Hemodynamic modelling of Prandtl blood flow in Jeffrey–Hamel arterial structures under Newtonian heating: A regression-based approach

This study examines the blood rheology in a two-dimensional, incompressible Jeffrey-Hamel flow of Casson fluid within convergent/divergent channels, simulating the dynamics of inflated/deflated arteries. A uniform external magnetic field is enforced along the channel walls to reflect the impact of magnetically stimulated blood flow regulations. The stretching phenomenon of the arterial walls representing the wall driven acceleration and are influenced by porous medium such as surrounding tissue perfusion and atherosclerotic plaques. The realistic thermal responses of thermal radiation, Joule heating, viscous dissipation, and heat source are captured through energy equation in biological flow. The mechanism of Newtonian heating is carried out at the arterial walls to model thermal transportation between blood and nearby tissue. The flow model is normalized with the help of similarity transformation to attain the simplified governing equations while preserving key non-linear and rheological features. The reduced system of governing equations is then solved through Runge–Kutta–Fehlberg (RKF-45) numerical technique, generating precise velocity and thermal profiles. Graphical results exhibit the impacts of key physical parameters on blood velocity and temperature profiles in both convergent and divergent arterial sections. The skin-friction co-efficient and Nusselt number are also computed at the upper wall in case of divergent channel and are critical for understanding the microvascular blood flow. This study also integrates advance regression techniques to capture behavior of parameters on wall sheer stress and Nusselt number. Unlike conventional approaches, the adaptive models provide statistically robust predictions with quantified uncertainty, ensuring reliability under perturbed data conditions. A special case of axial symmetric channel flow for radial velocity field is considered along convergent/divergent channels configurations. The blood rheology on flow regulation in terms of Casson parameter depicts an enhancement of velocity field in convergent arterial channel and a decline of velocity profiles in a divergent conduit. The temperature intensity is reduced due to modification in conjugate parameter.