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In the oil and gas industry, enhanced oil recovery (EOR) strategies for unconventional reservoirs, characterized by complex geometries, differ significantly from those used in conventional reservoirs. This research focuses on the impact of 3D hexagonal prism geometries on EOR in hypothetical oil reservoirs using silicon dioxide (SiO₂) magnetic nanoparticles under liquid-phase flow conditions, a topic not extensively explored in existing literature. We developed an improved magnetohydrodynamic (MHD) mathematical models to simulate oil recovery processes in these geometries, using ANSYS Fluent for finite volume analysis. We developed an improved magnetohydrodynamic (MHD) model by incorporating magnetic field-induced pressure terms, nanoparticle transport losses, and a 3D hexagonal prism geometry that reflects complex reservoir behavior. These enhancements extend beyond traditional Darcy-based models by integrating magnetic permeability, viscosity alteration, and magnetic field-pore interactions. The model evaluates the impact of key reservoir parameters including porosity (ϕ = 0.1–0.4), injection flow rate (0.01–0.05 mL/min), and nanoparticle concentration (Ψ = 0.01–0.04), under different magnetic field configurations. Porosity and flow rate were also found to significantly influence recovery performance, highlighting the practical adaptability of the model for diverse reservoir conditions. Findings indicate that proximity of a magnetic field to cavity structures enhances oil recovery rates, with a significant 29.08% increase in recovery from nanoflooding compared to water flooding.Future research will extend this framework to study green, eco-friendly nanoparticles under elevated temperature and pressure, aiming to improve thermal stability, reduce environmental risks, and enhance recovery efficiency in more extreme reservoir conditions.

This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure (cavity) to determine the oil extraction rate using three distinct nanoparticles, SiO2, Al2O3, and Fe2O3, in unconventional oil reservoirs. The simulation is conducted for different parameters of volume fractions, porosities, and mass flow rates to determine the optimal oil recovery. The impact of nanoparticles on relative permeability ( and water is also investigated. The simulation process utilizes the finite volume ANSYS Fluent. The study results showed that when the mass flow rate at the inlet is low, oil recovery goes up. In addition, they indicated that silicon nanoparticles are better at getting oil out of the ground (i.e., oil reservoir) than Al2O3 and Fe2O3. Most oil can be extracted from SiO2, Al2O3, and Fe2O3 at a rate of 97.8%, 96.5%, and 88%, respectively.

A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish. This article investigated the development of glioma cells in treating brain tumors. Mathematically, reaction-diffusion models have been developed for brain glioma growth to quantify the diffusion and proliferation of the tumor cells within brain tissues. This study presents the formulation the two-stage successive over-relaxation (TSSOR) algorithm based on the finite difference approximation for solving the treated brain glioma model to predict glioma cells in treating the brain tumor. Also, the performance of TSSOR method is compared to the Gauss-Seidel (GS) and two-stage Gauss-Seidel (TSGS) methods in terms of the number of iterations, the amount of time it takes to process the data, and the rate at which glioma cells grow the fastest. The implementation of the TSSOR, TSGS, and GS methods predicts the growth of tumor cells under the treatment protocol. The results show that the number of glioma cells decreased initially and then increased gradually by the next day. The computational complexity analysis is also used and concludes that the TSSOR method is faster compared to the TSGS and GS methods. According to the results of the treated glioma development model, the TSSOR approach reduced the number of iterations by between 8.0 and 71.95%. In terms of computational time, the TSSOR approach is around 1.18–76.34% faster than the TSGS and GS methods. •The development of glioma cells was investigated in the treatment of brain tumors.•To predict glioma cells in the treatment of brain tumor, the formulation of a two-stage sequential hyperrelaxation algorithm based on the finite difference approach to solve the treated brain glioma model is presented.•The performance of the TSSOR method was compared with the Gauss-Seidel (GS) and two-stage Gauss-Seidel methods (TSGS) in terms of the number of iterations, the time taken to process the data, and the data processing speed.•The computational complexity analysis is also used and it is concluded that the TSSOR method is faster than the TSGS and GS methods.

