Numerical treatment of hybrid water based nanofluid flow with effect of dissipation and Joule heating over a shrinking surface: Stability analysis

Abstract

In the current work, the steady flow of magnetohydrodynamic of Cu-Al2O3/water hybrid nanofluid was investigated along with Joule heating and viscous dissipation effect across a porous shrinking sheet. Using an appropriate similarity transformation, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). The system of ODEs is solved using the bvp4c function in MATLAB. The present findings are numerically and visually compared to the available literature, and excellent agreements are discovered. The impacts of several new physical governing factors on velocity and temperature profiles, while the variation of heat transfer and skin friction, are visually shown and explicated hypothetically. In addition, the findings demonstrate the presence of duality within a limited range of suction parameters. Increasing the solid volume fraction ϕCu increases the values of f′′(0) for an initial solution and reduces them for an unstable solution. The investigation of the temporal stability of the solutions concludes that the first solution is stable only. The values of smallest eigenvalues values (γ>0) are positive for first solution indicated the stability of solution while the values of smallest eigenvalues values (γ<0) are negative for second solution indicates the instability of solution. The quantitative outcomes are in Table 4. The concentration of Al2O3 and Cu is almost 20% (0.01≤ϕAl2O3≤0.2 and 0.01≤ϕCu≤0.2).