Heat transfer of nanofluids in turbulent pipe flow

Heat transfer of nanofluids in turbulent pipe flow

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Heat transfer of nanoparticle suspensions in turbulent pipe flow is studied theoretically.
The main idea upon which this work is based is that nanofluids behave more like singlephase
fluids than like conventional solidliquid mixtures. This assumption implies that
all the convective heat transfer correlations available in the literature for single-phase
flows can be extended to nanoparticle suspensions, provided that the thermophysical
properties appearing in them are the nanofluid effective properties calculated at the
reference temperature. In this regard, two empirical equations, based on a wide variety
of experimental data reported in the literature, are used for the evaluation of the
nanofluid effective thermal conductivity and dynamic viscosity. Conversely, the other
effective properties are computed by the traditional mixing theory. The novelty of the
present study is that the merits of nanofluids with respect to the corresponding base
liquid are evaluated in terms of global energetic performance, and not simply by the
common point of view of the heat transfer enhancement. Both cases of constant
pumping power and constant heat transfer rate are investigated for different operating
conditions, nanoparticle diameters, and solidliquid combinations. The fundamental
result obtained is the existence of an optimal particle loading for either maximum heat
transfer at constant driving power or minimum cost of operation at constant heat
transfer rate. In particular, for any assigned combination of solid and liquid phases, it is
found that the optimal concentration of suspended nanoparticles increases as the
nanofluid bulk temperature is increased, the Reynolds number of the base fluid is
increased, and the length-to-diameter ratio of the pipe is decreased, while it is
practically independent of the nanoparticle diameter.



The usual design requirements for modern heat transfer equipment are reduced size and
high thermal performance. In this connection, in the past decades a considerable
research effort has been dedicated to the development of advanced methods for heat
transfer enhancement, such as those relying on new geometries and configurations, and
those based on the use of extended surfaces and/or turbulators. On the other hand,
according to a number of studies executed in recent times, a further important
contribution may derive by the replacement of traditional heat transfer fluids, such as
water, ethylene glycol and mineral oils, with nanofluids, i.e., colloidal suspensions of
nano-sized solid particles, whose effective thermal conductivity has been demonstrated
to be higher than that of the corresponding pure base liquid.
The main results of prior work on pipe flow, that is undoubtedly one of the most
investigated topics in the field of convection in nanofluids, clearly show that
nanoparticle suspensions offer better thermal performance than the base liquids at same
Reynolds number, and that heat transfer increases with increasing the nanoparticle

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volume fraction  see, e.g., Yu et al. [1], Kakaç and Pramuanjaroenkij [2], and Godson
et al. [3]. For the turbulent flow regime, which our interest is focused on, increased heat
transfer data were reported by Pak and Cho [4], Xuan and Li [5], Maїga et al. [6],
Behzadmehr et al. [7], Williams et al. [8], and Bianco et al. [9].
However, it must be pointed out that the increase in effective thermal conductivity
consequent to the dispersion of nanoparticles into the base liquid is accompanied by a
contemporary growth of the effective dynamic viscosity, which could represent a
serious limitation. In fact, an excessive increase in pressure drop may result in an
exaggerated pumping power requirement, as detected by Pak and Cho [4], and Williams
et al. [8]. This means that the merits of nanofluids need to be evaluated necessarily in
terms of global energetic performance, and not simply by the common point of view of
the heat transfer enhancement, as pointed out by Gosselin and da Silva [10] in a paper
on external boundary layer flow. Actually, two options are possible. The first option is
aimed at determining how much the heat transfer rate changes as the nanoparticle
volume fraction is increased, keeping constant the pumping power. The second option
has the scope to evaluate in what measure the pumping power changes with increasing
the nanoparticle concentration, for an assigned heat transfer rate. Obviously, the
addition of nanoparticles to the base liquid is advantageous in all those cases in which
either a heat transfer enhancement occurs at a fixed cost of operation or a lower amount
of power is dissipated in friction at same thermal performance.
Framed in this general background, the aim of the present paper is to undertake a
comprehensive theoretical study on the overall energetic performance of nanofluids in
turbulent pipe flow with the primary scope to determine if and when the dispersion of
nanoparticles into a base liquid is beneficial. Both cases of constant driving power and
constant heat transfer rate are investigated for different operating conditions,
nanoparticle diameters, and solidliquid combinations.



Although strictly speaking a nanofluid is a solidliquid mixture, the majority of the
studies performed on this subject are based on the assumption that the nanofluid
behaves more like a single-phase fluid than like a conventional solidliquid mixture. In
fact, since the suspended nanoparticles have usually small size and concentration, the
hypothesis of a solidliquid mixture statistically homogeneous and isotropic can
reasonably be advanced. This means that, under the further assumptions that the
nanoparticles and base liquid are in local thermal equilibrium, and no-slip motion
occurs between the solid and liquid phases, to all intents and purposes the nanofluid can
be treated as a pure fluid. Therefore, all the convective heat transfer correlations
available in the literature for single-phase flows can easily be extended to the
corresponding nanofluid applications, provided that the thermophysical properties
appearing in them are the nanofluid effective properties calculated at the reference
temperature. Notice that a similar approach was previously used by Kim et al. [11],
Gosselin and da Silva [10], Hwang et al. [12], and Corcione [13, 14], mainly for
buoyancy-induced applications. Certainly, the trustworthiness of the results obtained
following this procedure is strongly related to the use of robust theoretical models or
empirical equations able to predict with adequate accuracy the nanofluid effective
properties.


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