Rheological behavior of unsteady Buongiorno nanofluid over a flat surface with variable pressure gradient under slip constraints

This study investigates the unsteady magnetohydrodynamic flow and heat–mass transfer of a Casson nanofluid through a flat surface under a variable pressure gradient and velocity-slip boundary condition. The non-Newtonian rheological behavior of the Casson fluid is considered to capture yield-stress effects in practical transport systems. The nanofluid is modeled using the Buongiorno framework, which accounts for nanoparticle transport due to Brownian motion and thermophoresis. The mathematical formulation consists of coupled momentum, energy, and concentration equations, incorporating the effects of viscous dissipation, Joule heating, and a homogeneous chemical reaction. The nonlinear governing equations are solved numerically using a finite-difference method combined with the successive over-relaxation (SOR) technique. The results indicate that increasing the Casson parameter enhances the velocity distribution, whereas a higher slip parameter reduces the near-wall velocity. Moreover, Brownian motion increases the fluid temperature, while thermophoresis significantly alters the concentration profile by driving nanoparticles away from the heated surface. These findings provide useful insight into the combined influence of rheology, magnetic forces, slip effects, and pressure variation on transport behavior, which can support the design of channel systems in thermal and industrial engineering applications. From a sustainability perspective, the enhanced thermal performance and controllable transport characteristics of nanofluids can contribute to energy-efficient thermal management systems, reduced energy consumption, and improved design of environmentally sustainable industrial and engineering processes.