Investigation of the effectiveness of the thermal conductivity of the Bingham fluid subjected to the dispersion of nanoparticles and dissipation effects

Abstract Several fluids exhibit viscoplastic behavior, and several rheological models for viscoplastic fluids have been proposed. The Bingham-Papanastasiou rheological model is one of them. This article examines heat transfer in a Bingham fluid over a heated wedge. Three types of nanoparticles are considered to be dispersed in the Bingham fluid, and their impact on enhancing the thermal effectiveness of the Bingham fluid is examined. For this purpose, the basic equations of fluid dynamics, energy equations, and Bingham-Papanastasiou rheological models are used for modeling of heat transfer under magnetic and porous medium forces. A set of partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) and numerically solved under no-slip boundary conditions by applying the Galerkin finite element method (GFEM). The roles of magnetic field and porous media forces in thermal enhancement are noted, and it is found that both porous medium and magnetic forces are not favorable for enhancing thermal transfer. An increase in thermal radiation intensity leads to an increase in the Nusselt number. The porous medium causes dissipation due to the resistive force experienced by the fluid flow. For thermal and cooling systems to be thermally efficient and sustainable, the working Bingham fluid should not be heat dissipative, either because of Joule heating or viscous dissipation. Among the different types of nanofluids, the most prominent is the case of tri-nanofluids due to their higher thermal conductivity and stronger fluid–thermal interactions, which makes them more sensitive to parameter variations compared to mono- and di-nanofluids. This study predicts that the skin friction coefficient increases when the Bingham number is increased. Hence, the viscoplastic fluids with higher yield stress exert higher drag on the solid surface to which such fluid interacts. Moreover, the viscoplastic fluid (the Bingham fluid) exerts higher drag on the surface in comparison with Newtonian fluids.