The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe₃O₄) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer’s differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials.

In the design of efficient nanodevices particularly microchannels used for cooling electronic components, precise control of fluid flow, and heat dissipation is essential to prevent overheating and potential damage to sensitive parts. By applying mathematical models based on Prandtl–Eyring theory, engineers can accurately predict temperature and velocity distributions within the microchannels during the design phase. Authors noted that there is a dearth of examinations conducted on Prandtl–Eyring fluid with the influence of activation energy, thermophoresis, and bioconvection. Authors utilized the research gap and studied the investigation of chemically reactive Prandtl–Eyring nanofluid driven by Darcy–Forchheimer media with the influence of Arrhenius activation energy and bioconvective gyrotactic microorganisms. The tiny organisms were suspended in the liquid to stabilize the particles and prevent them from precipitating out of solution, which is known as bioconvection. Through suitable transformations, the governing partial differential equations were reduced to a complex system of coupled ordinary differential equations. A model of the nanofluid was then developed using Buongiorno's well-established approach. The numerical solver “bvp4c” with Shooting method was employed to determine the numerical responses for the problem under investigation. The impact of various influential factors was examined numerically for several important physical quantities, with results reported concisely in tabular form. Validation against previous work in a limiting case demonstrated excellent agreement, verifying the accuracy of the model. To the best of the authors' knowledge, this analysis is novel, and there is no earlier published work relevant to the current study.

This article studies the flow of Ostwald–de Waele ternary nanofluid over a permeable shrinking sheet. The governing partial differential equations are converted into ordinary differential equations using similarity variables and solved analytically. The article includes closed-form algebraic solutions and graphical flow dynamics analysis, dependent on Darcy number, volume fraction, and mass transpiration. The study shows that the presence of porous media significantly upsurges the mass transpiration and magnitude of skin friction. The calculation uses a combination of Titanium dioxide (TiO₂), Cobalt ferrite (CoFe\(_{2}O_{4}\)), and Magnesium oxide (MgO) nanoparticles in pure water, and the ternary nanofluid performs better than the conventional fluid in terms of thermal conductivity. This is important in the fields of manufacturing, machine operations, and engineering, where improving heat transfer is crucial.