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A simple mathematical model for calculating the effective thermal conductivity of nanofluids has been developed based on the thermal resistance approach. The model is developed by considering both effects of a solid-like nanolayer and convective heat transfer caused by Brownian motion which have not been considered simultaneously by most available models in the literature. In addition the correlation of Prasher and Phelan for the convective heat transfer coefficient is modified to take into account the effect of the solid-like nanolayer. In addition a general value for n (different from the one presented by Tillman and Hill) is introduced to modify the thickness of the solid-like nanolayer. The latter is done by considering both conduction and convection heat transfer mechanisms. Comparisons with previously published experimental results and other mathematical models show that the presented model could well predict a nanofluids effective thermal conductivity as a function of the nanoparticles mean diameter, volume fraction, and temperature for different kinds of nanofluids.

Laminar mixed convection of a nanofluid consisting of water and Al2O3 in an inclined tube with heating at the top half surface of a copper tube has been studied numerically. The bottom half of the tube wall is assumed to be adiabatic (presenting a tube of a solar collector). Heat conduction mechanism through the tube wall is considered. Three-dimensional governing equations with using two-phase mixture model have been solved to investigate hydrodynamic and thermal behaviours of the nanofluid over wide range of nanoparticle volume fractions. For a given nanoparticle mean diameter the effects of nanoparticle volume fractions on the hydrodynamics and thermal parameters are presented and discussed at different Richardson numbers and different tube inclinations. Significant augmentation on the heat transfer coefficient as well as on the wall shear stress is seen.

An inverse analysis is employed to estimate the unknown heat flux distribution over the heater surface of an irregular 2-D domain with participating media from the knowledge of a desired temperature and heat flux distributions over a given design surface. The discrete transfer method is employed to solve the radiative transfer equation and a conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired heat fluxes. The performance of the present technique for inverse radiation analysis is evaluated by several numerical experiments.