Abstract
In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a curved rectangular duct. The outer wall of the duct is heated while the inner one is cooled. Numerical calculations are carried out by using the spectral method covering a wide range of the Dean number,D n , 0 ≤ D n ≤ 1500 and the curvature, δ , 0 n is increased no matter what δ is. Effects of curvature on the unsteady solutions are also obtained. The transition to the periodic or the chaotic state is retarded, if the curvature is increased.
Highlights
The outer wall of the duct is heated while the inner one is periodic oscillations for the fully developed flow in a cooled
One of the interesting phenomena of the flow through a curved duct is the bifurcation of the flow because generally there exist many steady solutions due to channel curvature
Detailed bifurcation structures and linear stability of the steady solutions for fully developed flows in a curved square duct were investigated by Winters (1987) and by Mondal et al (2007)
Summary
The eigenvalue problem is solved which is constructed by the application of the function expansion method together with the collocation method to the perturbation equations obtained from Eqs. In order to solve the non-linear time-evolution equations, we use the Crank-Nicolson and Adams-. For Navier-Stokes equations, it is frequently applied to the viscous and pressure gradient components It is a second-order implicit time step method which calculates the average of t(n) and t(n + 1) for all terms except for time differentials. The Adams-Bashforth Method, on the other hand, is used for numerically solving initial value problems for ordinary differential equations This method is an explicit linear multistep method that depends on multiple previous solution points to generate a new approximate solution point. It should be noted here that for other values of δ , the bifurcation diagram is topologically unchanged from Fig. 2
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