Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation

A mathematical model is presented and analysed for steady two-dimensional non-isothermal boundary layer flow from a heated horizontal surface which is embedded in a porous medium saturated with a non-Newtonian power-law nanofluid. It is assumed that the wall temperature and nanoparticle volume fraction vary nonlinearly with the axial distance. By applying appropriate group transformations, the governing transport equations are reduced to a system of coupled, nonlinear ordinary differential equations with associated boundary conditions. The reduced equations are then solved numerically using the Runge-Kutta-Fehlberg fourth-fifth-order numerical method with Maple 13 software. The effects of several thermophysical parameters including rheological power-law index, non-isothermal index, Lewis number, Brownian motion parameter, thermophoresis parameter, buoyancy ratio and internal heat generation/absorption parameter on the non-dimensional velocity, temperature, nanoparticle volume fraction (concentration) and also on the friction factor, heat and mass transfer rates are investigated. A comparison of the present results with the existing published results shows excellent agreement, verifying the accuracy of the present numerical code. The study finds applications in nano biopolymeric manufacturing processes and also thermal enhancement of energy systems employing rheological working fluids.