Lie group analysis on brownian motion and thermophoresis effect on free convective boundary-layer flow on a vertical cylinder embedded in a nanofluid-saturated porous medium

Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. the model used for the nanofluid incorporates the effects of brownian motion and thermophoresis. lie groups analysis is used to get the similarity transformations,which transform the governing partial differential equations to a system of ordinary differential equations. two groups of similarity transformations are obtained. numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters. © 2015 mohammad ferdows et al.