Numerical analysis of unsteady CNT–suspended Casson nanofluid flow in engine oil through a Darcy–Forchheimer porous vertical microchannel with temperature-dependent viscosity

Abstract This study investigates the impact of temperature-dependent viscosity on the unsteady magnetohydrodynamic flow of incompressible, electrically conducting Casson nanofluids containing single and multi-walled carbon nanotubes (SWCNTs and MWCNTs) dispersed in engine oil through a vertical Forchheimer porous channel. The model also accounts for the effects of the Péclet number, radiation, heat generation/absorption, and buoyancy. The governing coupled partial differential equations (PDEs) for momentum and thermal transport are numerically solved using the overlapping multidomain bivariate local linearization method. The influence of key parameters, including the Casson fluid index, variable viscosity, magnetic field, Forchheimer resistance, radiation, heat generation/absorption, Grashof number and Brinkman number are analyzed numerically. Velocity and temperature fields are enhanced by higher Casson parameter, viscosity variation, Grashof and Brinkman numbers, while they are reduced by magnetic, Forchheimer, radiation, and heat absorption effects. Overall, MWCNT nanofluids consistently demonstrate higher velocity, temperature, and Nusselt number, as well as greater entropy generation and lower Bejan number than SWCNT nanofluids.