Mixed convection in Bingham fluids: A comprehensive analysis of yielded and unyielded regions and their heat transfer implication using OpenFOAM

Three-dimensional (3D) simulations of the laminar, incompressible, mixed convective flow of a Bingham viscoplastic fluid between two concentric cylinders of finite length are discussed here. Thermal exchange of a viscoplastic fluid is widely required; therefore, we aim to understand the characteristics of fluid flow and heat transfer in nonlinear fluids typically encountered in applications such as drilling. The simulations employ the regularized Papanastasiou constitutive model within the OpenFOAM framework, and results are validated against benchmark numerical and experimental data for Newtonian and Bingham plastic flows. The rheological behavior of four materials-heavy crude oil, Adriatic sea sediments, self-compacting cement and crushed glass is investigated to highlight the influence of cylinder rotation on the flow field. The thermophysical properties of these materials are considered constant, except density which obeys the Boussineq approximation. The flow characteristics, for instance, the streamlines pattern, the development of rigid/unyielded zones, viscosity distributions and strain-rate distributions, are analyzed. Heat transfer, which is quantified by the Nusselt number, showed a symmetric distribution with the highest values for heavy crude oil. The yielded region percentage (YRP) increases from 75% to 100% as the material yield stress decreases, with the unyielded zone expanding significantly at higher Bingham numbers, up to 50% for certain materials. This growth in the unyielded region impacts operational factors, such as pumping cost in drilling applications.