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

Abstract

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 $\left(\chi >{\chi }_{ci}\right)$ for shrinking disk with varying values of distinct factors, while no solution occurs in the sector $\left(\chi <{\chi }_{ci}\right)\text{.}$ It also found that the critical point $\left({\chi }_{ci}\right)$ stay constant at $\left(-0.4277\right)\text{,}$ despite variation of $Rd\left(=0.3,0.4,0.5\right)$ and $Ec\left(=2,2.5,3\right)$ 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.