Nanofluid flow and heat transfer in boundary layers at small nanoparticle volume fraction: Zero nanoparticle flux at solid wall

Abstract

The continuum formulation is applied to the developing boundary layer problem, which approximates the entrance region of nanofluid flow in micro channels or tubes. The thermophysical properties are expressed as “equations of state” as functions of the local nanofluid volume fraction. Based on experimental utilization of nanofluid prevalently at small volume fraction of nanoparticles, a simple perturbation procedure is used to expand dependent variables in ascending powers of the volume fraction. The zeroth order problems are the Blasius velocity boundary layer and the Pohlhausen thermal boundary layer. These are accompanied by the volume fraction diffusion equation. In detailed applications, the boundary condition of zero-volume flux at a solid wall is specified and yields an “insulated wall” solution of constant volume fraction. Two property cases are calculated as comparisons: one is the use of mixture properties for the nanofluid density and heat capacity and the transport properties prevalently used in the literature attributed to Einstein and to Maxwell. Results for alumina are compared to experiments. The theory underestimates the experimental results. This leads to the second comparison, between “conventional” properties and those obtained from molecular dynamics computations available for gold-water nanofluids. The latter properties considerably increased the heat transfer enhancement relative to “conventional” properties and heat transfer enhancement is comparable to the enhanced skin friction rise. To fully appreciate the potential of nanofluids and heat transfer enhancement, further molecular dynamics computations of properties of nanofluids, including transport properties, accompanied by careful laboratory experiments on velocity and temperature profiles are suggested.