Heat transfer analysis in membrane-based pumping flow of hybrid nanofluids

Hybrid nanofluids have emerged as a game-changer in thermal management, offering enhanced thermal conductivity, heat transfer, and fluid flow characteristics. By combining the benefits of different nanoparticles, hybrid nanofluids exhibit improved performance, making them an attractive solution for advanced thermal management systems. This study presents a comprehensive analysis of heat transfer in hybrid nanofluids propelled by membrane pumping and controlled by a radial magnetic field. A mathematical model is developed to investigate the thermal behaviour of copper–alumina/water nanofluid in a vertical microtube. By employing a lubrication approach, analytical solutions are derived for velocity profiles, temperature fields, and heat transfer characteristics. Results show significant enhancements in heat transfer rates due to the combined effects of membrane pumping and magnetic field. By using the MATLAB code, results for velocity profiles, volumetric flow rates, wall shear stress, stream functions, and pressure differences are illustrated. Additionally, heat transfer analysis for hybrid nanofluid (copper–alumina/water) flow is scrutinized, yielding insights into temperature, Nusselt numbers, and isotherms. The result reveals that the Nusselt number increases by 3.102% with higher alumina concentration\(\left( {\phi_{1} } \right)\), while it decreases slightly from 3.102% to 3.098% as copper concentration \(\left( {\phi_{2} } \right)\) increases, which signifies that alumina nanoparticles are more effective than copper nanoparticles. The present study showcases the potential of the proposed model to transform biomedical sciences, particularly in the development of smart pumping devices. This research lays the groundwork for future investigations, aiming to harness the power of mathematical modelling to create innovative, patient-centred solutions.