Peristaltic blood flow with gold nanoparticles as a third grade nanofluid in catheter: Application of cancer therapy

Highlights: • Blood flow (non-Newtonian model) containing gold nanoparticles in a catheter is studied. • Nanoparticles concentration is obtained. • The gold nanoparticles control the velocity through $N_b$ and $N_t$. • The temperature distribution enhances with increase of $N_t$ and $N_b$. - Abstract: Cancer is dangerous and deadly to most of its patients. Recent studies have shown that gold nanoparticles can cure and overcome it, because these particles have a high atomic number which produce the heat and leads to treatment of malignancy tumors. A motivation of this article is to study the effect of heat transfer with the blood flow (non-Newtonian model) containing gold nanoparticles in a gap between two coaxial tubes, the outer tube has a sinusoidal wave traveling down its wall and the inner tube is rigid. The governing equations of third-grade fluid along with total mass, thermal energy and nanoparticles are simplified by using the assumption of long wavelength. Exact solutions have been evaluated for temperature distribution and nanoparticles concentration, while approximate analytical solutions are found for the velocity distribution using the regular perturbation method with a small third grade parameter. Influence of the physical parameters such as third grade parameter, Brownian motion parameter and thermophoresis parameter on the velocity profile, temperature distribution and nanoparticles concentration are considered. The results pointed to that the gold nanoparticles are effective for drug carrying and drug delivery systems because they control the velocity through the Brownian motion parameter $N_b$ and thermophoresis parameter $N_t$. Gold nanoparticles also increases the temperature distribution, making it able to destroy cancer cells.