Impact of gold and silver nanoparticles on the thermally radiating MHD slip blood flow within the stenotic artery using stability analysis and entropy optimisation

The main aim of this investigation is to study the heat transport and entropy generation of human blood as a hybrid nanofluid (HNF) containing gold (Au) and silver (Ag) nanoparticles inside a Darcy–Fochheimer porous stenotic artery in the presence of thermal radiation and magnetic field. The primary reason for adopting Au and Ag nanoparticles as nanomaterials for drug delivery is because they exhibit potential drug transport and imaging properties for treating stenosed artery. Furthermore, velocity slip and convective boundary conditions at the surface of the artery are considered in this study. A method of suitable similarity transformations has been utilised to convert the partial differential equations (PDEs) into dimensionless ordinary differential equations (ODEs) and using the bvp4c built-in solver in MATLAB mathematical software, numerical solutions have been obtained. The plots of the results show that the hybrid nanofluid (Au–Ag/blood) has greater thermal conductance than the normal nanofluid (Au/blood). The temperature and velocity of the blood gradually increase as the percentage of nanoparticles in the blood flow grows. The heat transference rate increases with increase in Biot number (Bi) and radiation (Nr) effect, which helps in removing the toxic plaque from the artery. Due to the contraction of the artery, dual solutions are found, but dual solutions cannot be found beyond the critical values of suction (S) and shrinking (\(\lambda \)) parameters. The critical values \(S_C\) from computation are 1.5851, 1.5949 and critical values \(\lambda _C\) are 0.652, 0.781 for Au/blood nanofluid (NF) and Au–Ag/blood hybrid nanofluid (HNF), respectively. Also, the stability of blood flow is achieved by finding the lowest eigenvalue. A positive minimum eigenvalue (\(\beta _1\)) denotes the upper stable solution branch, whereas a negative minimal eigenvalue indicates the bottom unstable solution branch. The entropy of the blood as the HNF flow was found to increase with nanoparticle volume fraction (\(\phi _1, \phi _2\)), porous parameter (P) and magnetic parameter (M). These results will help greatly to avoid brain stroke or heart attack caused by the burst of an artery.