Transient free convective heat transfer in nanoliquid-saturated porous square cavity with a concentric solid insert and sinusoidal boundary condition

In this study, we use the finite-difference method to numerically investigate the problem of transient free convective heat transfer in a nanoliquid-saturated porous square cavity with a sinusoidal boundary condition. The left vertical wall of the cavity is maintained at a constant temperature and the right wall is heated sinusoidally. The horizontal insulated walls allow no heat transfer to the surrounding. To regulate the heat transfer, we insert a solid square at the centre of the cavity in such a way that there is symmetry in the flow configuration. We use the Darcy law along with the Boussinesq approximation for the flow, and for the investigation, we employ water-based nanoliquids with Cu, Al2O3 or TiO2 nanoparticles. We obtain the results of this study for various parameters such as Rayleigh number, periodicity parameter, nanoparticle volume fraction, thermal conductivity ratio, length of the inner solid, modified conductivity ratio, and dimensionless time. We explain the differ