An analytical consideration has been made to explore the velocity, temperature and nanoparticle distributions and heat transfer characteristics associated with thermal dispersion and nanoparticle mechanical dispersion within a nanofluid-saturated homogeneous metal foam. A volume-averaging theory was rigorously applied to integrate locally a set of governing equations based on the modified Buongiorno model at the pore scale. Thus, a macroscopic set of volume-averaged governing equations were derived allowing interstitial heat transfer between the nanofluid and metal phases. Unknown terms were modelled mathematically to obtain a closed set of volume-averaged governing equations. Subsequently, a pore-scale analysis was carried out to find possible functional forms for describing thermal dispersion and nanoparticle mechanical dispersion in a nanofluid-saturated metal foam. Using the resulting set of volume-averaged governing equations, forced convective flows in nanofluid-saturated metal foams were analytically investigated for the steady-state case. Eventually, it has been predicted that an unconventionally high level of the heat transfer rate (about 80 times more than the case of base fluid convection without a metal foam) may be achieved by combination of metal foam and nanofluid.

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