Heat transfer of nanoparticle suspensions in turbulent tube flow is studied theoretically. The main idea on which this work is based is that nanofluids behave more like single-phase fluids than conventional solid-liquid mixtures. This assumption implies that all 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 effective properties of the nanofluid 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 effective thermal conductivity and dynamic viscosity of tenanofluid. In contrast, the other effective properties are calculated by traditional mixing theory. The novelty of the present study is that the merits of nanofluids compared to the corresponding base liquid are evaluated in terms of overall energy performance, and not simply from the common point of view of heat transfer improvement. 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 load for maximum heat transfer at constant driving power or for minimum operation cost at constant heat transfer rate. In particular, for any assigned combination of solid and liquid phases, the optimal concentration of suspended nanoparticles was found to increase as the overall temperature of the nanofluid increased, the Reynolds number of the base fluid increased, and the length/diameter ratio of the tube decreased. , while it is practically independent of the diameter of the nanoparticles. The usual design requirements of modern heat transfer equipment are small size and high thermal performance. In this regard, in recent decades a considerable research effort has been dedicated to the development of advanced methods for improving heat transfer, such as those based on new geometries and configurations, and those based on the use of extended surfaces and/or turbulators . According to some studies conducted recently, however, a further important contribution could derive from the replacement of traditional heat transfer fluids, such as water, ethylene glycol and mineral oils, with nanofluids, i.e. colloidal suspensions of nanometric-sized solids. particles, whose effective thermal conductivity has been demonstrated to be higher than that of the corresponding pure base liquid. The main results of previous work on tube flow, which 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 base liquids at the same Reynolds number and that heat transfer increases with the size of the nanoparticle
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