Abstract
The slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube is theoretically studied. The power-law rheology is adopted to describe the non-Newtonian characteristics of the flow, in which the fluid consistency coefficient and the flow behavior index depend on the nanoparticle volume fraction. The velocity profile, volumetric flow rate and local Nusselt number are calculated for different values of nanoparticle volume fraction and slip length. The results show that the influence of nanoparticle volume fraction on the flow of the nanofluid depends on the pressure gradient, which is quite different from that of the Newtonian nanofluid. Increase of the nanoparticle volume fraction has the effect to impede the flow at a small pressure gradient, but it changes to facilitate the flow when the pressure gradient is large enough. This remarkable phenomenon is observed when the tube radius shrinks to micrometer scale. On the other hand, we find that increase of the slip length always results in larger flow rate of the nanofluid. Furthermore, the heat transfer rate of the nanofluid in the microtube can be enhanced due to the non-Newtonian rheology and slip boundary effects. The thermally fully developed heat transfer rate under constant wall temperature and constant heat flux boundary conditions is also compared.
Highlights
Besides the pressure gradient, there exist another two parameters affecting the value of these four variables: one is the volume fraction of the nanoparticle w which is related with the fluid consistency coefficient m and the flow behavior index n; the other is the slip length L0s representing the slip effect
In the following discussion, we first study the influence of these two parameters on the flow of the nanofluid by analyzing the variation of velocity profile and volumetric flow rate with w and L0s respectively; for revealing their effects on the heat transfer of the non-Newtonian nanofluid, the axial temperature distribution and the local Nusselt number are calculated
Influences of nanoparticle volume fraction and slip length on the flow of the nanofluid It is shown in equation (4) that the flow velocity is proportional to the pressure gradient and the slip length
Summary
Nomenclature a tube radius (m) tà shear stress (Pa) pà pressure (Pa) uà axial velocity (m/s) zà axial location (m) rà radial location (m) n flow behavior index of power-law fluid m consistency coefficient of power-law fluid (N:sn/m2) L: 0s slip constant (m) c: shear rate (s-1) cc critical shear rate at which the slip length diverges (s-1) r density (kg/m3) cp specific heat of the nanofluid (J/kg:K) k thermal conductivity (W/m:K) rp density of nanoparticle (kg/m3) cp,p specific heat of the nanoparticle (J/kg:K) cp,bf specific heat of the base fluid (J/kg:K) T à temperature (K) T0 constant entrance temperature (K) Nu Nusselt number h heat transfer coefficient (W/m2:K) rs slip radius r dimensionless radial location T dimensionless temperature z dimensionless axial locationPLoS ONE | www.plosone.orgPe Peclet number u average velocity (m/s) l eigenvalue h(r) eigenfunction w nanoparticle volume fraction Qà volumetric flow rate (m3/s) Subscripts w wall max maximum value b bulk fd fully developed Nanofluid is the mixture of a base fluid (i.e., water, oil etc.) and solid nanoparticles with the diameter varying between 1 to 100 nm. As nanofluids are treated as homogeneous single-phase fluids (with the assumption that the nanoparticles are uniformly distributed in base fluids) in most related works, the most efficient way is to use the macroscopic results from the numerous existed studies on the flow and heat transfer of fluids in large scale structures. The earliest slip boundary condition was proposed by Navier [6] He showed a linear relationship between the slip velocity and the shear rate at the wall. According to the results from molecular dynamics simulations, Thompson and Troian [7] discovered that the slip velocity is related to the slip length, the shear rate at the wall and a critical shear rate at which the slip length diverges
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