A theoretical investigation was conducted to understand the stability of boiling on annular fin surfaces with different boundary conditions. Lyapunov 's function was derived for boiling on annular fin surfaces; its characteristics near the steady distribution are particularly investigated. With no pre-assumed functional form for the temperature perturbation to be imposed to the boiling system, a general stability analysis was established by optimizing Lyapunov's function. The steady temperature distribution with isothermal or isoflux condition was obtained numerically, and the boiling heat transfer characteristic was noted to be dependent of the fin configuration and boundary conditions. Annular fin surfaces can significantly benefit the heat transfer, and the fins with small inner radii have better performance of base heat flux or temperature. The most unstable mode and maximum eigenvalue were employed to describe the boiling stability under various boundary conditions, and characteristics of the obtained maximum eigenvalue very well match with those of the boiling heat transfer on annular fin surfaces.
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