Nanofluid flows within porous enclosures using non-linear boussinesq approximation

In this paper, the Galerkin finite element method (FEM) together with the characteristic-based split (CBS) scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined enclosures filled with a non-Darcy porous media and nanofluids. The enclosure has an inclination angle and its side-walls have varying sinusoidal temperature distributions. The working fluid is a nanofluid that is consisting of water as a based nanofluid and Al₂O₃ as nanoparticles. The porous medium is modeled using the Brinkman Forchheimer extended Darcy model. The obtained results are analyzed over wide ranges of the non-linear Boussinesq parameter 0 ≤ ζ ≤1, the phase deviation 0⁰ ≤ Φ ≤ 180⁰, the inclination angle 0⁰ ≤ γ ≤ 90⁰, the nanoparticles volume fraction 0% ≤ φ ≤ 4%, the amplitude ratio 0 ≤ a ≤1 and the Rayleigh number 10⁴ ≤ Ra ≤ 10⁶. The results revealed that the average Nusselt number is enhanced by 0.73%, 26.46% and 35.42% at Ra = 10⁴, 10⁵ and 10⁶, respectively, when the non-linear Boussinesq parameter is varied from 0 to 1. In addition, rate of heat transfer in the case of a non-uniformly heating is higher than that of a uniformly heating. Non-linear Boussinesq parameter rises the flow speed and heat transfer in an enclosure. Phase deviation makes clear changes on the isotherms and heat transfer rate on the right wall of an enclosure. An inclination angle varies the flow speed and it has a slight effect on heat transfer in an enclosure.