Hybrid nanofluid is an advanced version of a nanofluid, which significantly boosts the heat transport mechanisms. Therefore, this can be considered a new alternative source to the traditional ways (involving certain fluids or nanofluids) of heating or cooling. The main concern of this manuscript is to scrutinize the flow field and heat transfer phenomena, for the flow of a hybrid (CNT - Fe3O4/H2O) nanofluid, inside an asymmetric long channel, whose porous walls exhibit embracing or parting motion. The equations, corresponding to the mass, momentum and energy conservations, have been modeled accordingly and after this, by making use of similarity transformations, a relevant set of nonlinear ordinary differential equations have been successfully achieved. In order to devise a numerical solution of the consequent equations, shooting method coupled with Runge-Kutta-Fehlberg algorithm have been employed. Furthermore, a graphical aid, to interpret the influential behaviors of various emerging entities on the velocity and temperature distributions, have also been provided. The dispersion of CNTs in (Fe3O4/H2O) nanofluid, have a considerable impact on the flow, temperature and heat transport properties, and these variations can be clearly visible at the both walls. Moreover, it has been observed that the SWCNTs, in most of the cases, seem to have a greater impact on the temperature profile as well as on the heat transport phenomenon. (C) 2019 Elsevier Ltd. All rights reserved.