Melting heat transfer analysis of electrically conducting nanofluid flow over an exponentially shrinking/stretching porous sheet with radiative heat flux under a magnetic field

Modern magnetic nanomaterials processing operations are progressing rapidly and require increasingly sophisticated mathematical models for their optimization. Stimulated by such developments, in this article, a theoretical and computational study of steady magnetohydrodynamic (MHD) flow of nanofluid from an exponentially stretching/shrinking permeable sheet with melting (phase change) and radiative heat transfer is presented. Wall transpiration i.e. suction and blowing (injection) is included. Buongiorno’s nanofluid model is deployed which simulates the effects of Brownian motion and thermophoresis. The transport equations and boundary conditions are normalized via similarity transformations and appropriate variables and similarity solutions are shown to depend on the transpiration parameter. The emerging dimensionless nonlinear coupled ordinary differential boundary value problem is solved numerically with the Newton-Fehlberg iteration technique. Validation with special cases from the literature is included. Increasing magnetic field i.e. Hartmann number is observed to elevate nanoparticle concentration and temperature whereas it damps the velocity. Higher values of melting parameter consistently decelerate the boundary layer flow and suppress temperature and nanoparticle concentration. Higher radiative parameter strongly increases temperature (and thermal boundary layer thickness) and weakly accelerates the flow. Increasing Brownian motion reduces nanoparticle concentrations whereas greater thermophoretic body force strongly enhances them. Nusselt number and Sherwood number are decreased with increasing Hartmann number whereas they are elevated with stronger wall suction and melting parameter.