Numerical study of MHD Casson model with SWCNT: MWCNT hybrid nanofluid flow over a stretching/shrinking sheet considering variable viscosity

This work examines unsteady magnetohydrodynamic boundary-layer transport of a SWCNT–MWCNT/engine-oil hybrid nanofluid across a stretching/shrinking sheet, accounting simultaneously for a time-varying magnetic field, temperature-dependent viscosity, and Casson-type viscoplasticity. Engine oil serves as the carrier fluid for SWCNT and MWCNT nanoparticles at volume fractions between 0.01 and 0.04. The governing partial differential equations are reduced to a system of ordinary differential equations through similarity transformations and solved numerically with MATLAB's bvp4c routine. Across the suction-to-injection range, skin friction falls by roughly 102% (from 0.428 to −0.008) while the Nusselt number climbs by more than four orders of magnitude, over the tested ranges of the viscoplastic parameter and Eckert number, skin friction instead rises by about 83% and 40%, respectively, accompanied by a Nusselt-number decline of up to 1.6%. A stronger magnetic field suppresses the velocity field through Lorentz-force drag while elevating the temperature field via enhanced viscous heating. Together, these results show how suction/injection, sheet stretching/shrinking, magnetic-field intensity, and viscoplasticity jointly control momentum and thermal transport in engine-oil-based carbon-nanotube hybrid nanofluids, with implications for thermal management in automotive lubrication, industrial cooling, and mechanical-engineering systems.