Multi-physics study on heat transfer enhancement of Cu–Au hybrid nanofluid in stenotic vessels with a shear-responsive boundary condition

Temperature control is crucial for magnetic nanofluid-based thermotherapy in stenotic vessels. Traditional boundary conditions lack the adaptability to local flow variations in complex geometries. To overcome this limitation, we introduce a novel shear-responsive boundary condition that dynamically couples boundary quantities with the local wall shear rate. Using this framework, a multi-physics analysis is performed to study the heat transfer enhancement in a Cu–Au hybrid nanofluid within a stenotic vessel under an induced magnetic field. This model incorporates the governing equations of momentum, magnetic induction and energy, which are solved numerically via a finite difference scheme. The results indicate that the shear-responsive condition effectively modulates the intensity of the induced magnetic field in response to the local wall shear rate, leading to enhanced heat transfer across various degrees of stenosis. In particular, as the shear-response parameter [Formula: see text] increases from 0 to 6, the Nusselt number rises consistently across all examined configurations. Meanwhile, the wall temperature increases significantly, even at the stenosis center, primarily attributed to enhanced Joule heating effects. This shear-responsive mechanism shows superior thermal performance compared with conventional fixed boundary conditions and enables effective regulation of wall shear stress through the parameter [Formula: see text]. This study presents a promising strategy for adaptive thermal management in biomedical applications.