Modified temperature similarity variable for Jeffery-Hamel flow in converging/diverging channels: application to carotid blood flow

Abstract

Purpose - This work aims to propose a modified temperature similarity variable for Jeffery-Hamel flow in convergent/divergent channels and applies it to a physiological blood flow case based on carotid arteries. The aim is to provide a more physically consistent thermal formulation by incorporating the channel geometry directly into the temperature field and by preserving a more interpretable dimensionless representation of the energy equation. Design/methodology/approach - Using the modified transformation, the energy equation yields a modified Eckert number and an additional coupling term (2RePr alpha fg) linking inertia, thermal diffusion and channel geometry. The momentum and energy equations are reduced to coupled ordinary differential equations and solved numerically with bvp4c, with validation against benchmark Jeffery-Hamel solutions. Findings - For low-Reynolds-number Newtonian blood flow in the external, internal, and common carotid arteries, converging and diverging cases produce nearly identical velocity profiles, while the temperature field distinguishes the two: centerline cooling in converging channels and centerline heating in diverging channels. The heat-transfer parameter increases with artery size and vessel length, whereas the skin-friction parameter remains nearly constant. Research limitations/implications - The study is limited to Newtonian blood under low-Reynolds-number conditions; the approach can be extended to non-Newtonian rheology, slip/temperature jump effects, porous media or nanofluid suspensions. Originality/value - The modified temperature similarity variable introduces the extra term 2RePr alpha fg and a modified Eckert number, which are absent from classical Jeffery-Hamel energy equations. This yields a more physically consistent thermal description for Jeffery-Hamel blood flow in convergent and divergent channels.