Lie symmetry analysis for nonlinear radiative mhd convective nanofluid slip flow with melting boundary condition

Motivated by possible manufacturing process involving fluid mechanics of magnetite nanofluid systems, we examine the 2-D magnetohydrodynamic boundary layer flow and heat transfer of a nanofluid along a stretching/ shrinking sheet. Nonlinear thermal radiation heat transfer is included to simulate thermophysical effects at high temperature. A mathematical model is developed with Brownian motion and thermophoresis, velocity slipand melting effects. Lie symmetry group transformations are implemented to transform the govering partial equations into ordinary differential equations before being solved numerically by using symbolic Maple 17 software. Our solutions are found to correlatewell with earlier results for specialized cases. Numerical computations for the dimensionless velocity, temperature, nanoparticle volume fraction profiles, skin friction coefficient, Nusselt and Sherwood numbers are presented through graphs and tables for various values of the physical parameters. Increasing transverse magnetic field is observed to decelerate the sheet flow for both the stretching and shrinking cases whereas it enhancesnanoparticle volume fraction rates. Furthermore the friction factor, heat transfer rates and nanoparticle volume fraction rates decrease with the melting parameter for both stretching and shrinking sheet. Our study is pertinent to the synthesis of bio-magnetic nanofluids ofpotential interest in wound treatments, skin repair and smart coatings for biological devices