Latent　heat　thermal　energy　storage　employing　phase　change　materials　is　widely　used　in　energy　storage　systems.　To　further　improve　the　low　thermal　conductivity　of　phase　change　materials　in　these　systems,　it　is　essential　to　investigate　different　thermal　enhancement　techniques.　In　this　work,　two　principal　thermal　enhancement　techniques　(i.e.,　finned　tubes　and　conductive　metal　foams)　are　numerically　investigated　for　melting　processes　in　a　shell-and-tube　latent　heat　thermal　energy　storage　system.　Topology　optimised　structures　are　used　as　fins,　and　the　simulation　predictions　are　validated　by　experimental　results　using　additive　manufactured　topology　optimised　fins.　For　metal　foams,　different　filling　ratios　(i.e.,　whole-foam　structure　and　half-foam　structure)　are　considered.　Compared　to　the　configuration　without　enhancement,　the　thermal　energy　storage　rates　are　3.3-5.8　times　higher.　In　addition,　the　results　show　that　the　topology　optimised　fins　can　achieve　the　best　performance,　but　can　only　be　an　economical　solution　when　the　unit　price　ratio　between　the　enhancement　technique　and　the　phase　change　materials　is　less　than　6.　For　the　first　time,　the　thermal　enhancement　performance　and　economic　efficiency　of　these　two　principal　techniques　are　quantitatively　analysed.　The　results　would　be　useful　for　appropriate　energy　storage　design　solutions　in　practice.　(c)　2022　Elsevier　Ltd.　All　rights　reserved.