Comparative analysis for flow of CNTs nanofluids is discoursed in the presence of non-Darcy porous medium. The consequences of homogeneous/heterogeneous process and heat transfer through convection are employed. The flow induced is due to non-linear stretching sheet of variable thickness. The bottom of the variable thickness sheet is heated by convective processes from a heated fluid. The velocity, temperature and concentration functions are formulated for the stretched flow problem. Convergence control variables and square residual errors for series solutions are obtained through OHAM (Optimal Homotopy Analysis Method). Biot number corresponds to larger temperature distribution in case of MWCNT than SWCNT. Comparison of nanoparicles SWCNT and MWCNT for the CNTs nanofluid fluids is highlighted. Water and engine oil CNTs fluids have higher magnitude of Nusselt number when compared with kerosene oil CNT fluid. The heat transfer rate in the presence of MWCNT is higher than SWCNT. Comparison of present study with previous published data is made. The outcomes are found in favorable agreement. (C) 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.