Temporal stability analysis and thermal performance of non-Newtonian nanofluid over a shrinking wedge

The authors use a temporal stability analysis to examine the hydrodynamics performance of flow response quantities to investigate the impacts of pertained parameters on Casson nanofluid over a porous shrinking wedge. Thermal analysis is performed in the current flow with thermal radiation and the viscous dissipation effect. Boungiorno's model is used to develop flow equations for Casson nanofluid over a shrinking wedge. An efficient similarity variable is used to change flow equations (PDEs) into dimensionless ordinary differential equations (ODEs) and numerical results are evaluated using MATLAB built-in routine bvp4c. The consequence of this analysis reveals that the impact of active parameters on momentum, thermal and concentration boundary layer distributions are calculated. The dual nature of flow response output i.e. $C{f}_x$ is computed for various values of ${\beta }_T=2.5,3.5,4.5$, and the critical value is found to be $-1.544996$, $-1.591$, and $-1.66396$. It is perceived that the first (upper branch) solution rises for the temperature profile when the value of thermal radiation is increased and it has the opposite impact on the concentration profile. Thermal radiation has the same critical value for ${Nu}_x$ and ${Sh}_x$. The perturbation scheme is applied to the boundary layer problem to obtain the eigenvalues problem. The unsteady solution $f\left(\eta ,\tau \right)$ converges to steady solution $f_o\left(\eta \right)$ for $\tau \to \infty$ when $\gamma \ge 0$. However, an unsteady solution $f\left(\eta ,\tau \right)$ diverges to a steady solution $f_o\left(\eta \right)$ for $\tau \to \infty$ when $\gamma <0$. It is found that the boundary layer thickness for the second (lower branch) solution is higher than the first (upper branch) solution. This investigation is the evidence that the first (upper branch) solution is stable and reliable.