The analysis of solute and thermal dispersion in pulsatile flow through the stenotic tapered blood vessel is presented. The present problem is an extension of the work done by Ramana et al. who considered the time-invariant arterial wall. In the present model, the flexible nature of the arterial wall through the obstruction (called stenosis) is considered and it is achieved with the help of period trigonometric function. In the present study, the impact of the time-dependent arterial wall on the blood flow dynamics is discussed in details. The rheology of the blood is modeled as a couple stress fluid. The proposed fluid model is the isothermal inclusion of temperature-sensitive drug coated Titanium dioxide Nano-particles in the couple stress fluid for examining the concentration and temperature dispersion. The effects of the catheter and permeability of the stenosis are considered in the model. Care has been taken to model the thermo-physical properties of the fluid with the immersed nanoparticle, e.g., TiO2, Ag and Cu. The modeled non-linear and coupled equations are solved by using the Homotopy Perturbation Method. The temperature and concentration dispersion effects are in the flexible stenotic arterial vessel under the pulsatile physiological pressure gradient are studied and reported in details. The alterations in the axial velocity, resistance to the flow, and wall shear stress are studied and found out that the high intense vortex regions are identified in the stenotic region. The model has direct applications in the pharmaceutical industry in design and developing the drug to treat stenotic conditions.