Applied Mathematics and Scientific Computing pp 255-263 | Cite as

# Natural Convection of Newtonian Liquids and Nanoliquids Confined in Low-Porosity Enclosures

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## Abstract

Natural convection of nanoliquids confined in a low-porosity enclosure when the lateral walls are subject to constant heat and mass fluxes is studied analytically using modified Buongiorno-Darcy model and Oseen-linearised approximation. For the study we considered water-copper nanoliquid and aluminium foam, glass balls as porous materials. The effective thermophysical properties are calculated using phenomenological laws and mixture theory. An analytical solution is obtained for boundary layer velocity and Nusselt number. The study shows that dilute concentration of high thermal conductivity nanoparticles significantly facilitates enhanced heat transport. The porous medium, however, diminishes heat transport when the thermal conductivity of the porous material, *k*_{pm}, is less compared to that of nanoparticles, *k*_{np}. When *k*_{pm} ≥ *k*_{np} then the presence of nanoparticles does not affect the heat transport.

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