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Targeted magnetic drug delivery (TMDD) is a promising approach relevant to multimodal cancer therapy. A majority of the TMDD models represent a mixture of blood and nanoparticles as a one-phase solution. However, in many cases it is an oversimplistic assumption. The existing two-phase models are usually one-way coupled, i.e. the blood flow has an impact on the MN flow. However, the inverse impact of the MNs on the the blood is not included. To eliminate these drawbacks the model is governed by two–way coupled momentum and temperature equations for the blood flow and the MN. The numerical procedure invokes the stream function–vorticity formulation and an efficient numerical procedure. The model, validated by experimental results, has been applied to analyze the formation of vortices generated by a combination of the magnetic force (MF) and the drag force (DF). The model also simulates the zones of TMDD and the corresponding changes in the vorticity. Finally, the model includes the impact of the size and concentration of the MNs on the temperature of the blood. These important scenarios cannot be analyzed by the earlier models.