A mathematical approach for modeling the blood flow containing nanoparticles by employing the Buongiorno’s model

Abstract

A mathematical model has been suggested for the numerical study of blood flow in a vessel due to the pumping action of the heart. Blood is assumed to contain some impurities in the form of chemically reactive species (undergoing a first-order irreversible reaction) and, being a hybrid nanofluid, also contains the nano-sized solid particles, thus forming a homogeneous mixture which is subjected to a pressure gradient (of trigonometric nature) in the horizontal direction. Human vessel is subjected to a transverse magnetic field and is presumed to be filled with plaque which is considered as a porous medium, and is mathematically modeled by applying the Darcy–Forchheimer theory. The nonlinear nature of the governing equations steered toward the decision of using the numerical approach to obtain the solution of the governing system, which led to the discovery of a linear concentration variation across the vessel at higher values of the Reynolds number. Finally, a 38% rise in the heat transfer has been noted due to the presence of solid particles in the human blood.

Keywords

• hybrid nanofluid
• blood flow
• darcy–forchheimer medium
• pressure gradient
• fully implicit scheme