We numerically investigate the melting and solidification behavior of phase-change materials (PCMs) encapsulated in a small-radii cylinder subjected to a cyclic convective boundary condition (square-wave). First, we explore the effects of the Stefan and Biot numbers on the nondimensionalized time required for a PCM initially held at to melt and reach the crossflow temperature (i.e., reference Fourier number ). The increase in either Stefan or Biot number decreases which can be predicted accurately using the correlation developed in this work. The variations of the PCM melt fraction, surface temperature, and heat transfer rate as a function of Fourier number are reported and analyzed. We further study the effect of the cyclic Fourier number on the periodic melting and freezing process. The melting or freezing front initiates at the outer periphery of the PCM and propagates toward the center. At higher frequencies, multiple two-phase interfaces are generated (propagating inward), and the surface temperature oscillates in the vicinity of the melting temperature. This increases the effective temperature difference with the crossflow and leads to a higher overall heat transfer.