The baffle shape effects on natural convection flow and entropy generation in a nanofluid-filled permeable container with a magnetic field.

Enhancing heat transfer rates within enclosures is a topic of considerable interest since it has several technical applications. Most heat transfer research projects focus on increasing the heat transfer rates of thermal systems since this will raise the systems' total efficiency. The geometry of the enclosure might have a substantial impact on heat transfer rates. This research studies quantitatively the natural convection of a nanofluid in a complicated form geometry with many baffle configurations. The system's governing equations were addressed by the Galerkin Finite Element Method (GFEM). The main consideration was given to the effects of the following factors: The Darcy number (Da), which ranges from 10-2 to 10-5; the Hartmann number (Ha), which ranges from 0 to 100; the volumetric fraction (ϕ), which ranges from 0 to 0.08, and the Rayleigh number (Ra) (102 to 106). The results suggested that raising Ra increases heat transfer discharge, whereas raising Ha and Da decreases it. In terms of heat transmission, case 1 (the case with a wavenumber of 1 and the zigzag pointing outward) is determined to be the optimum cavity structure, as it obtained the highest mean Nusselt (Nuavg) number when compared to other cases. At the highest studied Ra number, growing (ϕ) from 0 to 0.8 improved Nuavg by 25%, while growing Da from 10-2 to 10-5 and Ha from 0 to 100 declined Nuavg by 57% and 48%, respectively. The reason for the improvement in the values of the (Nu) is due to the speed of fluid movement within the compartment. Also, the shape of fins plays a major role in strengthening and weakening thermal activity.

Nanoencapsulated phase change material in a trapezoidal prism wall under the magnetic field effect for energy storage purposes.

Recently, Nano-encapsulated phase change materials (NEPCM) have attracted the attention of researchers due to their promising application in thermal management. This research investigates magnetohydrodynamic mixed convection of NEPCM contained within a lid-driven trapezoidal prism enclosure containing a hot-centered elliptical obstacle. The upper cavity wall is moving at a constant velocity; both inclined walls are cold, while the rest of the walls are insulated. The Galerkin Finite Element Method was used to solve the system's governing equations. The influence of Reynolds number (Re 1-500), Hartmann number (Ha = 0-100), NEPCM volumetric fraction φ (0-8%), and elliptical obstacle orientation α (0-3π/4) on thermal fields and flow patterns are introduced and analyzed. The results indicated that the maximum heat transfer rate is observed when the hot elliptic obstacle is oriented at 90°; an increment of 6% in the Nu number is obtained in this orientation compared to other orientations. Reducing Ha from 100 to 0 increased Nu by 14%. The Maximum value of the Bejan number was observed for the case of Ha = 0, α = 90° and φ = 0.08.

Corrigendum: Numerical study of perforated obstacles effects on the performance of solar parabolic trough collector.

[This corrects the article DOI: 10.3389/fchem.2022.1089080.].

2D MHD Mixed Convection in a Zigzag Trapezoidal Thermal Energy Storage System Using NEPCM.

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.

Natural Convection within Inversed T-Shaped Enclosure Filled by Nano-Enhanced Phase Change Material: Numerical Investigation.

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%).

Enhancing the Melting Process of Shell-and-Tube PCM Thermal Energy Storage Unit Using Modified Tube Design.

Recently, phase change materials (PCMs) have gained great attention from engineers and researchers due to their exceptional properties for thermal energy storing, which would effectively aid in reducing carbon footprint and support the global transition of using renewable energy. The current research attempts to enhance the thermal performance of a shell-and-tube heat exchanger by means of using PCM and a modified tube design. The enthalpy-porosity method is employed for modelling the phase change. Paraffin wax is treated as PCM and poured within the annulus; the annulus comprises a circular shell and a fined wavy (trefoil-shaped) tube. In addition, copper nanoparticles are incorporated with the base PCM to enhance the thermal conductivity and melting rate. Effects of many factors, including nanoparticle concentration, the orientation of the interior wavy tube, and the fin length, were examined. Results obtained from the current model imply that Cu nanoparticles added to PCM materials improve thermal and melting properties while reducing entropy formation. The highest results (27% decrease in melting time) are obtained when a concentration of nanoparticles of 8% is used. Additionally, the fins' location is critical because fins with 45° inclination could achieve a 50% expedition in the melting process.

