In the last two decades, nanotechnology has flourished due to its vast number of applications in many fields such as drug delivery, oil and gas, and thermal applications, like cooling and air-conditioning. This study focuses on the applications of nanoparticles/nanofluids in the Enhanced Oil Recovery (EOR) process to increase oil recovery efficiency. To understand the nanoparticle-assisted EOR process, the first step is to understand the flow characteristics of nanoparticles in porous media, including entrapment and release in the pores and the behavior of nanoparticles under high temperatures, pressures, and salinity levels and in the presence of external electric and magnetic fields. Also, the process looks at the roles of various pore distributions during their application as EOR agents. The experimental approaches are not only time consuming, but they are also cumbersome and expensive. Hence, the mathematical models could help to facilitate the understanding of the transport and interaction of nanofluids in a reservoir and how such processes can be optimized to get maximum oil recovery and, in turn, reduce the production cost. This paper reviews and critically analyzes the latest developments in mathematical modeling and simulation techniques that have been reported for nanofluid-assisted EOR. One section is dedicated to discussing the challenges ahead, as well as the research gaps in the modeling approach to help the readers to also contribute to further enlightening the modeling nanofluid-assisted EOR process.

Integration of a larger stiff system of initial value problems emerging from chemical kinetics models requires a method that is both efficient and accurate, with a large absolute stability region. To determine the solutions of the stiff chemical kinetics ordinary differential equations that help in explaining chemically reactive flows, a numerical integration methodology known as the 3-point variable step block hybrid method has been devised. An appropriate time step is automatically chosen to give accurate results. To check the efficiency of the new method, the numerical integration of a few renowned stiff chemical problems is evaluated such as Belousov–Zhabotinskii reaction and Hires, which are widely used in numerical studies. The results generated are then compared with the MATLAB stiff solver, ode15s.

A major challenge in simulating chemical reaction processes is integrating the stiff systems of Ordinary Differential Equations (ODEs) describing the chemical reactions due to stiffness. Thus, it would be of interest to search systematically for stiff solvers that are close to optimal for such problems. This paper presents an implicit 3-Point Block Backward Differentiation Formula with one off-step point (3POBBDF) for the solutions of first-order stiff chemical reaction problems. In deriving the method, the Lagrange polynomial was adopted as the basis function. The paper further analyses the basic properties of the 3POBBDF which include order of accuracy, consistence, zero-stability, and convergence. The stability region as well as the interval of instability of the method was also computed. To demonstrate the accuracy of the proposed approach, some famous stiff chemical reaction problems such as Robertson problem and Chemical AKZO were solved, and the results obtained were compared with those of some existing methods. The results obtained clearly show that the 3POBBDF performs better than the existing methods with which we compared our results.

This paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safeguarding strategy and its Hessian matrix is positive and definite throughout the iteration process. Numerical experiments are conducted on a range of test problems, with 120 instances to demonstrate the efficacy of the proposed algorithm by comparing it with existing techniques in the literature. However, the results obtained validate the effectiveness of the proposed method in terms of the standard metrics of comparison. Additionally, the proposed approach is applied to address motion-control problems in a robotic model, resulting in favorable outcomes in terms of the robot’s motion characteristics.

In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation.

The use of hybrid nanofluid as an alternate heat transfer fluid has shown great potential, and ongoing research to improve its thermal conductivity is important. This study focuses on the impact of heat generation/ absorption on the unsteady Hiemenz flow of aqueous hybrid nanofluid containing copper and silica nanoparticles. Mathematical equations for the hybrid nanofluid model are derived using suitable similarity transformations and solved numerically using bvp4c codes in Matlab software. The results indicate that increased heat generation/absorption leads to an increase in both momentum and thermal boundary layer thickness. The effects of suction and nanoparticle concentration are also analysed and presented graphically. Additionally, a stability analysis is also performed, which discloses that the first solution produced is stable, however, the second solution is not. The findings of this study provide valuable insights into the behaviour of hybrid nanofluid in unsteady flow and can aid in the development of more efficient heat transfer fluids for various engineering applications.