Discussion on the Effect of a Fluid Domain Around Fins and Grid Discretization in Buoyancy-driven Convection Sven De Schampheleire, Kathleen De Kerpel, Bernd Ameel, Özer Bağcı, Michel De Paepe Department of Flow, Heat and Combustion Mechanics, Ghent University – UGent, Ghent, Belgium Address correspondence to Sven De Schampheleire, Department of Flow, Heat and Combustion Mechanics, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium. E-mail: . Phone Number: +32 9 264 33 55. Fax Number: +32 9 264 35 75. Abstract
. This heat transfer coefficient is an average heat transfer coefficient over all the available fin surfaces. If a fluid domain is added to e.g. the sides of the fin row, the heat transfer coefficient of the frontal fins will also be taken into account. Therefore is in fact a lumped heat transfer coefficient. . This is the heat transfer coefficient only for the left, right and bottom side of the fin, independent of which mesh (Table 2) being studied. This heat transfer coefficient is an area-averaged value of and . All the results with their percentage difference compared to the base case (Mesh-Ref) are reported in Table A.1 in the Appendix. First of all, the largest influence of the domain is observed when the rectangular fin shape is compared to the inverted triangular one. The results for the interrupted rectangular fin shape are very similar to those for the rectangular fin shape. Locally the flow resistance in the middle of the interrupted fin is decreased due to the interruption. However, as a single chimney pattern is observed in both the rectangular case and the interrupted case, no extra fluid will be drawn to the middle of the interrupted fin. Furthermore, the region where the fin is interrupted has a symmetric boundary condition, this makes it more difficult for air to penetrate from above the heat sink. As can be seen from Figures 5 to 8, an increase in the height of the fluid domain on top of the fin from 50 mm to 100 mm does not have any significant influence on the heat transfer coefficients (the uncertainty on the fine grid is 1.77%, as shown in Table 3 and discussed in Section ‘Mesh and Uncertainty analysis’). Higher and/or wider fluid domains result in no further significant changes to the heat transfer coefficient. The results for a 200 mm high fluid domain are reported in Table A.1 and depicted in Figures 5 to 8, however, they will not be discussed further in this work as the boundary conditions for this grid are slightly different. When the fluid
(dimensionality – fluid – turbulence – radiation) Ahmadi et al. [23] 2014 Rectangular interrupted fins 2D – Boussinesq approximation – no turbulence model - included One fin row is simulated. Fluid added before the fin, but not after the fin (2D). Length of this fluid domain: not reported. Dialameh et al. [14] 2008 Rectangular fins 3D – constant properties, except – no turbulence model – not included A half fin row is simulated. Fluid added at sides and on top of the fin. Dimension of this fluid domain: ¾ times the fin length to the sides, 9 times the fin height on top of the heat sink. Only one fin is taken in to account, other side is open. Shen et al. [26] 2014 Rectangular fins 3D – incompressible ideal gas – no turbulence model – included Several half fin rows are simulated. Fluid domain added before, after and underneath the fin. Length of this fluid domain: 1 time the fin length to the sides, 5 times the fin height on top of the heat sink and 1 time the fin height underneath the fin. Mehrtash and Tari [27] and Tari and Mehrtash [28] 2013 Rectangular fins 3D – air is ideal gas - zero order turbulence model – included Complete heat sink is simulated together with insulating material. Square 3m x 3m box. Length of fluid domain: 6 times the fin length to the sides, min. 116 times the fin height on top of the heat sink. Dogan et al. [11] 2014 Thin-fin arrays with various shapes 3D – constant properties except – no turbulence model – included One fin row is simulated. The fins at either side are taken into account. No calming section before or after.
Table 2. Overview of all geometries used in this study per fin shape side side side 10mm 20mm 30mm 50mm 100mm Side 5 mm x Side 10 mm x x Side 20 mm x x x x Side 30 mm x Top 10 mm x Top 20 mm x Top 30 mm x Top 50 mm x Top 100mm x Mesh