Impact of nanoparticle shape on electro-osmosis Oldroyd-B nanofluid flow subject to second-order slip and exponential heat source/sink

Electro-osmosis is an important transporting effect, which has already been comprehensively investigated in the current scientific/engineering world, in the context of micro/nano process operations. This research aims to study the stationary electro-osmotic transport of a nanofluid [Formula: see text] with a permeable stretching wall that is aligned in the direction of x-axis. In the end, the nonlinear boundary value problem that is produced is solved numerically by using the BVP4C solver in MATLAB. The major results indicate that augmenting the Oldroyd-B parameter ([Formula: see text] from 0.2 to 1.0 decreases fluid velocity by 10–15% for spherical shapes. Conversely, increasing the retardation parameter ([Formula: see text] from 0.4 to 1.2 enhances velocity gradients by 15–20%. The electro-osmosis parameter is also lowering the velocity of the sphere-shaped nanoparticles by 10–12%. Furthermore, raising the Dufour number from 0.6 to 0.8 elevates the Nusselt number by 9% for spheres and 6.5% for blades. The outcomes of this study are useful for the design and optimization of electro-osmotic microfluidic systems, thermal management in microscale devices, and biomedical transport processes where precise control of heat and mass transfer using non-Newtonian nanofluids is required.