Numerical approach of Casson nanofluid with heat and mass transfer amplification over the cone: combined cross-diffusion with Brownian and thermophoresis impacts

There are two main categories of fluids namely Newtonian and non-Newtonian according to their rate of shear stress and the force or tension. Polymer blending and plastic manufacturing industries require non-Newtonian fluids for substantial velocity resistance and heat transfer rate. In response to this, a numerical study is carried out to examine an unsteady naturally convective Casson nanofluid flow through a vertical cone in the presence of radiation, viscous dissipation, and chemical processes. It also considers the implications of Soret and Dufour effects along with Brownian and thermophoresis. The equations are altered into a dimensionless form by using appropriate transformations and the interrelated equations that arise are employed by the Crank–Nicolson finite difference technique. The expressions for the momentum, thermal, and concentration trends were exhibited by the graphical representations. This study reveals the skin friction, Nusselt and Sherwood numbers of the flow regime. An elevating Casson parameter value in the range (\(\mathrm{0.5 }\le \gamma \le 1.5\)) improves 14.71% of plastic dynamic viscosity and promotes fluid flow resistance that minimizes the strain over the cone surface. The Dufour parameter value between (\(\mathrm{0.1 }\le Du\le 1.0\)) contributes to a 30.59% rise in the temperature profile. The Soret parameter value in the range (\(\mathrm{0.1 }\le Sr\le 1.0\)) scatters the particles more effectively and increases the concentration distribution by 15.76%. The cross-diffusion is crucial in systems where both heat and mass transfer occur simultaneously such as in chemical reactors, environmental engineering, or biological systems where the interplay between concentration gradients and temperature changes needs to be accurate.