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Fundamentals of Nanoparticle Flow and Heat Transfer

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Nanofluidics

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Abstract

Nanofluids are suspensions of nano-size particles (typically 2–100 nm) in liquids, which are called base fluids. Several research projects of the late 1990s and the first decade of the twenty-first century indicated that the addition of very small amounts of nanoparticles in commonly used base fluids, such as water and ethyl glycol, increased significantly the effective thermal conductivity of these mixtures. Choi et al. (Appl Phys Lett 79:2252–2254, 2001) used a dilute suspension of carbon nanotubes in water and observed that the conductivity of the resulting nanofluid more than doubled. Some experiments on the mass transfer coefficients with nanofluids reported more dramatic results: Olle et al. (Ind Eng Chem Res 45(12):4355–4363, 2006) detected mass transfer enhancements with ferromagnetic nanoparticle suspensions as high as six times the corresponding coefficients of the base fluid alone. The significantly enhanced transport properties of the nanofluids brand these suspensions as ideal media for heat and mass transfer with widespread applications including the cooling of very small electronic components, which will comprise the next generation of computer chips; absorption of gases by liquid carriers; increase of the rate of gas–liquid chemical reactions; electricity generation; cooling of smaller internal combustion engines; space applications under microgravity; advanced nuclear reactor cooling; and biomedicine.

All the available experimental data point to the fact that the rates of heat and mass transfer in base fluids are significantly enhanced with the addition of 1–2 % of nanoparticles by volume. This characteristic will establish certain types of nanofluids as the heat and mass transfer media for the future, with an enormous economic potential. Because of this, a significant amount of research was conducted during the first decade of the twenty-first century on the transport properties and the applications of nanofluids, hundreds of journal articles were written, and several conferences were devoted to the subject.

This chapter presents the fundamentals of the flow and heat and mass transfer processes of nanoparticles in liquids. The chapter starts with useful definitions for particles and suspensions that assist with the exposition of the subject. The time scales and length scales for the nanofluid suspensions and the individual particles are derived, and dimensionless numbers that are pertinent to the nanofluids are presented. A short section explains the meaning of the limit mathematical operation within the molecular model of matter and the analytical complexities introduced by the small size of the nanoparticles in a continuum model of matter. The fundamental equation of motion for a nanoparticle in a fluid is derived, in the presence of velocity slip at the interface, and closure equations for the interfacial slip are presented. The hydrodynamic force on the nanoparticles is derived, for both steady and transient flows. Expressions for the rates of heat and mass transfer for nanoparticles with both velocity and temperature discontinuities at the interface are also derived and presented for steady and transient conditions.

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Notes

  1. 1.

    In order to avoid confusion with the differential operator, d, the expression 2α will be preferentially used in this monograph to denote the diameter, rather than the symbol d.

  2. 2.

    Basset originally used the stipulation v θ  = kσ rθ . The form of the closure equation that has been used by most subsequent researchers is also used here.

  3. 3.

    For incompressible substances such as solids and liquids, the specific heats at constant pressure and constant volume are approximately equal and are denoted simply by the symbol c, c p  = c v  = c.

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    Efstathios E. (Stathis) Michaelides

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Michaelides, E.E.(. (2014). Fundamentals of Nanoparticle Flow and Heat Transfer. In: Nanofluidics. Springer, Cham. https://doi.org/10.1007/978-3-319-05621-0_1

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