Effects of thermal radiation and variable density of nanofluid heat transfer along a stretching sheet by using Keller Box approach under magnetic field

Most of research has been discovered with lower temperature differential and constant density between the ambient fluid and the surface. The density is assumed as exponential function of temperature due to larger temperature difference with radiation. The magnetohydrodynamics (MHD) acts like a coating material to protect technological devices from excessive heating. Main focus of this mechanism is the variable density, MHD and radiation effects on heat and mass characteristics of nanofluid across stretching sheet with thermophoresis and Brownian motion to reduce excessive heating in high temperature systems. This is first temperature-dependent density problem of nanofluid across the stretching surface. The coupled (PDEs) partial differential equations of the present nanofluid mechanism are changed in nonlinear coupled ordinary differential equations (ODEs) with defined stream functions and similarity variables for smooth algorithm and integration. The changed ODEs are again converted in similar form for numerical outcomes by applying Keller Box approach. The numerical outcomes are deduced in graphs and tabular form with the help of MATLAB program. In this phenomenon, the velocity, temperature, and concentration profile along with their slopes has been plotted for various parameters for current issue. The range of parameters has selected according as Prandtl number 0.07 < Pr < 70.0, buoyancy parameter 0 < xi < infinity and the choice of magnetic force parameter set the effects of magnetic diffusion and magnetic energy respectively. The novelty of the current work is to compute radiation, MHD and temperature dependent density effects along the stretching sheet due to high temperature difference between the surface and ambient fluid. By the encountering the radiation fluid becomes optically dense gray fluids. So, the thermal radiation is just used as a supporting agent for heat transfer assessment due to exponentially temperature dependent density.