Purpose <p>The linear and nonlinear dynamic characteristics analysis of the clamped–clamped single walled carbon nanotube (SWCNT) sensors transporting fluids in a longitudinal magnetic field are investigated. The 6th-order fluid–structure interaction (FSI) motion equation is derived through the Hamilton principle. This equation is established based on Euler–Bernoulli beam theory and takes into account nonlinear effects. Meanwhile, according to the nonlocal strain gradient theory, nonlocal size effect and strain gradient scale effect are also considered. Then the non-classical higher order boundary conditions are obtained employing the weighted residual method.</p> Method <p>The boundary value problem of 6th-order linear partial differential equation (PDE) of motion is solved using the differential transformation method (DTM), whereas the nonlinear boundary value problem of motion is solved using polynomial approximation mode shape function of the Galerkin method and the variational iteration method.</p> Results and Conclusions <p>The investigation extends to dimensionless natural frequencies, dimensionless critical flow velocities. Factors such as nonlocal coefficients, strain gradient parameters, higher order boundary conditions and longitudinal magnetic field are considered. Besides, the nonlocal frequency shift percentage (NFSP), strain gradient frequency shift percentage (SFSP) are further analyzed to facilitate the design of CNT sensors conveying fluid. At last, the nonlinear amplitude-frequency curves and amplitude-critical fluid velocity curves are explored. The insights provided in this study aim to elucidate scale-dependent phenomena observed experimentally in nano mechanics and contribute to the effective design of CNT conveying fluid sensors.</p>