Fully developed slip flow in a concentric annuli via single and dual phase nanofluids models

In the present work it is aimed to obtain closed-form exact solutions for the fully developed momentum, thermal and concentration layers through a concentric annulus filled with various nanoparticle mixtures of water-based nanofluids in the presence of wall slip nanofluid velocity. The thermal boundary conditions of either both walls at fixed temperatures or of the inner wall at prescribed temperature and of the outer wall at specified heat flux are considered. Initially, the classical single phase model is adopted leading to simple formulas for the nanofluid flow and heat transfer. Then, the two-phase model of Buongiorno is considered by modifying it to incorporate the effects of nanoparticle volume fraction distribution in the full governing equations. This complex model also yields analytical formulas with regard to the momentum and thermal transport of nanoparticles of different nanofluids flowing in the concentric annuli. The essential features of nanofluids concerning the velocity, temperature and nanoparticle concentration fields as well as the rate of heat transfer are easily captured via the presented cute formulae. Particularly, the effects of Brownian and thermophoretic diffusivities as numerically examined in the literature can be investigated analytically by means of the derived solutions here valid under two distinct thermal conditions. Both models successfully explain the enhancement of heat transfer character of nanofluids by analysing the obtained exact Nusselt numbers involving several parameters of physical interest.