The magnetohydrodynamic (MHD) stagnation point flow of a nanofluid over a permeable stretching/shrinking sheet is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of parameters. The numerical results show that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. For the stable solution, the skin friction is higher in the presence of magnetic field and increases when the suction effect is increased. It is also found that increasing the Brownian motion parameter and the thermophoresis parameter reduces the heat transfer rate at the surface.
The boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective boundary condition is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the local Nusselt number and the local Sherwood number as well as the temperature and concentration profiles for some values of the convective parameter, stretching/shrinking parameter, Brownian motion parameter, and thermophoresis parameter. The results indicate that the local Nusselt number is consistently higher for higher values of the convective parameter. However, the local Nusselt number decreases with increasing values of the Brownian motion parameter as well as the thermophoresis parameter. In addition, the local Sherwood number increases with increasing Brownian motion parameter and decreases with increasing convective parameter and thermophoresis parameter.
The stagnation point flow of a nanofluid towards a permeable stretching/shrinking sheet using the Buongiorno's model is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of the governing parameters. The numerical results show that dual (upper and lower branch) solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the physical realizable in practice of the dual solutions. It is found that the skin friction decreases when the sheet is stretched, but increases when the suction effect is increased. It is also found that increasing the thermophoresis parameter reduces the heat transfer rate at the surface, while increasing the Brownian motion parameter increases the mass transfer rate at the surface.
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