Enhanced oil recovery (EOR) has been offered as an alternative to declining crude oil production. EOR using nanotechnology is one of the most innovative trends in the petroleum industry. In order to determine the maximum oil recovery, the effect of a 3D rectangular prism shape is numerically investigated in this study. Using ANSYS Fluent software(2022R1), we develop a two-phase mathematical model based on 3D geometry. This research examines the following parameters: flow rate Q = 0.01–0.05 mL/min, volume fractions = 0.01–0.04%, and the effect of nanomaterials on relative permeability. The result of the model is verified with published studies. In this study, the finite volume method is used to simulate the problem, and we run simulations at different flow rates while keeping other variables constant. The findings show that the nanomaterials have an important effect on water and oil permeability, increasing oil mobility and lowering IFT, which increases the recovery process. Additionally, it has been noted that a reduction in the flow rate improves oil recovery. Maximum oil recovery was attained at a 0.05 mL/min flow rate. Based on the findings, it is also demonstrated that SiO2 provides better oil recovery compared to Al2O3. When the volume fraction concentration increases, oil recovery ultimately increases.

The rapid changes in nanotechnology over the last ten years have given scientists and engineers a lot of new things to study. The nanofluid constitutes one of the most significant advantages that has come out of all these improvements. Nanofluids, colloid suspensions of metallic and nonmetallic nanoparticles in common base fluids, are known for their astonishing ability to transfer heat. Previous research has focused on developing mathematical models and using varied geometries in nanofluids to boost heat transfer rates. However, an accurate mathematical model is another important factor that must be considered because it dramatically affects how heat flows. As a result, before using nanofluids for real-world heat transfer applications, a mathematical model should be used. This article provides a brief overview of the Tiwari and Das nanofluid models. Moreover, the effects of different geometries, nanoparticles, and their physical properties, such as viscosity, thermal conductivity, and heat capacity, as well as the role of cavities in entropy generation, are studied. The review also discusses the correlations used to predict nanofluids’ thermophysical properties. The main goal of this review was to look at the different shapes used in convective heat transfer in more detail. It is observed that aluminium and copper nanoparticles provide better heat transfer rates in the cavity using the Tiwari and the Das nanofluid model. When compared to the base fluid, the Al2O3/water nanofluid’s performance is improved by 6.09%. The inclination angle of the cavity as well as the periodic thermal boundary conditions can be used to effectively manage the parameters for heat and fluid flow inside the cavity.

Two-phase Darcy’s law is a well-known mathematical model used in the petrochemical industry. It predicts the fluid flow in reservoirs and can be used to optimize oil production using recent technology. Indeed, various models have been proposed for predicting oil recovery using injected nanofluids (NFs). Among them, numerical modeling is attracting the attention of scientists and engineers owing to its ability to modify the thermophysical properties of NFs such as density, viscosity, and thermal conductivity. Herein, a new model for simulating NF injection into a 3D porous media for enhanced oil recovery (EOR) is investigated. This model has been developed for its ability to predict oil recovery across a wide range of temperatures and volume fractions (VFs). For the first time, the model can examine the changes and effects of thermophysical properties on the EOR process based on empirical correlations depending on two variables, VF and inlet temperature. The governing equations obtained from Darcy’s law, mass conservation, concentration, and energy equations were numerically evaluated using a time-dependent finite-element method. The findings indicated that optimizing the temperature and VF could significantly improve the thermophysical properties of the EOR process. We observed that increasing the inlet temperature (353.15 K) and volume fraction (4%) resulted in better oil displacement, improved sweep efficiency, and enhanced mobility of the NF. The oil recovery decreased when the VF (>4%) and temperature exceeded 353.15 K. Remarkably, the optimal VF and inlet temperature for changing the thermophysical properties increased the oil production by 30%.

