Second law analysis on cross flow of hybrid nanoliquid in a Darcy–Forchheimer medium with thermal radiative flow

Abstract

This article’s objective is to examine the optimization of entropy in Darcy–Forchheimer cross-hybrid nanofluids as they flow toward a stretchy surface. There is a current because the surface is being stretched. The energy equation is broken down into its component parts including thermal radiation, heat source sink, and convective flow. In this case, copper oxide $(\mathrm{\text{CuO}})$ and titanium dioxide ${(\mathrm{\text{TiO}}}_2)$ are taken into consideration as nanoparticles, while engine oil (EO) is taken into consideration as a continuous phase fluid. In addition, we carried out an investigation into the relative performance of copper oxide $(\mathrm{\text{CuO}})$ and titanium dioxide ${(\mathrm{\text{TiO}}}_2)$ while they were suspended in water engine oil. The application of the second law of thermodynamics allows for the calculation of the rate of entropy optimization. Using a suitable transformation, nonlinear partial differential equations can be transformed into a standard system. In this work, we use the numerical built-in BVP4c solution method to generate numerical results for the derived nonlinear flow equation. Both copper oxide $(\mathrm{\text{CuO}})$ and titanium dioxide ${(\mathrm{\text{TiO}}}_2)$ undergo a graphical analysis of the effects of varying technical factors on entropy optimization, velocity, the Bejan number, and temperature. Numerical computations of the skin friction coefficient and Nusselt number for a range of fascinating parameters are performed for both nanoparticles (${\mathrm{\text{TiO}}}_2$ and $\mathrm{\text{CuO}}).$ It is clear from the data that entropy optimization improves as the size of the radiation and porosity estimates reduces. The porosity parameter exhibits direct relationships to both temperature and velocity. Tabular comparisons of the current study with the previously published literature show a high degree of agreement. Copper and titanium oxide nanoparticles are used to increase Engine oil ($\mathrm{\text{EO}}$) thermal enactment, making it a more useful base fluid. Further, some significant industrial and engineering applications are related to the present problem discourse.

Keywords:

• Cross-hybrid nanofluid
• engine oil
• stagnation point
• stretching surface
• thermal radiation

Acknowledgments

This study is supported via funding from Prince Sattam Bin Abdulaziz University project number (PSAU/2023/R/1444).

Disclosure statement

The authors declare that they have no competing interests.

Availability of data and materials

All data used in this manuscript have been presented within the article.

Additional information

Funding

This study is supported via funding from Prince Sattam Bin Abdulaziz University project number (PSAU/2023/R/1444).