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The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy’s law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by this law. To overcome this difficulty, Brinkman proposed a new idea of Brinkman-type fluid in highly porous media. In this study, the Brinkman-type fluid flow is analyzed with hybrid nanoparticles (a hybridized mixture of clay and alumina), suspended in water taken as a base fluid under the effect of an applied magnetic field. The fluid motion is taken inside a vertical channel with heated walls. Free convection is induced due to buoyancy. The momentum and energy equations are written in dimensionless form using the non-dimensional variables. The energy equation is modified to fractional differential equations using the generalized Fourier’s law and the Caputo fractional derivatives. The fractional model is solved using the Laplace and Fourier transformation. Variations in velocity and temperature are shown for various fractional parameter values, as well as charts for the classical model. For the volume fractions of nanoparticles, the temperature distribution increases, with maximum values of hybrid nanoparticles with the highest specified volume fractions. Moreover, due to hybrid nanoparticles, the rate of heat transfer is intensified.

The present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

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.

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.

A new scheme to formulating the Caputo time-fractional model for the flow of Brinkman-type fluid between the plates was introduced by using the generalized laws of Fourier and Fick. Within a channel, free convection flow of the electrically conducted Brinkman-type fluid was considered. A newly generated transformation was applied to the heat and mass concentration equations. The governing equations were solved by the techniques of Fourier sine and the Laplace transforms. In terms of the special function, namely, the Mittag-Leffler function, final solutions were obtained. The entropy generation and Bejan number are also calculated for the given flow. To explain the conceptual arguments of the embedded parameters, separate plots are represented in figures and are often quantitatively computed and presented in tables. It is worth noting that for increasing the values of the Brinkman-type fluid parameter, the velocity profile decreases. The regression analysis shows that the variation in the velocity for time parameter is statistically significant.

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.

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.

The increase of crude palm oil prices can significantly affect the worldwide economic activities. Therefore, an accurate model to forecast the crude palm oil prices is crucial so that necessary precautionary steps can be taken. In this study, a hybrid between Sliding Window and GARCH model was proposed to improve the forecasting accuracy of crude palm oil prices series. In this model, sliding window partitions is used to aggregate / cluster the original series into several number of constitutive series while GARCH model is utilized to forecast prices based on the selected window to complete variance calculation. A dataset of crude palm oil prices from Malaysian Palm Oil Board was used to test the performance of the proposed model. Direct application of GARCH model was used as a benchmark for effectiveness measurement with the proposed model by comparing mean percentage of absolute error and mean square error. The result has shown that the proposed hybrid sliding window and GARCH model demonstrates better forecasting performance than single GARCH model.