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Molecular communication via diffusion in vessellike environment targets critical applications such as detection of abnormal and unhealthy cells. In this work, we derive the analytical formulation of the channel model for diffusion dominated movement, considering ring-shaped (i.e., patch) observing receivers and Poiseuille flow with the aim of localization of the transmitter cell. Then, we derive formulations using this channel model for two different application scenarios. We assume that the emission start time is known in the first scenario, and unknown in the second one. We successfully localize the transmitter cell using a single receiver for the first scenario, whereas two receivers are used to localize the transmitter cell in the second scenario. Lastly, the devised analytical framework is validated with simulations.