Analytical study of steady state axisymmetric stagnation-point gold–blood Casson nanofluid through a rotating stretchable disk

Nanofluids find extensive applications in enhancing the thermodynamic efficiency of thermal systems across various domains of engineering and scientific disciplines. This study aims to explore the complex relationship between the varying thermal conductivity and viscosity impact in nanofluid dynamics. The main objective of this study is to examine the three-dimensional stagnation flow of Casson nanofluid across a stretching and spinning disk, influenced by a magnetic source. The Navier–Stokes model for flow systems includes Brownian diffusion and thermophoresis. By using scaling variables, the complex system of partial differential equations is simplified into a set of coupled high degree nonlinear ordinary differential equations with convective boundary conditions. The homotopy technique is applied for analytic solutions. The optimization analysis is conducted on heat transfer rate and surface drag force coefficient using response parameters. The influence of the different parameters for the flow problem has been discussed and is shown through graphs. The finding of our study is that the velocity profiles increase in both radial directions as well as in the azimuthal direction by varying the rotation parameter strength, while the temperature gradient profile dwindles. Finally, the precision of the presented model is reaffirmed by means of a graphical juxtaposition with published data under a specific limiting scenario.