Numerical analysis of entropy optimization and viscous nanofluid over a nonlinear parabolic stretching surface

The exploration of heat transmission in nanofluid flow over curved geometries is dynamic for improving the significance of advanced thermal systems used in manufacturing, energy, and biomedical applications. In this paper, we consider two dimensional in-compressible viscous flow with water based nanofluids ($Cu$-water, $Ti{O}_2$-water) flowing over a nonlinear parabolic stretched surface past a porous medium using heat generation/absorption effect. For this objective we used $Cu$ and $Ti{O}_2$ as nanoparticals and water as a base fluid. Basically, in this study we compared two nanofluids $Cu$-water and $Ti{O}_2$-water due to their high heat transfer characteristics. The governing nonlinear mathematical model of continuity, momentum and temperature equations are transformed into nonlinear ODEs by using similarity transformations. Furthermore, the transformed ODEs are than inspected numerically in MATLAB using computational procedure of Bvp4c. The combination of $Cu-Ti{O}_2$ hybrid nanoparticles, porous parabolic surface shape, and entropy generation analysis, and this combination analysis never previously reported. Moreover, the graphs are plotted against temperature and velocity fields for two distinct nanofluids ($Cu$-water, $Ti{O}_2$-water). An entropy production analysis is also performed for an incompressible viscous nanofluid model. According to the results, adding Cu–TiO₂ nanoparticles greatly improves thermal conductivity, which raises entropy production from fluid friction while also improving heat transfer rates.