Numerical Study of Heat Transfer Enhancement within Confined Shell and Tube Latent Heat Thermal Storage Microsystem Using Hexagonal PCMs.

Thermophoresis represents one of the most common methods of directing micromachines. Enhancement of heat transfer rates are of economic interest for micromachine operation. This study aims to examine the heat transfer enhancement within the shell and tube latent heat thermal storage system (LHTSS) using PCMs (Phase Change Materials). The enthalpy-porosity approach is applied to formulate the melting situation and various shapes of inner heated fins are considered. The solution methodology is based on the Galerkin finite element analyses and wide ranges of the nanoparticle volume fraction are assumed, i.e., (0% ≤ φ ≤ 6%). The system entropy and the optimization of irreversibility are analyzed using the second law of the thermodynamics. The key outcomes revealed that the flow features, hexagonal entropy, and melting rate might be adjusted by varying the number of heated fins. Additionally, in case 4 where eight heated fins are considered, the highest results for the average liquid percentage are obtained.

Lid-Driven Chamber with 3D Elliptical Obstacle under the Impacts of the Nano-Properties of the Fluid, Lorentz Force, Thermal Buoyancy, and Space Porosity.

In this work, we have performed an investigation to increase our understanding of the motion of a hybrid nanofluid trapped inside a three-dimensional container. The room also includes a three-dimensional heated obstacle of an elliptic cross-section. The top wall of space is horizontally movable and adiabatic, while the lower part is zigzagged and thermally insulated as well. The lateral walls are cold. The container's space is completely replete with Al2O3-Cu/water; the concentration of nanoparticles is 4%. The space is also characterized by the permeability, which is given by the value of the Darcy number (limited between 10-5 and 10-2). This studied system is immersed in a magnetic field with an intensity is defined in terms of Hartmann number (limited between 0 and 100). The thermal buoyancy has a constant impact (Gr = 1000). This study investigates the influences of these parameters and the inclination angle of the obstacle on the heat transfer coefficient and entropy generation. The Galerkin finite element method (GFEM) was the principal technique for obtaining the solution of the main partial equations. Findings from our work may be exploited to depict the conditions for which the system is effective in thermal cooling and the case in which the system is effective in thermal insulation.

Numerical Study of Lid-Driven Hybrid Nanofluid Flow in a Corrugated Porous Cavity in the Presence of Magnetic Field.

The lid-driven top wall's influence combined with the side walls' waviness map induce the mixed convection heat transfer, flow behavior, and entropy generation of a hybrid nanofluid (Fe3O4-MWCNT/water), a process analyzed through the present study. The working fluid occupies a permeable cubic chamber and is subjected to a magnetic field. The governing equations are solved by employing the GFEM method. The results show that the magnetic force significantly affects the working fluid's thermal and flow behavior, where the magnetic force's perpendicular direction remarkably improves the thermal distribution at Re = 500. Also, increasing Ha and decreasing Re drops both the irreversibility and the heat transfer rate. In addition, the highest undulation number on the wavy-sided walls gives the best heat transfer rate and the highest irreversibility.

Review of Heat Transfer Analysis in Different Cavity Geometries with and without Nanofluids.

Many strategies have been attempted for accomplishing the needed changes in the heat-transfer rate in closed cavities in recent years. Some strategies used include the addition of flexible or hard partitions to the cavities (to split them into various pieces), thickening the borders, providing fins to the cavities, or altering the forms or cavity angles. Each of these methods may be used to increase or decrease heat transmission. Many computational and experimental investigations of heat transport in various cavity shapes have been conducted. The majority of studies focused on improving the thermal efficiency of heat transmission in various cavity containers. This paper introduced a review of experimental, numerical, and analytical studies related to heat transfer analyses in different geometries, such as circular, cylindrical, hexagonal, and rectangular cavities. Results of the evaluated studies indicate that the fin design increased heat transmission and sped up the melting time of the PCM; the optimal wind incidence angle for the maximum loss of combined convective heat depends on the tilt angle of the cavity and wind speed. The Nusselt number graphs behave differently when decreasing the Richardson number. Comparatively, the natural heat transfer process dominates at Ri = 10, but lid motion is absent at Ri = 1. For a given Ri and Pr, the cavity without a block performed better than the cavity with a square or circular block. The heat transfer coefficient at the heating sources has been established as a performance indicator. Hot source fins improve heat transmission and reduce gallium melting time.

