The current study explores the entropy production rate in the flow induced by ciliary pumping systems through cylindrical tubules created under consequences of a magnetic field acting externally in the direction normal to flow. Impacts of Hall currents, viscous dissipation and ohmic heating on heat and mass transferals in bio-magnetic viscous materials are the prominent features of the present model.The governing equations make up a nonlinear coupled system of five partial differential equations in velocity components, pressure gradient, temperature and concentration distributions. However, implication of creeping flow approximation in the wave frame of reference makes the problem linear such that solutions of the aforementioned quantities are obtained analytically. Expressions for entropy production rate and Bejan number are also formulated for the present flow scenario. Effects of heat and mass transfers, Hartmann number, Hall current and cilia length parameters on the flow field, pumping characteristics, temperature, concentration, entropy production rate and Bejan number are discussed in details. Key observations are also summarized in the concluding section. It is found that the inclusion of Hall current not only overcomes the damping effects of magnetic field but also controls the disorderness of thermodynamic systems. Also, cilia with higher lengths stimulate the momentum transfer in the axial flow direction and consequently promote the pumping rate.