The study of flow through cylindrical structures holds significant importance in fields such as biomedical engineering, petroleum extraction, and industrial processes. In particular, understanding blood flow in cylindrical geometries that mimic small arteries is crucial for advancing cardiovascular health, treatment methods, and drug delivery systems. Traditional models often fail to capture the complex nonlocal and memory effects inherent in blood flow dynamics, limiting their accuracy in predicting heat transfer and flow characteristics essential for medical applications. This study addresses these limitations by developing an innovative fractional-order magnetohydrodynamic (MHD) model for blood flow using a tri-hybrid nanofluid composed of TiO2${rm TiO}_2$, Au${rm Au}$, and Al2O3${rm Al}_2{rm O}_3$. The model uniquely integrates boundary slip velocity effects within the fractional Maxwell rheology framework and employs the fractional Cattaneo bioheat transfer model, applied to a porous cylindrical structure. The mathematical formulation is based on the Caputo approach to model fractional-order time derivatives in both the thermal and momentum equations. Numerical solutions are obtained using finite difference techniques, incorporating L1 and L2 approximations for the Caputo fractional derivatives. The study investigates the effects of fractional orders α1$alpha _1$ and α2$alpha _2$, along with parameters such as wall slip velocity and thermal radiation, on velocity, temperature, skin friction, and Nusselt number. Results indicate that the tri-hybrid nanofluid achieves up to a 10% enhancement in heat transfer compared to blood or di-hybrid nanofluids, also exhibiting 25%–40% lower skin friction. Furthermore, the fractional-order models offer more realistic and stable predictions across flow conditions. The fractional Maxwell model shows gradual velocity and friction responses, while the fractional Cattaneo model yields lower heat transfer rates than its classical counterpart. By incorporating fractional calculus, the model improves simulation of complex transport in small arteries, aiding development of better cardiovascular treatments. |
