In a series of articles, Jang and Choi (1-3) listed and explained their effective thermal conductivity $(keff)$ model for nanofluids. For example, in the 2004 article (1), they constructed a $keff$ correlation for dilute liquid suspensions interestingly, based on kinetic *gas* theory as well as nanosize boundary-layer theory, the Kapitza resistance, and nanoparticle-induced convection. Three mechanisms contributing to $keff$ were summed up, i.e., base-fluid and nanoparticle conductions as well as convection due to random motion of the liquid molecules. Thus, after an order-of-magnitude analysis, their effective thermal conductivity model of nanofluids readsDisplay Formula

$keff=kf(1\u2212\phi )+knano\phi +3C1dfdpkfRedp2Pr\phi $

(1)

where

$kf$ is the thermal conductivity of the base fluid,

$\phi $ is the particle volume fraction,

$knano=kp\beta $ is the thermal conductivity of suspended nanoparticles involving the Kapitza resistance,

$C1=6\xd7106$ is a constant (never explained or justified),

$df$ and

$dp$ are the diameters of the base-fluid molecules and nanoparticles, respectively,

$Redp$ is a “random” Reynolds number, and Pr is the Prandtl number. Specifically,

Display Formulawhere

$C\xafRM$ is a random motion velocity and

$\nu $ is the kinematic viscosity of the base fluid.