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ISSN Online: 2377-424X

ISBN Print: 0-85295-345-3

International Heat Transfer Conference 10
August, 14-18, 1994, Brighton, UK

LAMINAR MIXED CONVECTION IN HORIZONTAL CIRCULAR SECTOR DUCTS

Get access (open in a dialog) DOI: 10.1615/IHTC10.3220
pages 447-452

Résumé

For laminar mixed convection in horizontal circular sector ducts with uniform heat input axially, fully developed Nusselt numbers (Nu) [and similarly for the product of friction factor (f) and Reynolds number (Re)] depend on duct apex angle (2φ) (see Fig. 1) and are functions of modified Grashof number (Gr+) (average heat flux level), Prandtl number (Pr) (fluid type) and duct orientation with respect to the gravity vector (as would occur, for example, in horizontal multi-passage tubes). Regarding the latter, the steady pattern of secondary flow (buoyancy induced) varies as the duct changes its cross-sectional orientation, thus influencing heat transfer and pressure drop. A theoretical/numerical study was made of the fully developed results for the H1 thermal boundary condition. Nu and fRe were computed (via finite difference method; modified SIMPLER algorithm) for various φ, each at various orientations and Pr over a range of Gr + up to approximately 5 × 107. For a fixed Gr + , Pr, and orientation, it was found that Nusselt ratios (relative to pure forced convection) first increased rapidly with 2φ but tended to plateau between about 2φ = 120 ° and 180 °. In these plateau regions, enhancements, for example for Gr+ - 107 and Pr = 4, reached factors of between about 3.7 and 4.4 depending on orientation. On the other hand, under the same condition, fRe ratios fell in the range of about 1.4 to 1.6. For a given circular sector duct in a fixed orientation, it was found (as expected) that for a given Pr that Nu and fRe increased with Gr + in an exponential fashion, i.e. buoyancy effects became progressively more influential as the heat flux level was increased. For a fixed duct and orientation, for a given (Gr+, Nu increased with Pr whereas fRe decreased with Pr. These dependencies could be removed by scaling Nu on the product Gr+ Pr and fRe on the parameter (Gr +/Pr2. Concerning the effect of orientation, for a fixed duct operating at fixed (Gr+ and Pr, orientation was a fairly significant factor, being largest for large φ. For example, for 2φ = 120°, these differences were about 15% at Gr+: = 107 with Pr = 4.