**ABSTRACT**

In this paper, Galerkin’s decomposition-differential transformation method has been applied to analyze the simultaneous impacts of various parameters on the nonlinear vibration of carbon nanotube hot fluid-conveying nanotube resting on elastic foundations in a magnetic environment. Partial differential equation of motion governing the vibration of the nanotube was derived using Erigen’s theory, Euler-Bernoulli’s theory and Hamilton’s principle. The developed analytical solutions are employed to explore the effects of various parameters such as surface energy, initial stress and nonlocality, etc. on the dynamic behaviour of the nanostructure The results are presented graphically for illustrations and discussion. It is hoped that the present work will assist in the control and design of the nanostructures.

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