Nowadays, oil companies employ nanofluid flooding to increase oil production from oil reservoirs. Herein the present work, a multiphase flow in porous media was used to simulate oil extraction from a three-dimensional porous medium filled with oil. Interestingly, the finite element method was used to solve the nonlinear partial differential equations of continuity, energy, Darcy’s law, and the transport of nanoparticles (NPs). The proposed model used nanofluids (NFs) empirical formulas for density and viscosity on NF and oil relative permeabilities and NP transport equations. The NPs thermophysical properties have been investigated and compared with their oil recovery factor (ORF) to determine the highest ORF. Different NPs (SiO2, CuO, and Al2O3) were used as the first parameter, keeping all parameters constant. The simulation was run three times for the injected fluid using the various NPs to compare the effects on enhanced oil recovery. The second parameter, volume fraction (VF), has been modeled six times (0.5, 1, 2, 3, 4, and 5%), with all other parameters held constant. The third parameter, the injected NF inlet temperature (293.15–403.15 K), was simulated assuming that all other parameters are kept constant. The energy equation was applied to choose the inlet temperature that fits the optimum NP and VF to determine the highest ORF. Findings indicated that SiO2 shows the best ORF compared to the other NPs. Remarkably, SiO2 has the lowest density and highest thermal capacity. The optimum VF of SiO2 was 4%, increasing the ORF but reduced when the VF was higher than 4%. The ORF was improved when the viscosity and density of the oil decreased by increasing the injected inlet temperature. Furthermore, the results indicated that the highest ORF of 37% was obtained at 353.15 K when SiO2 was used at a VF of 4%. At the same time, the lowest recovery is obtained when a volume of 5% was used at 403.15 K.

Nanofluids and nanotechnology are very important in enhancing heat transfer due to the thermal conductivity of their nanoparticles, which play a vital role in heat transfer applications. Researchers have used cavities filled with nanofluids for two decades to increase the heat-transfer rate. This review also highlights a variety of theoretical and experimentally measured cavities by exploring the following parameters: the significance of cavities in nanofluids, the effects of nanoparticle concentration and nanoparticle material, the influence of the inclination angle of cavities, heater and cooler effects, and magnetic field effects in cavities. The different shapes of the cavities have several advantages in multiple applications, e.g., L-shaped cavities used in the cooling systems of nuclear and chemical reactors and electronic components. Open cavities such as ellipsoidal, triangular, trapezoidal, and hexagonal are applied in electronic equipment cooling, building heating and cooling, and automotive applications. Appropriate cavity design conserves energy and produces attractive heat-transfer rates. Circular microchannel heat exchangers perform best. Despite the high performance of circular cavities in micro heat exchangers, square cavities have more applications. The use of nanofluids has been found to improve thermal performance in all the cavities studied. According to the experimental data, nanofluid use has been proven to be a dependable solution for enhancing thermal efficiency. To improve performance, it is suggested that research focus on different shapes of nanoparticles less than 10 nm with the same design of the cavities in microchannel heat exchangers and solar collectors.

In the field of biomedical image reconstruction, functional near infra-red spectroscopy (fNIRs) is a promising technology that uses near infra-red light for non-invasive imaging and reconstruction. Reconstructing an image requires both forward and backward problem-solving in order to figure out what the image’s optical properties are from the boundary data that has been measured. Researchers are using a variety of numerical methods to solve both the forward and backward problems in depth. This study will show the latest improvements in numerical methods for solving forward and backward problems in fNIRs. The physical interpretation of the forward problem is described, followed by the explanation of the state-of-the-art numerical methods and the description of the toolboxes. A more in-depth discussion of the numerical solution approaches for the inverse problem for fNIRs is also provided.

This paper concerns the study of the concept of bipolar vague soft s-open set, bipolar vague soft s-interior, bipolar vague soft s-closer, and bipolar vague soft s-exterior in bipolar vague soft topological spaces. By using such concepts, some results are addressed in bipolar vague soft topological spaces. The engagements among these results are also addressed by using bipolar vague soft s-open sets.