Numerical study of non-isothermal flow with convective heat transfer in a curved rectangular duct

Abstract

Non-isothermal flow with convective heat transfer through a curved rectangular duct of aspect ratio 2 is numerically studied by use of the spectral method with a temperature difference between the vertical outer (heated) and inner (cooled) sidewalls. Numerical calculations are carried out for the Grashof numbers 100 < Gr ⩽ 1000 over the Dean number 0 ⩽ Dn ⩽ 1000 . In the present paper, two cases of the Grashof numbers Gr = 500 and Gr = 1000 are discussed in detail. After a comprehensive survey over the parametric ranges, five branches of steady solutions are found using the Newton–Raphson iteration method for both the cases. Linear stability characteristics of each branch are then studied. It is found that among multiple steady solutions obtained, only one steady solution is linearly stable for a single range of the Dean number for Gr = 500 , for Gr = 1000 , on the other hand, linear stability region exists in three different intervals of the Dean number on the same branch. Nusselt numbers are calculated as an index of the horizontal heat transfer for differentially heated vertical sidewalls. It is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid, and whence the flow becomes periodic and then chaotic, as the Dean number increases, the rate of heat transfer increases remarkably with respect to a straight channel.