Analysis of average Nusselt numbers at various zones for heat flow visualizations during natural convection within enclosures (square vs triangular) involving discrete heaters

Abstract

Finite element analysis of average Nusselt numbers during natural convection within the triangular (type 1 and type 2) and square enclosures with various discrete heater configurations along the side walls (cases 1–4) is carried out for various elements (24×24, 28×28, 32×32 and 34×34) with Pr=0.7 fluids. The adaptive finite elements have been used for all the grid sizes as they are useful in accurately predicting the average Nusselt number. The average Nusselt numbers further demonstrate the heat balance within the enclosures. The fractional error in the heat balance (ε) has been evaluated for all the cases and various elements. It was found that the fractional error is lesser for the elements corresponding to 32×32 (ε≤0.109) and 34×34 (ε≤0.105). The fractional error is mostly due to the sharp variation of the heat transfer rate at the hot–cold interface along the side walls and that is also correctly predicted by the local Nusselt number profiles for various elements. The present work on the discrete heating along the side walls also involve the derivation of various non-homogeneous Dirichlet boundary conditions for heatfunctions (Π) at the hot–cold junctions. The heatfunctions are inherently related to the average Nusselt number. It was finally concluded that the implementation of the heatfunction boundary conditions based on the average Nusselt numbers successfully predicts the heat flow visualizations via heatlines.