Abstract
The time parameter for thermal relaxation is essential to change the nanobeam resonator's energy damping and thermal quality. This paper has established a thermal analysis model to analyze the relaxation times and the effect of the static pre-stress on a nano-resonator made of silicone. In the fractional dual-phase heat-conducting model, the equations have been constructed. The thermal quality factor impacts were discussed of the fractional parameter, length-scale, static pre-stress, isothermal frequency, and thermal relaxation times. The model may expect a significant enhancement in thermal quality factors by tuning the static pre-stress and length scale. The isothermal frequency and fractional order parameter have significant effects on the thermal quality factor of a silicon nanobeam resonator.