Combined thermophoresis, Brownian motion and Dufour effects on natural convection of nanofluids

The objective of the present work is to investigate theoretically the basics of natural convection heat transfer of nanofluids. On this regard thermophoresis of nanoparticles and the Dufour effect on natural convective heat transfer on nanofluids are investigated simultaneously. Positive thermophoresis implies that nanoparticles move from a hot wall to a cold wall and the Dufour effect implies that heat transfer will induce by volume fraction gradients. By using simple formulation the combined effects of Brownian motion and thermophoresis are considered to get the volume fraction distribution and its difference between hot and cold walls. Having volume fraction gradient of nanofluid, the implication of Dufour effect on the variation of heat transfer and Nusselt number of natural convection is computed. For approximate conditions closed form expression is derived to estimate Nusselt number of natural convection heat transfer for different volume fractions based on the pure water (base fluid) Nusselt number. This expression is used to predict natural convective Nusselt number for three kinds of nanofluids related to three experimental measurements of other investigators and also compared to the most recent theoretical developments. Good agreements are observed between experimental results and the present estimation due to the Dufour effect and similar trends are found by comparing with theoretical computations.