Theoretical Analysis of Blood Rheology as a Non-Integer Order Nanofluid Flow with Shape-Dependent Nanoparticles and Thermal Effects

This study theoretically investigates blood rheology in arteries by modeling blood as an Oldroyd-B nanofluid with uniformly suspended Au, Cu, and Al2O3 nanoparticles. A fractional order framework is employed to capture memory and hereditary effects while preserving the invariance of governing equations. The influence of nanoparticle geometry is examined by considering spherical (isotropic), cylindrical (axial), and platelet-like (planar) shapes. Using integral transform techniques, a comparative analysis highlights how particle symmetry and system parameters affect flow behavior and heat transfer. Thermal effects are further analyzed as both a contributor to flow resistance and a source of symmetry breaking in conduction, with implications for optimizing nanofluid-based blood rheology in biomedical applications such as cryosurgery.