Document Type : Research Paper
Authors
1
1. Department of Mechanical Engineering, University of Lagos, Nigeria. 2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA.
2
Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria. Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria.
3
Department of Mechanical Engineering, University of Lagos, Nigeria.
4
Department of Mechanical Engineering, Federal University of Agriculture, Abeokuta, Nigeria.
5
Department of Mechanical Engineering, Lagos State University, Nigeria.
Abstract
The nonlinear vibration analysis of embedded multi-walled branching nanotubes with integrated nanofluids that are resting on a Winkler-Pasternak foundation in a thermal-magnetic environment is the main emphasis of this work. The coupled equations of motion controlling the transverse and longitudinal vibrations of the nanotube are derived using the Euler-Bernoulli theory, the Hamilton’s principle, and nonlocal elasticity theory. Additionally, the pressure variation in the tubes and the equation for the deformation of the nanotubes are derived. Furthermore, the vibration models are coupled with the Navier-Stokes equation and the energy equation for the fluid and nanotube. Since the dynamics of multi-walled carbon nanotubes differ from the typical assumption of plug flow, careful investigation is needed when combining them with Navier-Stokes and energy equations. Thus, the generated coupled systems of nonlinear partial differential equations in this work are solved using multi-dimensional differential transformation method. With the aid of the analytical solution, parametric studies are performed. The findings show that the system's stability reduces as the downstream angle increases. Furthermore, the system's dynamic behavior yielded results that show the magnetic effect has a 20% attenuating or damping effect. Additionally, there is a more than 11% discrepancy between the plug flow assumption and real functioning procedures. Existing analytical, numerical, and experimental results were used to verify and validate the analytical method. It is hoped that this study will provide further understanding of the design of nanotubes and act as a reference for further research in the field
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