ABSTRACT The primitive focus of this article is to examine the consequences of unsteady electrically conducting non-Newtonian magnetised tangent hyperbolic hybrid nanofluid flow which slides along the extensible surface with a porous medium along with Darcy–Forchheimer in a flow. Here we have taken into account the thermophoresis and Brownian movement for single- and multi-wall CNT dispersed in water. The temperature profile is accompanied by non-linear heat flux and viscous dissipation. The aftermath of activation energy on the concentration and the flow of gyrotactic microorganisms are taken into consideration. Differential equations after introducing various parameters are converted into ODE with the help of similarity transformations, which are later on, are solved using the bvp4c solver in the MATLAB software. For the range 0 ≤ Sq ≤ 4 there is an upsurge in the picture profiles of concentration and temperature obtained. However, the velocity of the flow gets diminished when the range of MHD and porosity parameter is confined between 0 ≤ M , K p ≤ 6 .