Vibrational characteristics analysis of a thermoelastic nanoparticle submerged in an incompressible viscous fluid

In this article, we develop an analytical approach to characterize the breathing mode vibration of a thermoelastic nanosphere submerged in an incompressible fluid. The inclusion of temperature is under the concept of heat wave and the energy equation is combined with elastic theory in the fluid-structure interaction method. The bi-harmonic function is derived from the coupling of the velocity and temperature fields by the coupled thermoelasticity theory. Whereas for an incompressible fluid, these two fields are decoupled. This leads to the convenience of separating thermal conduction and dynamic viscosity parts in the frequency equation. The validation of frequency equation is confirmed by comparing other literatures. The thermal damping and viscosity are represented by Péclet number and Reynolds number respectively. The effects of two parameters on the vibration of the system are analyzed with multiple plots. The analysis could be a useful interpretation of experimental observation and an applicable measurement for vibrational and rheological properties of solids and fluids.