Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn.

The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for the considered model. Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions.

A New 3D Mathematical Model for Simulating Nanofluid Flooding in a Porous Medium for Enhanced Oil Recovery.

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).

A numerical investigation of mathematical modelling in 3D hexagonal porous prism on oil recovery using nanoflooding.

The use of nanomaterials as a means of recovering heavy and light oil from petroleum reservoirs has increased over the preceding twenty years. Most researchers have found that injecting a nanoparticle dispersion (nanofluids) has led to good results and increased the amount of oil that can be recovered. In this research, we aim to imitate the three-dimensional hexagonal prism in the existence of SiO2 and Al2O3 nanoparticles for better oil recovery.

The Impact of 3D Prism Cavity for Enhanced Oil Recovery Using Different Nanomaterials.

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.

The Impact of Cavities in Different Thermal Applications of Nanofluids: A Review.

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.

Thermophysical Properties of Nanofluid in Two-Phase Fluid Flow through a Porous Rectangular Medium for Enhanced Oil Recovery.

It is necessary to sustain energy from an external reservoir or employ advanced technologies to enhance oil recovery. A greater volume of oil may be recovered by employing nanofluid flooding. In this study, we investigated oil extraction in a two-phase incompressible fluid in a two-dimensional rectangular porous homogenous area filled with oil and having no capillary pressure.