Fractional order model of thermo-solutal and magnetic nanoparticles transport for drug delivery applications.

We examine the capturing efficiency of magnetic nanoparticles bound with drug molecules infused into the blood stream and monitored them by the application of an external magnetic field. We analyzed the motion of the nanoparticles along with the blood velocity through a porous medium vessel under the effect of periodic vibration. The thermo-solutal transport with Caputo-Fabrizio fractional-order derivative is modeled with non-Newtonian biviscosity fluid, Soret and Dufour effect, thermal radiation, and linear variation of the chemical reaction. The Laplace transform, finite Hankel transform and their inverse techniques are used to find analytical solutions. The study shows that both the velocity of blood and nano-particles increase with the increase of particle mass and the concentration parameter, while the opposite behaviour is observed with increasing the fractional parameter, magnetic field effect, and thermal radiation. The heat and mass transfer rates at the wall are enhanced with an increase in the Peclet number and the metabolic heat source. Thermal radiation effect signifies the higher rate of heat transfer at the vessel wall. The study bears potential applications in drug delivery with magnetic nanoparticles at the targeted region.