A Numerical Investigation of a Melting Rate Enhancement inside a Thermal Energy Storage System of Finned Heat Pipe with Nano-Enhanced Phase Change Material.

Thermal energy storage via the use of latent heat and phase transition materials is a popular technology in energy storage systems. It is vital to research different thermal enhancement techniques to further improve phase transition materials' weak thermal conductivity in these systems. This work addresses the creation of a basic shell and a tube thermal storage device with wavy outer walls. Then, two key methods for thermal augmentation are discussed: fins and the use of a nano-enhanced phase change material (NePCM). Using the enthalpy-porosity methodology, a numerical model is developed to highlight the viability of designing such a model utilizing reduced assumptions, both for engineering considerations and real-time predictive control methods. Different concentrations of copper nanoparticles (0, 2, and 4 vol%) and wavenumbers (4,6 and 8) are investigated in order to obtain the best heat transmission and acceleration of the melting process. The time required to reach total melting in the studied TES system is reduced by 14% and 31% in the examined TES system, respectively, when NePCM (4 vol% nanoparticles) and N = 8 are used instead of pure PCM and N = 4. The finding from this investigation could be used to design a shell-and-tube base thermal energy storage unit.

Entropy Generation in 2D Lid-Driven Porous Container with the Presence of Obstacles of Different Shapes and under the Influences of Buoyancy and Lorentz Forces.

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.

Melting enhancement of PCM in a finned tube latent heat thermal energy storage.

The current paper discusses the numerical simulation results of the NePCM melting process inside an annulus thermal storage system. The TES system consists of a wavy shell wall and a cylindrical tube equipped with three fins. The enthalpy-porosity method was utilized to address the transient behavior of the melting process, while the Galerkin FE technique was used to solve the system governing equations. The results were displayed for different inner tube positions (right-left-up and down), inner cylinder rotation angle (0 ≤ α ≤ 3π/2), and the nano-additives concentration (0 ≤ ϕ ≤ 0.04). The findings indicated that high values of nano-additives concentration (0.4), bigger values of tube rotation angle (3π/2), and location of the tube at the lower position accelerated the NePCM melting process.

Numerical Study of 3D MHD Mixed Convection and Entropy Generation in Trapezoidal Porous Enclosure Filled with a Hybrid Nanofluid: Effect of Zigzag Wall and Spinning Inner Cylinder.

A numerical study was performed to analyze the impact of the combination of several factors on heat transfer rate, flow behavior, and entropy generation in a hybrid nanofluid occupying a porous trapezoid enclosure containing a rotating inner tube. The governing equations were discretized and solved using the Finite Element Method using Comsol multiphysics. The effects of the Darcy and Hartman number, nanoparticle volume fraction (from 0 to 6%), the utilization of various zigzag patterns of the hot wall, and the rotation speed of the inner tube (Ω = 100. 250 and 500) are illustrated and discussed in this work. The outputs reveal that flow intensity has an inverse relationship with Hartman number and a direct relationship with the Darcy number and the velocity of the inner tube, especially at high numbers of undulations of the zigzag hot wall (N = 4); also, intensification of heat transfer occurs with increasing nanoparticle volume fraction, Darcy number and velocity of the inner tube. In addition, entropy generation is strongly affected by the mentioned factors, where increasing the nanoparticle concentration augments the thermal entropy generation and reduces the friction entropy generation; furthermore, the same influence can be obtained by increasing the Hartman number or decreasing the Darcy number. However, the lowest entropy generation was found for the case of Ø = 0, Ha = 0 and Da = 0.01.

Darcy-Forchheimer Flow of Water Conveying Multi-Walled Carbon Nanoparticles through a Vertical Cleveland Z-Staggered Cavity Subject to Entropy Generation.

To date, when considering the dynamics of water conveying multi-walled carbon nanoparticles (MWCNT) through a vertical Cleveland Z-staggered cavity where entropy generation plays a significant role, nothing is known about the increasing Reynold number, Hartmann number, and Darcy number when constant conduction occurs at both sides, but at different temperatures. The system-governing equations were solved using suitable models and the Galerkin Finite Element Method (GFEM). Based on the outcome of the simulation, it is worth noting that increasing the Reynold number causes the inertial force to be enhanced. The velocity of incompressible Darcy-Forchheimer flow at the middle vertical Cleveland Z-staggered cavity declines with a higher Reynold number. Enhancement in the Hartman number causes the velocity at the center of the vertical Cleveland Z-staggered cavity to be reduced due to the associated Lorentz force, which is absent when Ha = 0 and highly significant when Ha = 30. As the Reynold number grows, the Bejan number declines at various levels of the Hartmann number, but increases at multiple levels of the Darcy number.

