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Finite element treatment for nanofluids flow within enclosures filled with hydrodynamically and thermally anisotropic porous media: Impacts of sinusoidal heating

The local thermal non‐equilibrium model (LTNEM) in case of a sinusoidal heating is applied to investigate the unsteady nanofluid flow and thermal fields inside an inclined enclosure filled with a thermally and hydrodynamically anisotropic porous medium. The Galerkin finite element method (GFEM) together with the Characteristic‐based Split (CBS) Scheme is used to solve the dimensionless governing equations. Impacts of the controlling parameters are studied in two cases, namely, non‐Darcy Regime in which values of the Darcy number and the Rayleigh number are, respectively, Da=10−2,Ra=105 and the Darcy regime where Da=10−6,Ra=109 . Parametric studies are performed for wide ranges of the permeability ratio 0.1≤K∗≤10 , the Nield number 0≤H≤1000 , the inclination angle 0≤γ≤π2 , the nanoparticles volume fraction 0≤ϕ≤4% , the inclination of the principal axes 0≤ϑ≤π2 , the amplitude ratio 0≤a≤1 and the phase deviation 0≤Φ≤π2 . The main outcomes revealed that the sinusoidal heating results in multicellular flow components inside the geometry. Also, the increase in the Nield number causes that the system converts from the LTNE state to local thermal equilibrium (LTE) state. For the non‐Darcy regime, the convective process and the rate of the heat transfer are augmented as the inclination of the principal axes is increased.