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The modified model of magneto-hydrodynamic (MHD) flow and heat transfer of power-law fluid over a stretching permeable surface with prescribed heat flux in the presence of heat generation or absorption is investigated. The thermal conductivity is assumed to be dependent on the power law of velocity gradient. The general boundary conditions are given and Lie-group method is used to determine the appropriate boundary conditions suitable for the similarity solution. By using the achieved similarity transformations, the similarity equations are obtained and solved numerically by Bvp4c with Matlab. Graphical solutions for the dimensionless velocity and temperature as well as skin-friction coefficient and Nusselt number for various parameters are presented and discussed. [ABSTRACT FROM AUTHOR]