Optimization of laminar pipe flow using nanoparticle liquid suspensions for cooling applications

Heat transfer of nanoparticle suspensions in laminar pipe flow is studied theoretically. The main idea upon which this work is based is that nanofluids behave more like single-phase fluids than like conventional solid−liquid mixtures. This assumption implies that all the heat transfer and friction factor 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 for maximum heat transfer is only slightly higher than that for minimum cost of operation. These optimal concentrations increase as the nanofluid bulk temperature is increased, the length-to-diameter ratio of the pipe is decreased, and the Reynolds number of the base fluid is increased. Moreover, the optimal concentrations increase with increasing the nanoparticle average size at high bulk temperatures, whilst they are practically independent of the nanoparticle diameter at lower bulk temperatures.

► The existence of two optimal particle concentrations is pointed out and discussed.
► Optimal particle concentrations increase with temperature and Reynolds number.
► Optimal particle concentrations increase as the length-to-diameter ratio decreases.
► Optimal particle concentrations depend very little on the average particle size.
► Optimal particle concentrations depend much more on liquid phase than on solid phase.