Exact multiple solutions for rheological analysis of Darcy–Brinkman model on Bingham sodium alginate suspensions driven by 2D bidirectional moving plate with Navier and Biot conditions

In modern days, Bingham ternary nanofluid applications gain the attention of many researchers with their unique properties and potential applications in solar thermal energy conversion which significantly improve system efficiency and leverage modern machine learning techniques for performance prediction, and the authors observe that there is a dearth of research on Bingham ternary nanofluids with the circumstance of momentum slip and temperature jump conditions and influence of MHD (magnetohydrodynamics) and thermal radiation on ternary nanofluids; authors utilized the research gap and used GO, MoS₂, and TiO₂ nanoparticles mixed in sodium alginate solution to form non-Newtonian Bingham ternary nanofluid. Further, the heat transfer process was analyzed using variable thermophysical properties, momentum, and temperature-governing equations, which were transformed to nonlinear ordinary differential equations (ODEs) via similarity variables. The temperature equation was calculated using the hypergeometric series method, and several physical parameters are explained graphically. The outcomes reveal that upsurging the porous, magnetic field, and slip parameters decays the momentum profile, and enhancing the thickness of the thermal boundary layer, the present analysis has many useful applications in science and engineering industries, such as transportation, cooling systems, and heat exchangers.