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

Abstract

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.