Augmented thermal–hydrodynamic performance of tetra-hybrid metal nanofluids over a rough conical surface

Rough conical surfaces are widely encountered in solar-thermal collectors, heat shields, aircraft nose cones, chemical reactors, conical diffusers, nozzles, compact heat exchangers, and thermal management systems, where surface texture can strongly influence boundary-layer transport. Motivated by these applications, this study investigates steady mixed-convective Ag–Al–Au–Cu/H2O tetra-hybrid nanofluid flow over a vertically oriented rough cone subjected to a spatially periodic magnetic field. The wall roughness is modelled through a deterministic sinusoidal profile and incorporated via a slip-velocity condition. Using Mangler’s transformations, the governing boundary-layer equations are reduced to a non-similar dimensionless system and solved by quasilinearisation with an implicit finite-difference scheme. The effects of Richardson number, magnetic parameter, Eckert number, roughness frequency, slip velocity ratio, nanoparticle volume fraction, and particle sphericity are analysed for mono-, hybrid-, ternary-, and tetra-hybrid nanofluids. In particular, the comparison with and without viscous dissipation is performed for different particle shapes, with each nanoparticle volume fraction fixed at 5%, while the remaining governing parameters are kept constant. The results reveal that deterministic roughness induces pronounced sinusoidal variations in both skin friction and heat-transfer rate along the cone surface. Increasing the roughness frequency and slip velocity ratio intensifies these oscillations; for instance, at a slip velocity ratio of 0.5, the heat-transfer-rate measure increases from 0.11030 for a smooth cone to 4.22853 at n = 30. The periodic magnetic field suppresses velocity through Lorentz-force resistance, whereas viscous dissipation enhances thermal transport. Among the tested configurations, the Ag + Au + Cu/H2O ternary nanofluid provides a 35.50% reduction in skin friction under viscous dissipation. The numerical results are validated against published benchmark data, confirming the reliability of the present computational approach.