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Is thermal conductivity of nano sized particles and bulk particles the same? If not, what's the difference and is there any relation between thermal conductivity and and particle size?

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You should add more details to your question but since you added the fluid mechanics tag I'll assume you mean nanofluids. Yes, of course there is a difference between thermal conductivity of solid particles (nano) and base fluid. The addition of nano-sized particles to the main fluid has been found to enhance the thermophysical properties of the base fluid (the main concept of nanofluids) [a].

It was found that the thermal conductivity of the nanofluid depends on many factors [b]:

  • Thermal conductivity of the base fluid and nanoparticles $k_f$ and $k_p$
  • Volume fraction $\phi$
  • Surface area (shape of the nanoparticles suspended in the base fluid)

The effective thermal conductivity $k_{eff}$ of the nanofluid can be calculated using Maxwell and Hamilton and Crosser equations.

Maxwell equation (Valid for a fluid having a lower thermal conductivity than solid nanoparticles, and you can see that the effective thermal conductivity depends only on both $k$ values of fluid and solid nanoparticles and volume fraction):

$$k_{eff} = k_f (1 + \frac{3(k_p - k_f)\phi}{(k_p - k_f)-(k_p - k_f)\phi})$$

Hamilton and Crosser equation: $$k_{eff} = k_f (\frac{k_p + k_f (n-1) + (n-1)(k_p - k_f)\phi}{k_p + k_f (n-1)- (k_p - k_f)\phi})$$

This equation is valid for non-spherical particles, and $n$ is the shape factor that is obtained experimentally for different materials, you may refer to this paper for more details.

[a] Vincenzo Bianco, Oronzio Manca, Sergio Nardini and K Vafai -Heat Transfer Enhancement With Nanofluids (2015).

[b] D. C. Hernandez Aita - Design and Optimization of Volumetric Solar Receivers based on Nanoparticles with Supercritical CO2 (2014).

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