Effect of convective boundary condition on unsteady flow of CNT-H2O nanofluid towards a stagnation-point on a shrinking/expanding flat sheet

A model study of unsteady stagnation-point flow of most important nanoparticles, that is, carbon nanotubes suspended nanofluid towards shrinking/expanding sheet with convective boundary condition is demonstrated. Two types of carbon nanotubes, namely, single-wall and multi-wall nanotubes are carefully considered. Numerical solutions of converted equations from governing equation of the problem are obtained and those are graphically presented. Similar to without carbon nanotubes case, dual and unique solutions in specific ranges of velocity ratio parameter are achieved. Analysis disclosures that the condition on range where dual solutions exist is unaltered with solid-volume fraction and type of carbon nanotubes. The surface drag-force and heat transfer rate from wall are larger for single-walled carbon nanotubes nanofluid than multi-walled carbon nanotubes nanofluid. An increment in the parameter related to convective boundary condition generates high rate of heat transfer. After stability analysis, it is identified that in case of dual solutions, upper branch is stable and lower branch is unstable, while unique solution is always stable.