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Title: A complete heatline analysis on mixed convection within a square cavity: Effects of thermal boundary conditions via thermal aspect ratio
Authors: Ramakrishna, D.
Basak, T.
Roy, S.
Pop, I.
Keywords: Heatlines
Penalty finite element methods
Square cavity
Thermal aspects
Boundary conditions
Finite element method
Mixed convection
Natural convection
Nusselt number
Peclet number
Aspect ratio
Issue Date: 2012
Citation: International Journal of Thermal Sciences, 57, 98-111
Abstract: In this article, numerical investigation is carried out for mixed convection heat transfer within square cavities for various thermal boundary conditions on bottom and side walls based on thermal aspect ratio (A). A penalty finite element analysis with bi-quadratic elements has been used to investigate the results in terms of isotherms, streamlines, heatlines and average Nusselt numbers for a wide range of parameters (1 ? Re?100, 0.015 ? Pr?10, 10 3 ? Gr?10 5). A detailed analysis of flow pattern shows that natural convection or forced convection depends on both parameters: Ri (Ri = Gr/Re 2) and Pe (Pe = Re�Pr). Results indicate that, at low Pr (Pr = 0.015) with low Gr (Gr = 10 3), isotherms are decoupled with flow profile and conduction dominant heat transfer is observed irrespective of Re, due to low Peclet number. At Gr = 10 3, lid-driven force dominates and the non-symmetric flow distribution occurs irrespective of Re (1,10 and 100), Pr (0.015, 0.7 and 10) and thermal aspect ratio (0.1, 0.5 and 0.9). At Gr = 10 5 with Re = 1, natural convection dominates the flow irrespective of Pr and A. Considerably smaller dominance of lid-driven force is observed over buoyancy force at Gr = 10 5 with Re = 10 irrespective of Pr for A = 0.1 and 0.5, whereas strong effect of lid-driven force is found at Gr = 10 5 with Re = 100 irrespective of Pr and A. Multiple circulations are found in streamlines and heatlines especially for A = 0.5 and 0.9 at high Reynolds number (Re = 100) with Pr = 10 and Gr = 10 5. It is found that, streamlines and heatlines circulation cells follow qualitatively similar pattern for higher Pr (Pr ? 0.7) at Gr = 10 5 irrespective of Re. Thermal gradient is found to be high at the center of the bottom wall for A = 0.1 due to highly dense heatlines at that zone whereas that is low for A = 0.9 irrespective of Re, Pr and Gr. It is also found that, as thermal aspect ratio increases, the average Nusselt number decreases for Pr = 0.015 and Pr = 0.7 irrespective of Re. Finally, it is concluded that overall heat transfer rates are higher for A = 0.1 as compared to other thermal aspect ratios (A = 0.5, A = 0.9) irrespective of Pr (0.015 ? Pr?10), Re (1 ? Re?100) and Gr (10 3 ? Gr?10 5). � 2012 Elsevier Ltd. All rights reserved.
ISSN: 12900729
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