Radiative and magnetohydrodynamic micropolar hybrid nanofluid flow over a shrinking sheet with Joule heating and viscous dissipation effects

This study examines the radiative and magnetohydrodynamic micropolar fluid flow over a stretching/shrinking sheet consisting of Al2O3 and Cu nanoparticles. Besides, the effects of the Joule heating and viscous dissipation are taken into consideration. The similarity variables are employed to convert the governing equations into similarity equations. Then, the bvp4c in MATLAB is utilized to obtain the numerical results. The accuracy of the current formulation and method has been done by comparing the present results with those previously published data. Findings discovered that two solutions are obtained for the limited range of S and K, and these solutions are terminated at S = S-c and K = K-c .The influence of Ec and R is to reduce the local Nusselt number of Re(x)(-1/2)Nu(x). Meanwhile, the values of Re(x)(-1/2)Nu(x) increase with the increase in phi(hnf) when larger values of R are considered. The rise of M contributes to the increment in the values of (RexCf)-C-1/2, RexMw, and Re(x)(-1/2)Nu(x), but the effect of K lowers the values of these physical quantities. Lastly, it was discovered that the first solution is physically reliable and in a stable mode.