A truthful description of the energy transport process, which can be depicted by a physical quantity, namely power flow, is a significant angle to understand the Acoustic Black Hole (ABH) effect and its applications. To tackle the defect of existing semi-analytical models on ABH structures in calculating the higher-order derivatives of structural displacement, an energy formulation, in conjunction with a Rayleigh-Ritz procedure, is proposed for an ABH beam, in which the transverse displacement is constructed using Fourier series with supplementary terms. This treatment ensures the continuity and the smoothness of all relevant derivatives terms in the entire calculation domain, thus allowing the calculation of the power flow and structural intensity. Numerical examples are presented to illustrate the reliability and effectiveness of the established model. Numerical analyses on the dynamic behavior and power flow show the spatial and frequency characteristics of energy transmission process and reveal the ABH working mechanisms. While providing an efficient analysis tool, this work enriches the existing understanding on the dynamic behavior of ABH structures.