NUMERICAL INVESTIGATION OF LAMINAR MIXED CONVECTION IN A SQUARE CROSS-SECTIONED CYLINDRICAL ANNULAR ENCLOSURE

Abstract

Steady-state laminar mixed convection of Newtonian fluids in a square cross-sectioned cylindrical annular enclosure with rotating inner wall and heated top cover has been numerically analysed based on axisymmetric incompressible flow simulations. Richardson number, Reynolds number and r_i/R effects on heat and momentum transport have been investigated for the range of Richardson number 0 ≤ Ri ≤ 1, Reynolds number 500 ≤ Re ≤ 2000 and 0.25≤r_i/R≤8 at a representative value of Prandtl number (i.e. Pr=1.0). A scaling analysis has been also carried out in order to elucidate the possible influences of Reynolds, Richardson and Prandtl numbers and r_i/R on the mean Nusselt number. It has been found that the mean Nusselt number (Nu) ̅ demonstrates a monotonically decreasing trend with increasing Ri whereas (Nu) ̅ increases with increasing r_i/R and Re which is consistent with scaling estimation. It is also observed that the flow pattern in the case of purely forced convection (i.e. Ri = 0) is significantly different from those in mixed convection (i.e. Ri> 0). In the case of Ri = 0 (i.e. purely forced convection), a one-cell flow structure with two small vortexes on the top corners is observed for r_i/R≤1, whereas a second cell appears in the flow field for r_i/R> 1 at Re = 1000. On the other hand, in the case of mixed convection (i.e. Ri> 0), two-cell and four-cell flow structures occur in the flow field depending on Ri and r_i/R for the range of Ri, Re and r_i/R considered here at Pr⁡=1.0. Based these observations, a flow regime diagram has been proposed here for mixed convection (i.e. Ri> 0) for the range of Ri, Re and r_i/R analysed in this study.

Keywords

• Mixed Convection,Rotating Wall,Richardson number,Cylindrical Enclosure,Annular Enclosure

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