Theoretical modeling and Xue model analysis of non-isothermal fluid flow for enhanced energy sources cooling with hybrid Cu-Al2O3 nanofluids

Isothermal flows with hybrid nanofluids have demonstrated significant potential for improving heat transfer and cooling efficiency across various engineering applications. This study conducts a theoretical analysis of hybrid nanofluid-based cooling for energy sources within a square duct. A hybrid nanofluid consisting of Cu-Al2O3 nanoparticles is employed as the cooling medium. The mathematical equations governing the volume fractions of the two solid particles (Cu-Al2O3) are formulated based on the Xue model. Non-isothermal fluid flow is assumed, incorporating variations in fluid density and viscosity with temperature. The formulated equations are subsequently solved using the Galerkin finite element method on adaptively refined meshes composed of triangular elements. Analysis of temperature and Nusselt number values at the boundaries of the energy sources reveals noteworthy trends. Specifically, local Nusselt values decrease at the fluid-solid interface with increasing volume fractions of the solid particles, while temperature decreases at the solid-solid interface with increasing volume fraction values.