A novel fin-foam combination, applying upward fins to accelerate natural convection and downward foams to dominate thermal conduction, was established to comprehensively enhance the melting and solidifying performance of horizontal shell-and-tube latent heat storage devices. Enhancement mechanisms of the current design were numerically investigated and compared with the typical eccentric and concentric design the whole melting-solidifying process. Among investigated enhancement designs, the fin-foam combination achieved the best results, reducing the melting time and the solidifying time by 47.9% and 55.4% respectively. Meanwhile, the relative difference between the melting and solidifying time was reduced to 12%, indicating a significant mitigation of the buckets effect of solidifying caused by eccentric designs. Further, the effect of the total enhancement material usage was investigated. Results showed that the marginal effect of the heat transfer enhancement started at 9 fins and 0.91 porosity, but the relative difference between melting and solidifying time then dropped below 0.61%. The economic assessment showed that increasing the amount of enhancement material can significantly improve the storage capacity per unit cost when the price ratio of the enhancement material to PCM is less than 10, indicating a considerable applicability and cost performance of fin-foam combination under different power density demands.