A mathematical model is created to analyze the impact of Thompson and Troian slip boundaries over a contracting/expanding surface sustaining nanofluid-containing carbon nanotubes along a stagnation point flow. Both multi-wall (MWCNTs) and single-wall (SWCNTs) carbon nanotubes are taken into consideration, with water serving as the base liquid. The flow is obtained due to the stretching or contracting of the surface. The thermal radiation, activation energy, buoyancy impacts, and chemical processes called quartic autocatalysis are additionally added to the original mathematical model. The MATLAB-constructed bvp4c function involving the three-stage Lobatto IIIa formula for the numerical results of dimensionless velocity, concentration, and temperature profiles are used. By contrasting it against a published paper in this limited instance, it is determined whether the suggested mathematical model is legitimate. In this sense, a remarkable consensus is achieved. Graphical representations are used to depict the behavior of many non-dimensional flow variables, such as the slip velocity parameter, the inertia coefficient, the porosity parameter, and the solid volume fraction. Surface drag force computations are reported to examine the effects at the permeable stretching surface. It has been shown that increasing the slip velocity factor increases the fluid streaming velocity while decreasing the surface drag force. If the endothermic/exothermic coefficient increases, the local thermal transfer efficiency falls. For nanofluids, the changing viscosity factor increases axial velocity while decreasing temperature distribution. Additionally, the solid volumetric fraction improves the temperature distributions by lowering the concentration profile and speed.