Molecular communication (MC), one of the emerging techniques in the field of communication, is entering a new phase following several decades of foundational research. Recently, attention has shifted toward MC in liquid media, particularly within tubular environments, due to novel application scenarios. The spatial constraints of such environments make accurate modeling of molecular movement in tubes more challenging than in traditional free-space channels. In this paper, we propose a three-dimensional channel model for molecular communications with an absorbing ring-shaped receiver in a tubular environment. To the best of our knowledge, this is the first theoretical study to model the impact of an absorbing ring-shaped receiver on the channel response in tube-based MC systems. The problem is formulated as a partial differential equation with heterogeneous boundary conditions, and an approximate solution is derived under flow-dominated conditions. The accuracy of the proposed model is validated through particle-based simulations. We anticipate that the results of this study will contribute to the design of practical MC systems in real-world tubular environments.