In this research, the cross-section of a semi-transparent cylindrical chamber containing phase change materials (PCM) has been investigated under the solar radiation. For this purpose, the conduction heat transfer with the volumetric absorption of solar radiation has been simulated using the Lattice Boltzmann method (LBM). Besides, the effect of refraction of a semi-transparent cylindrical wall on the melting process of the PCMs in the enclosure has been evaluated under different conditions. Moreover, the effect of the wall thickness and its refraction index and the constant or variable intensity of the incoming solar radiation have been investigated. The opposing effect of the wall thickness in heat loss from the boundaries of the enclosure in companion to the refractive behavior of the wall is studied. The findings indicate that the refractive index of the wall notably impacts the duration required for charging. Specifically, it extends the charging period by approximately 22% in insulated enclosures and around 19% in enclosures with convective boundaries. The impact is more pronounced for values nearing one compared to those closer to 1.5. Additionally, increasing wall thickness contributes to a moderate improvement in charging time due to the refraction of the beam. However, this improvement is influenced by two conflicting factors: while thicker walls lead to increased heat loss to the environment, the higher conductive thermal resistance within the wall serves to impede this loss.