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•Exploration of magnetic field and rotating cylinder on mixed convection in a non-Newtonian nanofluid-filled oval enclosure.•Application of Galerkin Finite Element Method for analysis, considering differential heating and cooling on inner cylinder and enclosure walls.•Oval enclosure design with a cold outer wall and a heated inner cylinder wall, using a single-phase fluid (water) infused with copper nanoparticle.•Investigation of key parameters encompassing a range of Ri, Ha, φ, n index, eccentricity (e), and angle (β) to comprehensively analyze the system.•Enhanced convective heat transfer observed at e = -0.3, with peak rates at β = 60 and 240.

In nuclear power industry, the energy conservation of heat exchangers is a crucial demand. The current study addresses the influence of nano-encapsulated phase change material (NEPCM) on free convection under magnetic force in a porous enclosure involving two active cylinders. The curvilinear geometry of the enclosure is set with undulated top wall. The top, horizontal and the inclined walls are set cold while the two cylinders presented the hot surface. All other walls are assumed to be adiabatically isolated. The considered parameters are Rayleigh number, Ra(103–105), Hartmann number, Ha(0–64), fusion temperature, θf(0.1–0.9), Stefan number, Ste (0.1–0.9), volume concentration, ϕ (0–0.05), Darcy number, Da(10−5–10−2). Finite element method has been used in the numerical analysis. Some of the most important results stated that fusion temperature has a significant influence on heat transfer only with high Ranumber and low Ste number. Furthermore, the melting solidification region notably changed with the change of Daand θfwith less influec under the magnetic force. Also, the heat transfer is enhanced with the increase of Ra, Daand ϕ while it diminished with the increase of Stephan number and MHD. It found that a promotion in the percentage of Nuavgwhen the volume concentration is raised from 0 to 0.05 is about 65 %, while the Nuavgdwindles by 14 % when Hartman number is raised from 0 to 64. It can be concluded that using NEPCMs is crucial for enhancing heat transfer and hence the improving the related engineering applications.

•The entropy generation and natural convection in a Z-staggered cavity filled with a porous media filled with a TiO2-water nanofluid were investigated.•The fundamental equations are solved using the Galerkin Finite Element Method (GFEM), and the results are described in detail.•This study is essential for a variety of applications, including heat exchanger cooling of electronic equipment, solar pond, natural gas tank storage, material, and gas transference.•Increasing the volume fraction of nanoparticles enhanced the heat transfer but reduced the maximum values of streamlines owing to the more significant density of nanofluid.•The inclination angle considerably influenced natural convection; the most significant value of streamline occurred at an inclination angle (γ) of 60.