Energy saving has always been a topic of great interest. The usage of nano-enhanced phase change material NePCM is one of the energy-saving methods that has gained increasing interest. In the current report, we intend to simulate the natural convection flow of NePCM inside an inverse T-shaped enclosure. The complex nature of the flow results from the following factors: the enclosure contains a hot trapezoidal fin on the bottom wall, the enclosure is saturated with pours media, and it is exposed to a magnetic field. The governing equations of the studied system are numerically addressed by the higher order Galerkin finite element method (GFEM). The impacts of the Darcy number (Da = 10⁻²–10⁻⁵), Rayleigh number (Ra = 10³–10⁶), nanoparticle volume fraction (φ = 0–0.08), and Hartmann number (Ha = 0–100) are analyzed. The results indicate that both local and average Nusselt numbers were considerably affected by Ra and Da values, while the influence of other parameters was negligible. Increasing Ra (increasing buoyancy force) from 10³ to 10⁶ enhanced the maximum average Nusselt number by 740%, while increasing Da (increasing the permeability) from 10⁻⁵ to 10⁻² enhanced both the maximum average Nusselt number and the maximum local Nusselt number by the same rate (360%).

In a magnetic field, two-dimensional (2D) mixed convection is investigated within a zigzagged trapezoidal chamber. The lower side of the trapezoidal chamber is irregular, in particular, a zigzagged wall with different zigzag numbers N. The fluid particles move in the room due to the motion of the upper wall, while the porosity-enthalpy approach represents the melting process. The thermal parameters of the fluid are enhanced by what is called a nano-encapsulated phase change material (NEPCM) consisting of polyurethane as the shell and a nonadecane as the core, while water is used as the base fluid. In order to treat the governing equations, the well-known Galerkin finite element method (GFEM) is applied. In addition, the heat transfer (HT) irreversibility and the fluid friction (FF) irreversibility are compared in terms of the average Bejan number. The main results show that the melt band curve behaves parabolically at smaller values of Reynolds number (Re) and larger values of Hartmann number (Ha). Moreover, minimizing the wave number is better in order to obtain a higher heat transfer rate.

This paper includes a numerical investigation of a hybrid fluid containing 4% of Al₂O₃-Cu nanoparticles in a lid-driven container. The upper wall of the container has a high temperature and is movable. The lower wall is cool and wavy. An obstacle is set in the middle of the container for its effect on thermal activity. The medium is permeable to the fluid, and the entire system is immersed in a fixed-effect magnetic field. The digital simulation is achieved using the technique of Galerkin finite element (GFEM) which solves the differential equations. This investigation aims to know the pattern of heat transfer between the lateral walls and the lower wall of the container through the intervention of a set of conditions and criteria, namely: the strength of the magnetic field changes in the range of (Ha = 0 to 100); the chamber porosity varies in the range of (Da = 10⁻⁵ to 10⁻²); the strength of buoyancy force is varied according to the Grashof number (Gr = 10² to 10⁴); the cross-section of the baffle includes the following shapes—elliptical, square, triangular and circular; the surface of the lower wall contains waves; and the number changes (N = 2 to 8). Through this research, it was concluded that the triangular shape of the baffle is the best in terms of thermal activity. Also, increasing the number of lower-wall waves reduces thermal activity. For example, the change in the shape of the obstacle from the elliptical to triangular raises the value of Nu number at a rate of 15.54% for Ha = 0, N = 8, and Gr = 10⁴.

This paper presents a numerical simulation of a magneto-convection flow in a 3D chamber. The room has a very specific permeability and a zigzag bottom wall. The fluid used in this study is Al₂O₃-Cu/water with 4% nanoparticles. The Galerkin finite element technique (GFEM) was developed to solve the main partial equations. The hybrid nanofluid inside the container is subjected to the horizontal motion of the upper wall, an external magnetic field, and a thermal buoyancy force. The present numerical methodology is validated by previous data. The goal of this investigation was to understand and determine the percentage of heat energy transferred between the nanofluid and the bottom wall of the container under the influence of a set of criteria, namely: the movement speed of the upper wall of the cavity (Re = 1 to 500), the amount of permeability (Da = 10⁻⁵ to 10⁻²), the intensity of the external magnetic field (Ha = 0 to 100), the number of zigzags of the lower wall (N = 1 to 4), and the value of thermal buoyancy when the force is constant (Gr = 1000). The contours of the total entropy generation, isotherm, and streamline are represented in order to explain the fluid motion and thermal pattern. It was found that the heat transfer is significant when (N = 4), where the natural convection is dominant and (N = 2), and the forced convection is predominant.

The two-dimensional numerical investigation is well accomplished to understand the behavior of buoyancy-driven flow in closed annular space. The studied domain consists of a pair of equal-sized circular cylinders in tandem arrangement confined in a circular enclosure which is filled with incompressible Newtonian fluid. The inner cylinders are identical in size and they are supposed to be hot with constant temperature, the outer circular enclosure is kept cold with a constant temperature. The descriptive governing equations of continuity, momentum and energy for the present problem are solved numerically using the finite-volume method. The present research studies the effects of thermal buoyancy strength, the thermophysical characteristics of the fluid, and the size of the inner cylinders on the flow patterns inside the circular domain and rate of heat transfer exchanging between the inner cylinders and fluid flow. The results showed that the studied governing parameters significantly affect the fluid flow and heat transfer rate. An increase in the diameter of inner cylinders makes the effect of buoyancy strength on fluid flow and heat transfer negligible for all values of thermo-physical parameters. Also, the average Nusselt number of each inner cylinder is computed and plotted for industrial applications.