Significance of Buongiorno Model and Arrhenius Pre-exponential Factor Law to Entropy Optimized Darcy Forchheimer Hybrid Nanoparticle (Al₂O₃, Cu) Flow Over Thin Needle

In the fields of engineering, industry, and biology, thin needles serve a critical role. The thermocouple hot wire anemometer for wind speed monitoring, microscale heat extraction cooling systems, and electronic microstructure outfitting are only a few of the needle's key applications. In view of these applications the present investigation is carried out to study the Casson hybrid nanofluid flow for the entropy creation and the pre-exponential factor law in Darcy Forchheimer medium on the thin needle. The set of governing equations describing the flow problem will be converted to a system of ordinary differential equations with suitable similarity variables. The numerical solutions are obtained by the aid of mathematical computing software by applying the Runge Kutta Fehlberg 45 method with shooting scheme. The numerical results for various parameters are produced, and an entropy analysis is performed. Axial velocity falls as the porosity and Darcy parameters are increased. The thermal performance improves as the needle size and Brinkman number increase. The concentration profile is improved by thermophoresis, Brinkman number, and activation energy parameter. The entropy generation and surface drag force will increase as the porosity parameters are increased, while the Bejan number will decrease.