Dual solutions analysis of melting phenomenon with mixed convection in a nanofluid flow and heat transfer past a permeable stretching/ shrinking sheet

The 2-D MHD nanofluid with mixed convection above a stretching/shrinking plate has been investigated. Melting heat transfer near surface is contemplated. Consider the saline water as base fluid with containing single SWCNTs as well as MWCNTs. Suitable similarity variables are employed to transform the governing PDEs into ODEs. These transformed equations which are coupled, and of high nonlinearity, have been solved through applying the bvp4c solver. The consequences of the relevant parameters like, the MHD parameter, mixed convection parameter, melting parameter, volume fraction on the flow field along with the skin friction and heat transfer rate are displayedingraphical form. Results, 0 show0that 0 the thin layer thickness diminishes as magnetic parameter enhances andat the sametime temperature increases with magnetic parameter. It is also demonstrated that the melting parameter leads to a reduction in the thin layer thickness as well as dimensionless temperature. Obtain dual solutions for flow fields which delineates to identify the stable solution.