A stationary and a transient two-dimensional models, based on the universal conservation laws and coupled with electrochemical reactions, are firstly applied to describe a single thermally-regenerative ammonia-based flow battery (TR-AFB), and emphasis is placed on studying the effects of reactant concentrations, physical properties of the electrolyte, flow rates and geometric parameters of flow channels on the battery performance. The model includes several experimental parameters measured by cyclic voltammetry (CV), chronoamperometry (CA) and Tafel plot. The results indicate that increasing NH3 concentration has a decisive effect on the improvement of power production and is beneficial to use higher Cu2+ concentrations, but the endurance of membrane and self discharge need to be considered at the same time. It is also suggested that appropriately reducing the initial Cu (NH3)(4)(2+) concentration can promote power and energy densities and mitigate cyclical fluctuation. The relation between the energy and power densities is given, and the models are validated by some experimental data.