The role of transpiration in Prandtl blood flow of Jeffrey-Hamel arterial morphologies: Hemodynamic insights via Sobol sensitivity analysis

The convergent/divergent channel formations act as a theoretical model of arterial conduits that undergo bifurcation, expansion, or contraction. Blood rheology in such geometrical shaped objects is critical because deformations in vessel cross-sectional area significantly influence the transport phenomena, wall shear stresses, and heat/mass transfer characteristics. The insertion of wall transpiration in arteries further reveals biological processes such as endothelial drug transfer, and plasma filtration. Since blood demonstrates non-Newtonian features, its viscosity and transport nature are acquired by rheological models within the framework of Jeffrey-Hamel flow and thereby correlating the mathematical formulations of blood flow in convergent/divergent channel to the rheological mechanisms appearing in real arterial conduits. Therefore, the present study investigates the influence of transpiration in a two-dimensional, incompressible flow of Jeffrey-Hamel fluid within a deformable convergent/divergent channel and is embedded in a non-Darcian porous zone. The blood is subjected to externally imposed magnetic field, introducing Lorentz force that affects hemodynamic behavior. The thermal phenomena integrate the influence of radiative heat exchange, viscous dissipation because of vascular resistance, and Joule heating to regulate temperature homeostasis in biological tissues. A symmetric flow distribution is maintained along the centerline of the channel. The initial system of fundamental conservation equations consists of partial differential equations along with suitable boundary conditions and is transformed into a normalized form using appropriate transformations. The numerical solution is then obtained through Runge-Kutta-Fehlberg (RKF-45) method. The graphical results on transport phenomenon are established against physical parameters. Moreover, skin-friction co-efficient, Nusselt number, and Sherwood number are also evaluated at the channel walls. To quantify the relative influence of governing parameters on momentum, mass, and heat transfer characteristics in a non-linear flow, we have employed variance-based Sobol sensitivity analysis. Sobol analysis provides uncertainty-aware identification of dominant physical mechanisms.