Computational analysis of Squeezing Blood Flow in Compliant Venous Networks: Implications for Calf Muscle Hemodynamics

Calf muscles must contract cyclically to return blood from the lower limbs, but the effects of magnetic fields, hybrid nanoparticles, and motile microbes are unknown. This study uses a mathematical model to explore squeezing blood flow through a compliant venous tube representing the calf-muscle pump as a bio-hybrid nanofluid with thermal effects and an external magnetic field. Similarity transformations turn the conservation equations into a linked nonlinear system, which the Optimal Homotopy Asymptotic Method solves analytically. The results reveal that increasing the magnetic field reduces peak horizontal and axial velocities by 25-35% and increases flow pressure by roughly 30%. Increasing squeezing force increases peak blood velocity by 20–30% and maximum temperature by 15–20% due to viscous dissipation. Hybrid nanoparticles generate 20-25% more pressure than mono-nanofluid and much more than pure blood. Stronger squeezing reduces nanoparticle and motile microbe concentrations by 5-10%, promoting a more uniform flow domain distribution. A trade-off between therapeutic delivery and calf-muscle pump hemodynamic resistance was found. The unified mathematical framework for squeezing-induced venous flow, hybrid nanoparticles, motile microbes, magnetic effects, and heat transport in a medically justified calf-muscle model is innovative. This study provides fresh insights into the balance between improved drug-delivery capability and vascular flow resistance, unlike earlier research that solely examined subsets of these systems.