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This article explores the dynamics of nanofluids consisting of copper (TiO2) nanoparticles suspended in water, as they interact with sensor surfaces between two parallel squeezing plates with porous characteristics. This research specifically targets applications involving enhanced heat transfer and magnetohydrodynamic (MHD) control in nanofluid systems. The primary aim is to analyze the effects of nanoparticle aggregation and non-aggregation on sensor surfaces, considering MHD formations and heat transfer in the energy and momentum equations. The research adopts a steady-state fluid condition and utilizes similarity transformations to convert partial differential equations into more manageable ordinary differential equations. The methodology involves shooting methods for solving these nonlinear ordinary differential equations and employs graphical analyses to study the impacts of various parameters such as permeability, magnetic influence, squeeze flow, and radiation on the temperature and velocity profiles of the nanofluid. The results reveal significant dependencies of temperature and velocity profiles on the studied parameters, illustrating varied behaviors in scenarios of both aggregation and non-aggregation of nanoparticles. The findings emphasize how each parameter distinctively influences the heat and flow characteristics of the nanofluid, offering insights into optimizing conditions for better performance and control in practical applications. Future research could focus on extending the model to include transient fluid states and exploring the effects of other nanoparticle materials and shapes. There is also potential to investigate the interactions under different environmental conditions and to incorporate more complex boundary conditions to simulate real-world applications more accurately. Further experimental validation of the theoretical predictions would be beneficial to enhance the reliability and applicability of the findings.

This study investigates analytically the stability analysis of a nonlinear convective boundary layer (BL) flow of the nanofluids GO-EG and GO-W on a shrinking surface in the presence of a magnetic field and viscous dissipation. We provide a second-order nonlinear ordinary differential equation (NODE) for temperature distribution (TD) and a third-order NODE for velocity profile (VP) coupling based on the thermophysical characteristics of the base fluid and nanofluid as well as similarity transformations (STs) in the fundamental governing equations of momentum and energy. The analytical method HAM is used to answer the equations that have been gathered. In many different industries, such as manufacturing, automotive, microelectronics, and defense, cooling of various types of equipment and devices has very important challenges. To fulfill the demands of the engineering and industrial industries, it is hoped that this issue would significantly improve the heat transformation ratio. [ABSTRACT FROM AUTHOR]

In this paper, we explore how to generate solitary, peakon, periodic, cuspon and kink wave solution of the well-known partial differential equation Korteweg–de Vries (KdV) by using exp-function and modified exp-function methods. The presented methods construct more efficiently almost all types of soliton solution of KdV equation that can be rarely seen in the history. These methods appear to be straightforward and symbolic calculations are used to solve the problem. All resulting answers are verified for accuracy using the symbolic computation program with M a p l e. To show the physical appearance of the model, 3D plots of all the generated solutions are then displayed. The obtained solutions revealed the compatibility of the proposed techniques which provide the general solution with some free parameters. This is the key benefit of these methods over the other methods. [ABSTRACT FROM AUTHOR]

In this study, the Falkner–Skan stream (FSS) of ZnO-EG across a moving wedge is investigated using artificial neural networks backpropagated using a Bayesian regularization strategy (ANN-BRS). The PDEs of the Falkner–Skan are converted into a set of ordinary differential equations (ODEs). The reference dataset is created using the mathematical solver in Mathematica and includes moving wedge boundaries, radiation boundaries, nanoparticle volume division boundaries and Falkner–Skan power-regulation boundaries for all proposed scenarios (ANN-BRS). Examined is the effect of practical cut off points on the stream field and temperature profiles, including the radiation limit, moving wedge limit, nanoparticle volume division and Falkner–Skan power. When nanoparticles are present, viscosity and heat conductivity rise, which can be physically explained. Increases in Falkner–Skan power have both positive and negative effects. When the settings are adjusted to their highest values, the maximum rate of heat transmission is realized. The effects of radiation boundary and so on are identical due to the linear augment. As a result, as the parameters are increased, the rate of heat transmission increases. Based on the intended data points that were obtained, the estimated answer is calculated for every scenario utilizing the testing, training and validation procedures. The mean square error data (MSE), error histogram and regression analysis are used to validate the performance of (ANN-BRS). [ABSTRACT FROM AUTHOR]