A queuing-theoretic framework for magnetohydrodynamic flow and reactive mass transfer in Casson fluid systems with interruptions and recovery phases

This study presents a novel queuing-theoretic framework to analyze magnetohydrodynamic flow and reactive mass transfer in Casson fluid systems, particularly under conditions involving delays, interruptions, and recovery phases. The fluid is modeled as a non-Newtonian Casson fluid with yield stress, flowing over a vertical porous plate under the influence of a uniform transverse magnetic field. Transport and reaction processes are conceptualized as a two-stage queuing system, allowing the integration of real-world dynamics such as service delays, flow breakdowns, and mass reactivation events. The governing equations and boundary conditions are formulated using a birth–death transformation derived from queuing theory. Numerical simulations, conducted using MATLAB, reveal that magnetic effects and Casson fluid properties introduce substantial delays in both momentum and mass transport, ultimately reducing the overall efficiency of mass transfer. The findings provide meaningful insights for the design and optimization of microfluidic, electrochemical, and biomedical systems, where control over flow and reaction timing is critical. The proposed approach establishes a novel queuing-based paradigm for analyzing non-Newtonian transport behavior, allowing systematic prediction and control of delay-driven inefficiencies across a range of fluid engineering applications.