Exploring magnetic and thermal effects on MHD bio-viscosity flow at the lower stagnation point of a solid sphere using Keller box technique

The study of liquid comprising nanoparticles for energy transmission characteristics has gained prominence due to its diverse real-life applications in different energy systems. Recently, scientists have been endeavoring to introduce a new type of liquid, despite the already proven effectiveness of Nano liquid's thermal efficiency. To meet the demands of various engineering and industrial applications, scientists have developed a new class of liquid called hybrid Nano liquid by dispersing two types of nano-sized particles in a regular liquid. Given the significance of hybrid Nano liquid in this study, we have considered (titanium dioxide, sodium alginate, silver) and (graphite oxide) in an MHD Casson fluid (bio-viscosity blood) near the lower stagnation point of a solid sphere. Additionally, this research addresses thermal radiations and the effects of magnetic fields. For the numerical results of the proposed ODEs, the Keller box method was employed. Engineering quantities obtained from this investigation are discussed in tables. From the observed graphs, it is evident that the velocity of the liquid near the lower stagnation point decreases as the magnetic effects increase.