The effective thermal conductivity is a robust alternative to include the effect of natural convection during the melting of a phase-change material, while solving only the energy equation. With this approach, significant time savings may be obtained, maintaining satisfactory accuracy. However, it remains unclear how well the existing equations predict the enhanced conductivity for horizontal shell-and-tube heat exchangers, particularly in terms of accurately estimating the liquid fraction. In this paper, a simplified model for the melting of a phase-change material is developed based on the pure conduction formulation while considering natural convection. The model was solved using the finite volume method and implemented in Python. A previously validated computational fluid dynamics (CFD) model was used to calculate the enhanced conductivity, which was then applied to the simplified model. The simplified model was found to be 3500 times faster than the CFD model, with a maximum deviation of only 8.2%. Subsequently, existing correlations to predict the effective thermal conductivity were assessed. The results for the liquid fraction predictions indicated maximum deviations ranging from 33.6% to 144.8%, for predictors developed under melting conditions, and from 35.6% to 231.1%, for equations developed without considering phase-change. Further, new correlations, spanning all melting regimes, were proposed, revealing maximum deviations of 17.73% and 10.24% for the different scenarios evaluated. Therefore, the new correlations demonstrated to be the preferred choice to obtain more accurate models for the melting of phase-change materials inside horizontal shell-and-tube units.