Brownian diffusion, have been taken into account. The results are in good agreement with experimental observations. They indicate the Eulerian two-fluid model is more accurate than single-phase modeling as well as mixture two-phase model. Also, adding alumina nanoparticles to the base fluid would enhance natural convective heat transfer up to a volume fraction of 0.3%. Nusselt number at 0.3% volume fraction is 1.5–4.5% more than base fluid. The value of this enhancement in Nusselt number decreases with Rayleigh number. The lower limit is for Rayleigh number 2.5 × 106 and the upper limit is for 7.5 × 105. Adding more nanoparticle to the base fluid reduces the Nusselt number. At 2% volume fraction Nusselt number is up to 5% lower than base fluid. From nanoparticle distribution, it was observed that nanoparticle concentration is higher in regions where there is a lower velocity of fluid flow which is in agreement with recent experimental measurements.

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\(C_{P}\) :

Specific heat

d :


\(D_{B}\) :

Brownian diffusion coefficient

\(D_{T}\) :

Thermophoresis coefficient

f :

Friction factor

\(F\) :

Interaction force vector

\(g\) :

Gravitational acceleration vector

\(h_{pq}\) :

Heat transfer coefficient between phases

\(J\) :

Mass flux vector

\(k\) :

Thermal conductivity

\(k_{B}\) :

Boltzmann constant

\(k_{TH}\) :

Thermophoresis parameter

K drag :

Momentum exchange coefficient

L :

Height of enclosure

Nu :

Nusselt number

\(P\) :


\(Pr\) :

Prandtl number

\(q\) :

Heat flux vector

\(Q_{pq}\) :

Heat exchange between phases

Re :

Reynolds number

\(t\) :


T :


\(v\,\left( {u,v} \right)\) :

Velocity vector

x, y :

Cartesian coordinates


Reference value

\(avg\) :


B :


C :


drag :

Drag force

H :



Lift force

nf :


\(p\) :


TH :


\(f\) :

Base fluid

\(\alpha\) :

Nanoparticle radius

\(\beta\) :

Thermal expansion coefficient

\(\mu\) :

Dynamic viscosity

\(\nu\) :

Kinematic viscosity

\(\rho\) :


\(\tau\) :

Stress tensor

\(\varphi\) :

Volume fraction


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Correspondence to Hossein Ali Pakravan.

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Shammasi, G., Pakravan, H.A. & Emdad, H. The Superiority of Eulerian Two-Fluid Model for Simulation of Natural Convection of Nanofluids in Comparison with Other Models. Iran J Sci Technol Trans Mech Eng (2022).

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  • Brownian diffusion
  • Eulerian model
  • Nanofluid
  • Natural convection
  • Thermophoresis
  • Two-fluid model