Irreversibility Interpretation and MHD Mixed Convection of Hybrid Nanofluids in a 3D Heated Lid-Driven Chamber.

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.

Hydrothermal and Entropy Investigation of Nanofluid Natural Convection in a Lid-Driven Cavity Concentric with an Elliptical Cavity with a Wavy Boundary Heated from Below.

This work investigates mixed convection in a lid-driven cavity. This cavity is filled with nanofluid and subjected to a magnetic field. The concentric ovoid cavity orientation (γ), 0−90°, and undulation number (N), 1−4, are considered. The Richardson number (Ri) varies between 1 and 100. The nanofluid volume fraction (φ) ranges between 0 and 0.08%. The effect of the parameters on flow, thermal transport, and entropy generation is illustrated by the stream function, isotherms, and isentropic contours. Heat transfer is augmented and the Nusselt number rises with higher Ri, γ, N, and φ. The simulations show that the heat transfer is responsible for entropy generation, while frictional and magnetic effects are marginal.

Hydrothermal and Entropy Investigation of Nanofluid Mixed Convection in Triangular Cavity with Wavy Boundary Heated from below and Rotating Cylinders.

Nanofluids have become important working fluids for many engineering applications as they have better thermal properties than traditional liquids. Thus, this paper addresses heat transfer rates and entropy generation for a Fe3O4/MWCNT-water hybrid nanoliquid inside a three-dimensional triangular porous cavity with a rotating cylinder. The studied cavity is heated by a hot wavy wall at the bottom and subjected to a magnetic field. This problem is solved numerically using the Galerkin finite element method (GFEM). The influential parameters considered are the rotating cylinder speed, Hartmann number (Ha), Darcy number (Da), and undulation number of the wavy wall. The results showed that higher Da and lower Ha values improved the heat transfer rates in the cavity, which was demonstrated by a higher Nusselt number and flow fluidity. The entropy generation due to heat losses was also minimized for the enhanced heat transfer rates. The decrease in Ha from 100 and 0 improved the heat transfer by about 8%, whereas a high rotational speed and high Da values yield optimal results. For example, for Ω = 1000 rad/s and Da = 10-2, the enhancement in the average Nusselt number is about 38% and the drop in the Bejan number is 65% compared to the case of Ω = 0 rad/s and Da = 10-5. Based on the applied conditions, it is recommended to have a high Da, low Ha, one undulation for the wavy wall, and high rotational speed for the cylinder in the flow direction.

Numerical Simulations of Magnetohydrodynamics Natural Convection and Entropy Production in a Porous Annulus Bounded by Wavy Cylinder and Koch Snowflake Loaded with Cu-Water Nanofluid.

The current paper presents a numerical study of the magnetohydrodynamics natural convection and entropy production of Cu-water nanofluid contained in a porous annulus between a heated Koch snowflake and wavy cylinder with lower temperature with respect to the Koch snowflake. The numerical algorithm is based on the Galerkin Finite Element Method. The impacts of Rayleigh number (Ra = 103, 104, 105, and 106), Hartman number (Ha = 0, 25, 50, and 100), Darcy number (Da = 10-2, 10-3, 10-4, and 10-5), nanoparticle volumetric fraction (φ = 2%, 3%, 4%, and 5%), and the undulations number of the outer wavy cylinder (three cases) on the distributions of isotherms, streamlines, mean Nusselt number (Nuavg), as well as on total entropy production and Bejan number are thoroughly examined. The computational outcomes disclose that dispersing more Cu nanoparticles in the base fluid and creating a flow with higher intensity inside the annulus by raising the Rayleigh number bring about a boosted natural convective flow in the cavity, which improves the heat transmission rate. In addition, it can be noted that owing to the peculiar form of the heated Koch snowflake, nanofluid gets trapped between the angled parts, resulting in uneven temperature profiles with higher values in these places.