I performed forced convection experiments with nanofluids (DI Water as base fluid) through different shaped flow sections, thus obtaining 432 Nusselt number and friction factor data. As known, these values were functions of volume concentration (phi), Reynolds number, and Prandtl number.
The correlation is in the form of Nu = c1*[(1+phi)c2]*[Rec3]*[Prc4],
where c1, c2, c3, and c4 were constants.
When I developed correlations, I found that the power values of the Reynolds number (c3) vary between 0.53 and 0.63, whereas the power value of the Prandtl number (c4) varies between -0.05 to 0.133.
eg.
0.279*[(1+phi)0.7]*[Re0.55]*[Pr- 0.021] -----> negative powered Prandtl number for Nanofluid 1 inside pipe 1
0.154*[(1+phi)- 0.05]*[Re0.63]*[Pr0.133] -----> positive powered Prandtl number for Nanofluid 2 inside pipe 1
My question is as below.
Can we have negative power values for the Reynolds and Prandtl numbers while developing the correlations for the Nusselt number? Or should the Reynolds number be restricted between 0.6 and 0.8, and the Prandtl number power values between 0.2 and 0.4?
I appreciate the learned and bright Researchers to share your divine knowledge and experience for me to learn. I will sincerely appreciate and acknowledge your justifying solution and support.
In my study, I used air as the cooling fluid and not nanofluids. I don't have any results for nanofluids to guide you.
I'm sorry.
The correlations are empirical and there is no fundamental reason why the indices should be positive: they normally are for single component flow. The suspension that you are using makes this a two-phase flow problem as a solid phase exists.
It is interesting how closely your curve fits mirror single phase behaviour. For single phase the index on Re would usually lie between .5 and .65 (for turbulent conditions). Usually, two phase flows are treated either by adjusting the physical properties (i.e. viscosity and conductivity) to allow for the mixture (Einstien method), or, alternatively by developing a single-phase multiplier that allows for the fact that the second phase alters properties (Lockhart and Martinelli method).
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