Natural convection of viscoplastic fluids in a triangular enclosure

Abstract

This study extends the analysis of natural convection in a viscoplastic fluid to flow within a triangular enclosure. The finite-element approach provided a numerical solution to the continuity, momentum, and energy equations. The governing parameters for this problem are the Rayleigh number, $\left(Ra={10}^4-{10}^6\right)$, yield number, $\left(Y=0-Y_{max}\right)$, aspect ratio, $\left(\frac{H}{L}=0.5-2.5\right)$, and slope angle, $\left(\varnothing =0-\frac{\pi }{2}\right)$. The influence of these parameters on the heat and mass transfer, morphology of yielded/unyielded regions, and fluid flow were thoroughly examined. The results show that two opposing factors influence the flow behavior and heat transmission within the triangular enclosure. The proximity of the walls restricts the convective movement, leading to reduced heat transfer. However, the proximity of hot and cold sources increases the temperature gradient and heat transfer. The unique influence of the viscoplastic material properties, particularly the yield stress, further distinguishes the heat transfer in this triangular enclosure from other geometries. The results indicate that an increase in the Rayleigh number mitigates the effects of yield stress to some extent. However, the accumulation of unyielded material at the triangular apex hinders convection flow. Furthermore, the viscoplastic fluid flow and heat transfer changed significantly with changes in triangle height. In particular, the maximum yield stress increased by more than 100 % as the aspect ratio increased from 0.5 to 2.5. A change in the slope angle causes a continuous transition from subcritical to supercritical bifurcation, significantly affecting the morphology of the yielded and unyielded areas, and the maximum (critical) yield number. Finally, correlations were developed to predict the Nusselt number and maximum yield stress in all cases.