Fully developed mixed convection of nanofluids in microtubes at constant wall temperature: anomalous heat transfer rate and thermal performance

This is a theoretical investigation on fully developed mixed convective flow of nanofluids inside microtubes subjected to a constant wall temperature (CWT). The modified Buongiorno model is used for the nanofluids which fully accounts for the distribution of nanoparticles concentration on thermophysical properties. The effect of nanoparticles migration originating from the nano-scale diffusivities including thermophoretic diffusion (temperature-gradient driven force) and Brownian diffusion (concentration-gradient driven force) on the thermophysical characteristics of nanofluids has been considered. A Navier's slip condition is considered at the wall to model the non-equilibrium region at the fluid-solid interface in micro-scale channels. A scale analysis is performed to estimate the relative significance of the pertaining parameters that should be included in the governing equations. The effects of pertinent parameters including the ratio of Brownian motion to thermophoresis (N_BT), slip parameter (λ), mixed convective parameter (Nr), and bulk mean nanoparticle volume fraction (ϕ_B) on the flow and thermal fields are investigated. The figure of merit (FoM) is used to measure the thermal performance of equipment and finding the optimum thermal condition. It is shown that increasing the buoyancy force would enhance the heat transfer rate, especially for the larger nanoparticles. Also, larger nanoparticles enhance the thermal performance based on a required heat transfer rate with the lowest penalty in the pressure drop.