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Carbon nanotube (CNT) is very effective for disease treatment based on drug delivery to a target tissue, in which sustained drug release is undesirable. In the present study, magnetic-fluid flow effect and fluid and CNT size effects are investigated on the structural instability of a CNT conveying nanofluid under a longitudinal magnetic field. There is lack of research that evaluates the size-dependent problems using the appropriate robust non-classic theory. Therefore, in the present study size effects are captured using a combination of nonlocal elasticity theory and nonlocal couple stress theory. Governing equation of motion and related boundary conditions are derived using the Hamilton’s principle and they are solved by the Galerkin method. The Navier–Stokes equation of magnetic-fluid flow is coupled with the Euler–Bernoulli beam theory for modeling fluid-structure interaction (FSI). The CNT stability is evaluated by considering nonlocal sizing effect parameter, couple-stress sizing effect parameter, Knudsen number, magnetic field intensity, chirality of CNT, and velocity of fluid flow. Results indicate that a special CNT configuration can improve the stability by 16.2%. Additionally, increasing the couple stress sizing effect parameter can improve the system stability up to 48%. However, this value is reduced to 18% when a magnetic field is applied to the system. On the contrary, results indicate that the nonlocal sizing effect parameter reduces the critical speed and the system stability. Therefore, the couple-stress and nonlocal sizing effects have substantial roles in the stability assessment, which should be considered in the planning for a successful treatment.

Stability analysis of conveying-nanofluid CNT under magnetic field based on nonlocal couple stress theory and fluid-structure interaction