The melting process of paraffin wax placed in storage capsules of different shapes was experimentally and numerically studied. The phase change material (PCM) was initially at 27 °C. The effect of the mushy zone parameter (A_mush) value on the melting process of the PCM was studied with storage capsules of different shapes (circular, vertical oval, and horizontal oval). The results of the numerical model were validated with the experimental results to obtain the optimum A_mush value for each shape of the latent heat storage unit. The results showed that the value of the A_mush has a great impact on the numerical results of the PCM melting process and changes with the shape of the storage capsule. The rate of heat transfer, convection, and fluid velocity all decrease as the A_mush value rises. The experimental results of the circular, vertical oval, and horizontal oval capsules match very well with the numerical model with A_mush values equal to 2 × 10⁶, 1 × 10⁵, and 1 × 10⁶, respectively.