A simple homogeneous numerical solution for nanofluid natural convection in an enclosure with disconnected and conducting solid blocks

  • Gustavo Nascimento
  • Alan LugariniEmail author
  • Eduardo M. Germer
  • Admilson T. Franco
Technical Paper


Following a series of discrepancies in the literature regarding the effects of nanoparticle concentration on the heat transfer rate, this paper proposes a simple homogeneous modeling for natural convection of nanofluids. The proposed modeling allows a custom choice of correlations for the nanofluid’s thermophysical properties, which proved to be very convenient in validations carried out for the case of natural convection inside a clear enclosure. The general heat transfer decreasing behavior for high concentrations of nanoparticles, previously observed in experimental and two-phase numerical works, was successfully represented. A very interesting and pioneer case study of laminar natural convection of nanofluids in a laterally heated enclosure with conductive solid blocks uniformly distributed within the enclosure was numerically investigated with the proposed modeling. To compute the nanofluids characteristics, Corcione’s correlations for thermal conductivity and dynamic viscosity for effective properties and generic correlations for density, specific heat and thermal expansion coefficient were employed. Therefore, it was possible to isolate the nanoparticle’s influence on the heat transfer rate, evaluated by the average Nusselt number. By isolating the nanoparticle’s parameters, the effects of diameter and material have been interpreted from the homogeneous solution. A parametric investigation was conducted by varying the number of blocks inside the enclosure and the effective Rayleigh number. A numerical correlation for the average Nusselt number was derived for a wide range of effective Rayleigh number and number of blocks. The model developed herein is suitable to other applications in which the total heat transfer rate needs to be computed.


Nanofluid Natural convection Heterogeneous media Computational fluids dynamics 

List of symbols


Avogadro number


Specific heat at constant pressure (J/kg K)


Control volume


Mean diameter (m)


Acceleration of gravity (m/s2)


Height (m)


Thermal conductivity (W/m K)


Solid-to-nanofluid thermal conductivity ratio


Length (m)


Molar mass (kg/mol)


Normal direction unit vector


Number of blocks


Average Nusselt number


Pressure (Pa)


Non-dimensional pressure


Prandtl number


Coefficient of determination


Rayleigh number


Reynolds number


Temperature (K)


Velocity components in (x, y) directions (m/s)


Non-dimensional velocity components


Spatial coordinates (m)


Non-dimensional spatial coordinates

Greek symbols


Thermal diffusivity (m/s2)


Thermal expansion coefficient (1/K)


Distance between blocks


Distance between blocks and the enclosure walls




Nanoparticle concentration


Dynamic viscosity (Pa s)


Kinematic viscosity (m/s2)


Non-dimensional temperature


Density (kg/m3)


Stream function (kg/s)













Base fluid


Base fluid at 0 K


Base fluid at freezing point temperature





















This work was supported by the Research Center for Rheology and Non-Newtonian Fluids (CERNN). The first author is grateful for the funding of National Council for Scientific and Technological Development (CNPq).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Research Center for Rheology and Non-Newtonian FluidsFederal University of Technology—ParanáCuritibaBrazil

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