The present paper focuses on a numerical study for an inclined magneto-hydrodynamic effect on free convection flow of a tangent hyperbolic nanofluid embedded with carbon nanotubes (CNTs) over a stretching surface taking velocity and thermal slip into account. Two types of nanoparticles are considered for the study; they are single and multi-walled nanotubes. The presentation of single-parameter group (Lie group) transformations reduce the independent variable number by one, and hence the partial differential governing equations with the supplementary atmospheres into an ordinary differential equation with the appropriate suitable conditions. The obtained ordinary differential equations are then numerically solved by employing the fourth-order Runge-Kutta technique along with the shooting method. The effects of the various parameters governing the flow field are presented with the help of graphs. The investigation reveals that the non-Newtonian MWCNTs Tangent hyperbolic nano-liquid reduces the friction near the stretching sheet contrasting SWCNTs. This combination can be used as a friction lessening agent/factor. The usage of CNTs shows an excellent performance in enhancing the thermal conductivity of the nanoliquid and that single-wall carbon nanotubes (SWCNTs) have a higher thermal conductivity in comparison to multi-wall carbon nanotubes (MWCNTs) even in the presence of radiative heat transfer and heat source. The comparison with existing results available in the literature is made and had an excellent coincidence with our numerical method. © 2020, Shahid Rajaee Teacher Tarining University (SRTTU). All rights reserved.