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A mathematical model based on finite-element technique is developed for predicting the transport and capture of multiple magnetic nanoparticles in a microfluidic system that consists of a microfluidic channel enclosed by a permanent magnet. The trajectories and trapping efficiencies are calculated for multiple magnetic nanoparticles when released in the microsystem. It is demonstrated that not only the size but also the point of release of nanoparticles within the microchannel affects the capturing process. Influence of three important parameters, inlet velocities of fluid containing magnetic nanoparticles, diameter of magnetic nanoparticles and magnetic field strength on the trapping efficiency are investigated and optimised values of inlet velocity and magnetic field strength for completely trapping 50 nm magnetic nanoparticles are predicted. It is further demonstrated that the angular position of magnet around the microchannel is also critical in dictating the resulting bioseparation performance. Furthermore, combination of these analyses using the mathematical model will be very useful in the design and development of novel microfluidic bioseparation microsystems.