Numerical algorithm and stability analysis of unsteady Darcy Forchhemier nanofluid flow over a permeable shrinking inclined disc

• To study the Darcy Forchhemier nanofluid flow across a permeable inclined spinning disc. • To numerically solve the system of nonlinear system of PDEs using BVP4c package. • To examine the impact of cobalt ferrite nanoparticles on the velocity and energy transfer rate. • To study the consequences of different physical parameters on the fluid properties. • To perform the stability analysis, whether lower or upper branch solution is stable. The unsteady nanofluid (NF) flow across a slanted stretching and shrinking porous spinning disc is examined in the present study. The Darcy Forchhemier nanofluid flow across a permeable shrinking inclined spinning disc has several innovative applications in heat transfer and cooling mechanisms, such as turbines, and in electronic apparatus due to its upgraded heat transport abilities. It is also used in power systems, medical devices, and lubrication applications that demand fluid with high thermal conductivity and durability. Therefore, the NF flow is studied with the consequences of heat source/sink, Darcy medium, MHD (magnetohydrodynamics), multiple slip conditions, and heat radiation. The NF is synthesized by the accumulation of cobalt ferrite (CoFe 2 O 4 /water) nanoparticles (NPs) in the base fluid. The modelled equations are first reduced to their lowest order and then computationally resolved through the BVP4c package. The stability analysis demonstrates that the upper branch solutions are technically possible and practically stable, while the lower branch solution is unpredictable. It has been observed from the graphical outcomes that the azimuthal and radial velocity profiles decline with the variation in the magnetic field. The fluid velocity and energy curve drop with the addition of CoFe 2 O 4 NPs. This property of the nanofluid has remarkable applications in industrial sectors.