Charging performance optimization of a latent heat storage unit with fractal tree-like fins

•Fractal tree-like fin is developed for the melting heat transfer enhancement.•Convection-conduction synergy principle is responsible for melting enhancement.•RSM optimization is conducted for energy charging performance optimization.•Optimal length ratio and thickness index are 1.07 and 0.65, respectively.•Total melting duration time of the optimized LHS unit reduces by 26.7%.