A different algorithm for boundary layer flow characteristics of thermomicropolar alumina-copper/water hybrid nanofluid

The flow and heat transfer of thermomicropolar hybridnanofluid over a linear vertical shrinking and permeable surface with mixed convection effects in presence of magnetic field is studied. In this paper, we explore upper branches of solutions that have physical meaning in navel mass-based model, which was not considered in the previous works. The dimensional governing equations of this problem are transformed into nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs) by applying similarity variables. The resultant BVPs are converted into initial value problems (IVPs) by finite difference method which then resolved by employing Runge Kutta of order four. The impacts of the governing parameters, such as suction parameter, material parameter, Richardson number, magnetic parameter, shrinking parameter and micropolar heat conduction parameter on temperature, velocity, and angular velocity, are illustrated graphically. Also they are illustrated for engineering interests as a function of shrinking parameter. The results demonstrate that the velocity, angular velocity and temperature are increaed, by the augmenting of cu nanoparticles ( ) the same as shear stress, gradient of microrotation and heat transfer. Besides, the increasing of S and A have more influence on velocity and angular velocity than temperature. Finally, the reliable treatment of the mass-based model for the thermomicropolar hybrid nanofluid flow and the heat transfer is the substantial achievement of the present research.