An improved model of carbon nanotube conveying flow by considering comprehensive effects of Knudsen number

Although the theoretical model of carbon nanotube conveying flow has been evolving from under macroscale theory framework to under nanoscale theory framework, for now, the small-scale effects have yet to be considered thoroughly. Herein, after extending the compatibility condition, we propose an improved model. Compared with the previous models, the improved model is not only dependent on the nonlocal parameter, but also comprehensively takes all the factors related to Knudsen number, namely effective viscosity, slip boundary condition and non-uniform flow profile, into account. Based on this model, a formula of critical flow velocity is derived in addition to numerical results and our model gives a considerably decreased critical flow velocity. Besides, when Knudsen number and nonlocal parameter increase, the critical flow velocity goes down dramatically, which indicates that the effects of Knudsen number cannot be neglected, and we demonstrate that the dispute over nonlocal parameter may impair the reliability of theoretical prediction of critical flow velocity. We also find that the effects of nonlocal parameter and Knudsen number on critical flow velocity are probably uncoupled.