Numerical simulation of exponentially stratified magneto-nanofluid flow across stretchable surface in Darcy porous medium

• Magnetohydrodynamic flow of a barium hexaferrite–water nanofluid across an exponential stretched slimy sheet is analzed. • Barium hexaferrite nanoparticles in spherical, needle, blade, cylindrical, and brick geometries are applied. • Numerical treatment is accomplished by using the Mathematica software. • Spherical particles are excellent at reducing thermal effects, whereas needle-shaped particles exhibit greater temperature levels. In this work, the magnetohydrodynamic flow of a barium hexaferrite–water nanofluid across an exponential stretched slimy sheet in a penetrable medium is examined concerning the impacts of heat generation/absorption and thermal dissipation. Additionally, barium hexaferrite nanoparticles in spherical, needle, blade, cylindrical, and brick geometries are applied to evaluate the influence of shape parameters under convective boundary conditions, thermal stratification, and Joule heating effects. A set of nonlinear ordinary differential equations (ODEs) is created from the regulating non-linear partial differential equations (PDEs) by applying similarity transformations, and Mathematica is used to solve them numerically. The findings are evaluated for essential industrial and technical characteristics such as Nusselt numbers, temperatures, skin frictions, and velocity. According to the investigation, spherical particles are excellent at reducing thermal effects, whereas needle-shaped particles exhibit greater temperature levels. Additionally, the temperature outlines decrease as the thermal stratification value improves. The outcomes of this examination offer opportunities for novel treatments in a variety of fields, such as aerodynamic extrusion procedures, electromagnetic interference (EMI) shielding, bone plate operations, microwave technologies, and tumor therapies.