Lie Group Analysis of Natural Convective Flow from a Convectively Heated Upward Facing Radiating Permeable Horizontal Plate in Porous Media Filled with Nanofluid

Abstract

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed equations are solved numerically by Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Effects of the governing parameters on the dimensionless velocity, temperature and nanoparticle volume fraction as well as on the dimensionless rate of heat and mass transfer are presented graphically and the results are compared with the published data for special cases. Good agreement is found between numerical results of the present paper and published results. It is found that Lewis number, Brownian motion and convective heat transfer parameters increase the heat and mass transfer rates whilst thermophoresis decreases both heat and mass transfer rates.