Finite Element Methodology of Hybridity Nanofluid Flowing in Diverse Wavy Sides of Penetrable Cylindrical Chamber under a Parallel Magnetic Field with Entropy Generation Analysis

In a cylindrical cavity, the convection and entropy of the hybrid nanofluid were studied. We have introduced a rectangular fin inside the cylinder; the fin temperature is at [Formula: see text]. The right waving wall is cooled to [Formula: see text]. The upper and lower walls are insulated. This study contains the induction of a constant magnetic field. The Galerkin finite element method (GFEM) is utilized to treat the controlling equations obtained by giving Rayleigh number values between [Formula: see text] (10(3)–10(6)) and Hartmann number ratio [Formula: see text] (0, 25, 50, 100) and Darcy ranging between [Formula: see text] (10(−2)–10(−5)) and the porosity ratio is [Formula: see text] (0.2, 0.4, 0.6, 0.8), and the size of the nanoparticles is [Formula: see text] (0.02, 0.04, 0.06, 0.08). The range is essential for controlling both fluid flow and the heat transport rate for normal convection. The outcomes show how Da affects entropy and leads to a decline in entropy development. The dynamic and Nusselt mean diverge in a straight line. The domain acts in opposition to the magnetic force while flowing. Highest entropy-forming situations were found in higher amounts of [Formula: see text] , [Formula: see text] , and initial values of [Formula: see text]. Parameters like additive nanoparticles ([Formula: see text]) and porosity ([Formula: see text]) exert diagonal dominant trends with their improving values.