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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

journal of applied mathematics

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