Group analysis and numerical solution of slip flow of a nanofluid in porous media with heat transfer

The steady laminar viscous incompressible free convective boundary layer flow of a nanofluid past a chemically reacting horizontal plate situated in porous medium taking into account heat generation/absorption and the thermal slip boundary condition is studied numerically. Similarity transformations are generated by Lie group analysis. Using the similarity transformations, the transport equations are reduced to a branch of coupled similarity equations which are solved by Runge-Kutta-Fehlberg fourth-fifth order numerical method. Our analysis reveals that true similarity solution will exist provided thermal slip factor is inversely proportional to two third power of the axial distance. Effect of the governing parameters on the dimensionless velocity, temperature, nanoparticle volume fraction has been presented. Excellent agreement between our results and published is obtained. A sample of numerical results for the reduced Nusselt number and the Sherwood number is provided in a table for various values of the parameters. The reduced Nusselt number is increased with the Lewis number and reaction parameter whilst it is decreased with the order of chemical reaction, thermal slip and generation parameters. Further, the reduced Sherwood number is enhanced with the Lewis number, generation and reaction parameters whilst it is suppressed with thermal slip and order of chemical reaction parameters.