## 5 Conclusions

A multi-block RANS method was employed to predict three-dimensional flow and heat transfer in a rotating smooth and ribbed rectangular channel with aspect ratio of 4:1 and for various rotation numbers and inlet coolant-to-wall density ratios. Two channel orientations are studied: (5 = 90° and 135°. The present near-wall second-moment closure model results were compared with the experimental data of Griffith et al. [14]. It predicted fairly well the complex three-dimensional flow and heat transfer characteristics resulting from the large channel aspect ratio, rotation, centrifugal buoyancy forces and channel orientation. The main findings of the study may be summarized as follows.

A) Smooth duct:

I. The Coriolis force induces secondary flow, in the ( = 90° rotating case, which pushes the cold fluid from the leading to the trailing surface.

II. The Coriolis force induces secondary flow, in the (5 = 135° rotating case, which pushes the cold fluid from the leading corner to the bottom surface.

III. In the (5 = 135° rotating case, most of the top surface behaves as a leading side and thus the Nusselt number ratios on this surface are lower than the corresponding ones on the ( = 90° rotating case. Similarly, most of the bottom surface behaves as a trailing side. Thus, the increase in the Nusselt number ratios is higher on the bottom surface when compared with their counterparts in the ( = 90° rotating case.

B) Ribbed duct:

I. The inclined ribs start two counter-rotating vortices that oscillate in size along the streamwise direction. For case 4 (non-rotating), the secondary flow results in steep temperature gradients and high heat transfer coefficients on both the top and ribbed surfaces.

II. For case 5 (( = 90°), the rotation-induced cross-stream secondary flow distorts the rib-induced vortices and consequently, rotation shifts the temperature contours and affects the heat transfer coefficients from both the leading and trailing surfaces.

III. The rib-induced vortices are slightly distorted by low rotation-induced secondary flow (case 6) but significantly changed by the high rotation high density ratio induced secondary flow. This results into reversing the flow on the leading surface and reduces significantly the magnitude of rib-induced secondary flow on the trailing surface.

IV. The effect of increasing the rotation number (with fixed density ratio) is to monotonically increase the Nusselt number ratio on the trailing surface. On the leading surface, the Nusselt number ratio decreases first (case 6) and then increases (case 7).

V. The effect of increasing the density ratio (with fixed rotation number) is to have higher and uniform Nusselt number ratio on the leading and trailing surfaces.

VI. From design point of view, it is clear that the rib angle and the direction of rotation should be chosen such that the secondary flows that are induced by the rib angle and rotation direction should combine constructively to give maximum heat transfer.

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