Unsteady Heat and Fluid Flow through a Curved Channel with Rectangular Cross-section for Several Cases of Aspect Ratio

Samir Chandra Ray, Rabindra Nath Mondal


In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved rectangular duct with different aspect ratios 2 and 3 for a constant curvature 14δ=0.1"> . Unsteady solutions are obtained by using a spectral method and covering a wide range of Dean number 14100≤Dn≤1000">  and the Grashof number 141000≤Gr≤2000"> . The outer wall of the duct is heated while the inner wall is cooled. The main concern of this study is to find out the unsteady flow behavior i.e whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if the Dean number or the Grashof number is changed. For the aspect ratio 2, it is found that the unsteady flow is a steady-state solution for 14Dn=100">  and 14Gr=100, 500, 1500, 2000">  but periodic at 14Dn=100">  and 14Gr=1000. "> If the Dean number is increased i.e. at 14=500">  , it is found the unsteady flow is periodic at 14Gr=1000, 1500 ">  but chaotic at 14Gr=100, 500, 2000.">  If the Dean number is increased further i.e. at 14 Dn=1000"> , the unsteady flow becomes chaotic for any value of Gr in the range. For the aspect ratio 3, however, it is found that the unsteady flow is a steady-state solution for 14 Dn=100">  at 14 Gr=100 "> and 14 Gr=2000 ">  but periodic at 14Dn=100">  and 14Gr=500,1000,1500"> . If the Dean number is increased i.e. at Dn = 500 and 1000, the unsteady flow becomes chaotic for any value of Gr in the range. Contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of a single-, two-, three- , four-, five-, six-, seven- and eight-vortex solutions. It is also found that the chaotic flow enhances heat transfer more significantly than the steady-state or periodic solutions as the Dean number are increased.


Curved rectangular duct; secondary flow; unsteady solutions; Dean number; Taylor number; Grashof number; time evolution.

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