Role of multiple solutions in flow of nanofluids with carbon nanotubes over a vertical permeable moving plate

Numerical study has been carried out to investigate the impacts of suction and buoyancy force on heat transfer flow past a vertically moving plate in carbon nanotubes. Two kinds of base fluids, particularly water and kerosene, with single-walled and multi-walled carbon nanotubes are adopted in this analysis. The governing equations for this study are solved using the similarity transformation. The resulting equations are solved using Matlab's built in function (bvp4c) numerically. The effect of mixed parameter, moving parameter, suction parameter, nanoparticle volume fraction parameter on the reduced heat transfer, skin friction, local Nusselt number, local skin friction along with velocity and temperature profiles are presented in graphical form and discussed in details. Multiple solutions are visible for certain range of governing parameters and hence the analysis on stability of solutions has been executed to show that the first solution is stable while the second solution is unstable. It is found that multi wall carbon nanotube offer higher heat transfer rate compared to single wall carbon nanotube. The range of solution to exist when adding 0.1 nanoparticle volume fraction shows an increment of 0.511. Hence, it is concluded that addition of nanoparticle volume fraction could delay the boundary layer separation to occur. Meanwhile, suction parameter decelerates the separation of boundary layer flow. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.