Heat transfer in a symmetrical cavity with two semi-cylinders was explored in this study. Several parameters, such as (${10}^3\le Ra\le {10}^6$), (${10}^{-5}\le Da\le {10}^{-2}$), ($0.02\le \varphi \le 0.08$), ($0.2\le \epsilon \le 0.8$), and ($0\le Ha\le 100$) were selected and evaluated in this research. The outcome of the magnetic field and the temperature gradient on the nanofluid flow is considered. The geometric model is therefore described using a symmetry technique. The flow issue for the governing equations has been solved using the Galerkin finite element method (G-FEM), and these solutions are presented in dimensionless form. The equations for energy, motion, and continuity were solved using the application of the COMSOL Multiphysics^® software computer package. According to the results, there is a difference in the occurrence of the magnetic parameter and an increase in heat transmission when the right wall is recessed inward. The heat transmission is also significantly reduced when the right wall is exposed to the outside. The number of Nusselt grows directly proportional to the number of nanofluids in the environment. In contrast, all porous media with low Darcy and Hartmann numbers, high porosity, and low volume fraction have high Nusselt numbers. It is found that double streamlines for the hot side and single cooling for Darcy, Rayleigh, and Hartmann numbers. A cold isotherm at various physical parameters is needed in the top cavity. Rayleigh’s number and a solid volume fraction raise Darcy’s number, increasing heat transmission inside the cavity and thermal entropy determines entropy components.

This research presents a numerical investigation of the flow field and heat transfer of a Visco-plastic fluid, The Bingham-Papanastasiou model is used to examine the flow field and forced convection heat transfer of a Viscoplastic fluid between two concentric cylinders with a wavy inner surface. By focusing on this particular configuration (wavy inner cylinder shape), where the inner surface exhibits as the hot wall while the outer surface is considered as the cold wall. This investigation is numerically achieved by using the Comsol Multiphysics, which is based on the finite‐volume method, employing Galerkin’s method for solving the governing equations. The parameters studied in this research are expressed with the following values: r/ R=1/3, Reynolds number (Re=1, 10, 50), and undulation number (nu=0, 6, 12, 24). Increasing the inertia parameter results in a higher intensity of thermal buoyancy, positively influencing heat transfer, particularly at Re=50. Furthermore, the acceleration of flow within the investi-gated space improves the hydrodynamic behavior, facilitating the exchange of thermal energy between the hot and cold walls. Additionally, it has been discovered that an undulating shape with a specific number of undulations (nu=6) maximizes hydrothermal performance within the investigated volume. The presence of these undulations enhances fluid mixing and dis-rupts the formation of stagnant regions ,which leading to improved heat transfer.

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 $T_h$. The right waving wall is cooled to $T_c$. 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 $Ra$ (10³–10⁶) and Hartmann number ratio $Ha$ (0, 25, 50, 100) and Darcy ranging between $Da$ (10⁻²–10⁻⁵) and the porosity ratio is $\epsilon$ (0.2, 0.4, 0.6, 0.8), and the size of the nanoparticles is $\varphi$ (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 $Ra$, $Da$, and initial values of $Ha$. Parameters like additive nanoparticles ($\varphi$) and porosity ($\epsilon$) exert diagonal dominant trends with their improving values.