Partial Differential Equations in Applied Mathematics (Mar 2024)
Numerical investigation on the thermal-nanofluidic flow induced transverse and longitudinal vibrations of single and multi-walled branched nanotubes resting on nonlinear elastic foundations in a magnetic environment
Abstract
Carbon nanotubes (CNTs) have attracted great attention due to their tremendous mechanical, thermal, structural and electrical properties leading to many promising applications. The unique and interesting properties of CNTs, such as their mechanical and electrical features, have fascinated industries and researchers to implement CNTs for production of different electromechanical devices. However, it is established that the phenomenon of buckling often occurs when CNTs are subjected to compressive loads and their frequencies under vibration are in order of Tera-Hz and Giga-Hz. Moreover, the profound dynamic behaviours of nanotube under the influences of slip when conveying fluid and magnetic field require a serious and meticulous study. Therefore, this study focuses on the vibration analysis of nanofluid-conveying embedded multi-walled branched nanotubes resting on Winkler-Pasternak foundation in a thermal-magnetic environment. Using Euler-Bernoulli theory, Hamilton's principle and nonlocal elasticity theory, fully coupled equations of motion governing the transverse and longitudinal vibrations of the nanotube are developed. Also, the equation of the deformation of the nanotubes as well as the pressure variation in the tubes are developed. Additionally, Navier-Stoke's equation and energy equation for the fluid and nanotube are coupled with the vibration models. The dynamics of the multi-walled carbon nanotubes when coupled with Navier-Stokes and energy equations require meticulous study as it is different from the usual assumption of plug flow. Therefore, in this present work, the developed coupled systems of nonlinear partial differential equations are solved using multi-dimensional numerical PDEs solvers coupled with PDE-tools in MATLAB. With the aids of the solutions, parametric studies were performed. The results indicate that increasing the downstream angle decreases the stability of the system. Also, the results obtained from the dynamic behaviour of the system indicate that the magnetic effect has an attenuating or damping effect of about 20 %. Furthermore, the plug flow assumption deviates from actual working processes by over 11 %. The analytical solutions verified and validated with existing analytical, numerical and experimental results. It is envisaged that the present study will give better insight into nanotubes design and serve as an index for subsequent works in the research area.
