Abstract 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.