Lie group analysis and numerical solutions for magneto-convective slip flow of nanofluid over a moving plate with Newtonian heating boundary condition

Abstract

Magnetohydrodynamic laminar boundary layer slip flow of a nanofluid over a moving plate with Newtonian heating boundary condition in the presence of heat generation–absorption effects is studied using Lie group analysis and a numerical method. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis. The governing transport equations are non-dimensionalized and transformed into a set of similarity equations using similarity transformations generated by Lie group transformations. The transformed equations are then solved using the Runge–Kutta–Fehlberg fourth- and fifth-order numerical method in Maple 17, which is also used to generate relevant graphs and tables. The flow, heat, and nanoparticle volume fraction characteristics are shown to depend on a number of thermophysical parameters, namely, Brownian motion, thermophoresis, Lewis number, Prandtl number, linear momentum slip, magnetic field, suction–injection, Newtonian heating, and heat generation–absorption. The effects of these parameters on the dimensionless stream function, velocity, temperature, nanoparticle volume fraction, wall heat, and mass transfer rates are investigated. Comparisons of the present numerical solutions with published works show very good correlation. The study finds applications in nano-technological magnetic materials processing.