Magnetically targeted drug delivery system is gaining importance over recent years due to its efficiency and minimum side effects. There are many techniques proposed for delivering drugs to targeted sites within the human body. But magnetically targeted drug delivery surpasses because of its unique character and high efficiency. There are only few theoretical analyses done by researchers addressing the hydrodynamic models of magnetic fluids in the blood vessel. This paper presents a mathematical model on hydrodynamics of the fluid, blood flow and convective diffusive mass transfer of the species. Here we have tried to analyze a drug delivery method for delivering drug to a specific site in the body. For this analysis, we have considered a channel bounded by the tissue region where the drug is targeted. An exact analysis of unsteady convective diffusive solute transfer in a channel bounded by tissue region under the influence of magnetic field.