Hybrid nanofluid is considered a new type of nanofluid and is further used to increase the heat transfer efficiency. This paper explores the two-dimensional steady axisymmetric boundary layer which contains water (base fluid) and two different nanoparticles to form a hybrid nanofluid over a permeable moving plate. The plate is suspected to move to the free stream in the similar or opposite direction. Similarity transformation is introduced in order to convert the nonlinear partial differential equation of the governing equation into a system of ordinary differential equations (ODEs). Then, the ODEs are solved using bvp4c in MATLAB 2019a software. The mathematical hybrid nanofluid and boundary conditions under the effect of suction, S, and the concentration of nanoparticles, ϕ 1 (Al2O3) and ϕ 2 (TiO2) are taken into account. Numerical results are graphically described for the skin friction coefficient, C f , and local Nusselt number, N u x , as well as velocity and temperature profiles. The results showed that duality occurs when the plate and the free stream travel in the opposite direction. The range of dual solutions expand widely for S and closely reduce for ϕ . Thus, a stability analysis is performed. The first solution is stable and realizable compared to the second solution. The C f and N u x increase with the increment of S. It is also noted that the increase of ϕ 2 leads to an increase in C f and decrease in N u x .
An analysis has been performed using the Buongiorno model on the nanofluid steady 2D stagnation point flow magnetohydrodynamic (MHD) over the shrinking surface to test its stability. Transforming the governing partial equations into a set of ordinary differential equation (ODE) and solved the equations numerically. In this paper, the impact of Brownian motion and thermophoresis has been considered and can be seen in ODE. The physical quantities of interest such as skin friction, local Nusselt number, local Sherwood number as well as the velocity and temperature profiles are acquired by numerical findings for some values of governing parameters such as ?, M, Pr, Le, Nb and Nt. Results show that duality of solutions exist for certain values e <-1 while unique solution exist when e >-1. On the other hand, as the parameter of M increased, the gradient of velocity increased, the rate of transmission heat and mass improved. Throughout the analysis, it demonstrates a linearly stable first solution in comparison to linearly unstable second solution.
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