In the current study, for the first time, a semi-analytical technique is used for solving eigenvalue problem arising from linear hydrodynamics stability of fluid flow through the curved rectangular ducts at different curvature ratios and aspect ratios. To this accomplishment, symmetric disturbances are assumed and the Homotopy perturbation method (HPM) is applied to solve our eigenvalue problem for curvature ratios ranging from 0.01 to 0.8 and aspect ratios ranging from 0.05 to 20. Our semi-analytical results are validated through the existing numerical and experimental data, showing good agreement. The semi-analytical results indicate that, as the curvature ratio increases the critical Dean number (Dnc) is increased and the flow becomes more stable, especially for aspect ratios lower than 1.Moreover, for all intended curvature ratios, irregular behavior in variation of Dnc is detected by an increase in the aspect ratio. So that, the Dnc is decreased when the aspect ratio increases from 0.05 up to 1 and the fluid flow becomes unstable. When the aspect ratio is increased from 1 to 5, it causes to increase the Dnc and fluid flow becomes stable. Furthermore, when the aspect ratio increases from 5 to 20, the Dnc is decreased again. In addition, Dnc and eigenvalues of critical complex wave number corresponding to Dnc for the onset of Dean flow instability is reported under different curvature ratios and aspect ratios.
