A Volume Averaging Theory for Convective Flow in a Nanofluid Saturated Metal Foam

A rigorous derivation of the macroscopic governing equations for convective flow in a nanofluid saturated metal foam has been conducted using the volume averaging theory originally developed for analyzing heat and fluid flow in porous media. The nanoparticle conservation equation at a pore scale based on the Buongiorno model has been integrated over a local control volume together with the equations of continuity, Navier–Stokes and energy conservation. The unknown terms resulting from the volume averaging procedure were modeled mathematically to obtain a closed set of volume averaged versions of the governing equations. This set of the volume averaged governing equations was analytically solved to find the velocity, temperature and nanoparticle distributions and heat transfer characteristics resulting from both thermal and nanoparticle mechanical dispersions in a nanofluid saturated metal foam. Eventually, the analysis revealed that an unconventionally high level of the heat transfer rate (about 80 times as high as the case of base fluid convection without a metal foam) can be attained by combination of metal foam and nanofluid