Numerical simulations on heat flow visualization and entropy generation during natural convection in enclosures with curved side walls

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.In the present work, investigation of heat flow via heatlines in addition to entropy generation due to natural convection within differentially heated cavities with curved side walls is carried out. Galerkin finite element method with penalty parameter is used to solve the nonlinear coupled partial differential equations governing the flow and thermal fields and the finite element method is further used to solve the Poisson equation for streamfunction and heatfunction. The derivative terms in the expression of entropy generation is calculated using the elemental basis sets. Numerical sim- ulations are carried out for a range of Rayleigh numbers (Ra =103-105) and the Prandtl number, Pr = 0.01. The results are elucidated in terms of streamlines, heatlines and isotherms to present the heat flow patterns in the cavity. A comprehensive understanding on internal convective heat flow is illustrated using heatline concept. Entropy gener- ation due to heat transfer and fluid friction are also illus- trated concave and convex cases. Based on high heat trans- fer rate and lesser total entropy generation, case 3 (highly concave) may be chosen over cases 1 (less concave) and 2 (moderate concave) for all Ra. Similarly, in convex cases, case 1 with less convexity offers higher heat transfer rate with less entropy generation compared to that of cases 2 (moderate convex) and 3 (highly convex).