Comparative analysis of exact and FDM solutions with error analysis for thermal transport of copper-blood nanofluid in arteries with stenosis and thrombosis

This study explores the effects of magnetohydrodynamics on copper nanoparticle-enhanced blood flow through a vertically aligned artery with mild stenosis and thrombosis. By applying mild stenotic assumptions, the governing equations for mass, momentum, and energy are transformed into ordinary differential equations, yielding analytical solutions for axial velocity, wall shear stress, temperature distribution, and flow resistance. We validated the closed-form solution through FDM (finite difference method) computations and performed error analysis for accuracy assessment. Results indicate that increasing the stenosis shape parameter and maximum height reduces temperature and axial velocity, while increasing shear stress and resistance. The catheter model consistently shows greater flow resistance and temperature levels compared to the standard tube model. Graphical analysis illustrates the influence of key physical parameters on Cu-blood flow dynamics, offering insights for biomedical applications such as targeted drug delivery and vascular device optimization. The results demonstrate that magnetohydrodynamic effects, when combined with copper nanoparticles, can be effectively tailored to modulate both hemodynamic and thermal characteristics in diseased arteries. The analytical framework presented in this study facilitates a direct assessment of parameter sensitivities, thereby offering a robust basis for the optimization of catheter-based interventions. By integrating rigorous theoretical modeling with biomedical engineering considerations, the work provides actionable insights to enhance the efficacy of treatments for stenotic and thrombosed arterial conditions.