Abstract
An unsteady convection-radiation interaction flow of power-law non-Newtonian nanofluids using the time-fractional derivative is examined. The flow domain is an enclosure that has a free surface located at the top boundaries. Also, the geometry is filled by aluminum foam as a porous medium and the overall thermal conductivity as well as the heat capacity are approximated using a linear combination of the properties of the fluid and porous phases. Additionally, the dynamic viscosity and thermal conductivity of the mixture are expressed as a function of velocity gradients with a fractional power. Marangoni influences are imposed to the top free surface while the bottom boundaries are partially heated. Steps of the solution methodology are consisting of approximation of the time fractional derivatives using the conformable definition, using the finite differences method to discretize the governing system and implementation the resulting algebraic system. The main outcomes reveled that as the fractional order approaches to one, the maximum values of the stream function, the bulk-averaged temperature and cup-mixing temperature are reduces, regardless values of the time.