Effect of activation energy on mass transfer features of Powell-Eyring nanofluid via shrinking disk: Dual solutions and stability analysis

This study's main goal is to investigate the Darcy-Forchheimer model of Eyring-Powell nanofluid's mass and thermal transport mechanisms across a shrinking disk. Joule heating, magnetic field, thermophoresis, viscous dissipation, non-uniform energy sink/source, activation energy, and Brownian motion with convective constraint are all taken into account in the physical model. The non-linear ODEs model is tackled numerically and graphically with the help of the bvp4c approach. The key finding shows that a dual solution was performed in the region ( χ > χ c i ) for shrinking disk with varying values of distinct factors, while no solution occurs in the sector ( χ < χ c i ) . It also found that the critical point ( χ c i ) stay constant at ( − 0.4277 ) , despite variation of R d ( = 0.3 , 0.4 , 0.5 ) and E c ( = 2 , 2.5 , 3 ) against heat transportation rate. The heat transportation coefficient increases with the rising factor of the Powell fluid for the first solution. Furthermore, the mass curve shows a rising trend for both solutions with a positive variation in the value of energy activation. To identify which solution is stable or unstable, stability analysis is carried out.