<p>Tumor growth within physiological systems such as the gastrointestinal tract, ducts, or blood vessels can progressively obstruct fluid transport, impair organ function, and reduce the efficacy of therapeutic interventions like drug delivery and hyperthermia. In this study, a mathematical model is developed to investigate and characterize the mechanisms of peristaltic flow in a channel obstructed by transient tumor growth. The model incorporates fundamental conservation laws of mass and momentum, while a bump function is used to represent tumor-induced geometric deformation of the channel wall. In addition, a transverse magnetic field is introduced to account for magnetohydrodynamic effects relevant to biomedical applications such as magnetic hyperthermia. Tumor growth is modeled as a linear time-dependent process, and the flow is analyzed under low Reynolds number and lubrication theory assumptions, which are suitable for physiological flows. Analytical solutions are derived under simplified conditions to examine the influence of tumor growth rate and magnetic field strength on velocity distribution, pressure gradient, wall shear stress, streamline patterns and particle trajectories. The results suggest that early-stage tumor growth produces minimal flow disturbance, whereas progressive enlargement significantly obstructs flow, increases local pressure and skin friction and alters streamline patterns. An increase in Hartmann number enhances magnetic resistance, leading to a reduction in axial velocity and volumetric flow rate. Furthermore, parametric sensitivity analysis reveals that tumor geometric parameters play a dominant role in governing flow behavior compared with magnetic and peristaltic effects.</p>