Latent thermal energy storage systems (LTESS) have attracted increasing interest. However, the persistent challenge resides in the inherently low thermal conductivity of phase change materials (PCMs). Recent advancements in combined enhancement techniques offer promise for addressing this issue. This study introduces a novel approach by focusing on optimising the global melting and solidification of a horizontal double-pipe regenerator through the integration of hybrid techniques, specifically combining unevenly distributed fins and eccentricity. The response surface method (RSM) utilizing computational fluid dynamics (CFD) and non-linear programming by quadratic Lagrangian (NLPQL) was employed to find the optimum solution. The objective function is defined as the total melting and solidification time. The independent parameters are fins' angles (α & β) and eccentricity value (Ec). Ec ranges from 0.1 to 0.4 in scenario 1 and −0.4 to −0.1 in scenario 2. Angles α and β vary between 0–45° and 45–80°, respectively. Two scenarios are investigated: one featuring positive eccentricity with upper fins and the other with negative eccentricity and lower fins. The findings reveal that the first scenario outperformed the second, showing a substantial reduction in total charging and discharging time. Specifically, the optimal melting case in the first scenario achieved a 56.6 % time saving compared to 38.3 % in the second scenario. For the optimal solidification case, the time savings are 52.8 % and 40.8 % for the first and second scenarios, respectively. The optimal configuration, featuring Ec = 0.23, α = 22.27°, and β = 71.61°, resulted in a remarkable 47 % reduction in total melting and solidification time compared to the unenhanced reference case.