Unsteady Williamson nanofluid flow over a rotating cone: Effects of variable properties, thermal radiation, and chemical reactions

This study investigates the unsteady flow of Williamson nanofluid over a vertically rotating cone, incorporating the effects of variable thermophysical properties, chemical reactions, and thermal radiation. A self-similarity transformation reduces the governing PDEs to ODEs. The spectral relaxation method is utilized for numerical solutions under specified wall temperature and concentration (SWTC), as well as specified thermal and solutal flux (STSF) conditions. A grid independence and residual norm analysis confirm the robustness of the numerical scheme, which is further benchmarked against standard solvers. A parametric sensitivity analysis, involving $\pm 20\text{\%}$ perturbations, identifies the most influential parameters affecting thermal and solutal transport. Results reveal that tangential and azimuthal momentum components exhibit inverse responses to parameter variations. Variable thermal conductivity and solutal diffusivity enhance temperature and concentration fields under SWTC conditions but reduce them in the STSF scenario. A simultaneous increase in variable viscosity and suction/injection parameters significantly elevates the tangential and azimuthal skin friction coefficients. The Nusselt number rises by 58.34% with simultaneous increases in variable thermal conductivity and linear radiation parameters, and by 81.10% when nonlinear radiation parameter is considered instead, highlighting the effectiveness of nonlinear radiation in enhancing thermal performance. Moreover, chemical reactions increase mass transfer, while enhanced variable diffusivity suppresses it. The findings offer practical insights for optimizing heat and mass transfer in rotating systems such as drilling and rotary filtration units.