On the solution of linear hydrodynamic stability of dean flow by using three semi-analytical approaches
In the present paper, three semi-analytical techniques are examined for solving eigenvalue problem arising from linear hydrodynamics stability of Dean Flow. To this accomplishment, hybrid of Fourier transform and Adomian decomposition method (FTADM), differential transform method (DTM) and Homotopy perturbation method (HPM) is selected and applied on the eigenvalue problem. Semi-analytical results are validated against the existing data with high accuracy. The comparison between FTADM, DTM and HPM reveals that for the same number of truncated terms, the accuracy of the FTADM is more pronounced. This may be attributed to the incorporation of all boundary conditions into our solution when using the FTADM. The results also indicate that the value of wave number (i.e., parameter engaged in our eigenvalue problem) is remarkably impressive on the convergence trend and effectiveness (i.e., the occurrence of becoming nearer to the numerical results) of our solution. In addition, critical wave number and Dean number for the onset of Dean flow instability are successfully reported.
KeywordsHydrodynamic stability Dean flow Fourier transformation Differential transform method Homotopy perturbation method
- 16.Mondal RN, Islam MZ, Islam MM, Yanase S (2015) Numerical study of unsteady heat and fluid flow through a curved rectangular duct of small aspect ratio. Thammasat Int J Sci Technol 20:1–20Google Scholar
- 17.Helal MNA, Ghosh BP, Mondal RN (2016) Numerical simulation of two-dimensional laminar flow and heat transfer through a rotating curved square channel. Am J Fluid Dyn 6:1–10Google Scholar
- 21.Nourazar SS, Nazari-Golshan AA, Yıldırım A, Nourazar M (2012) On the hybrid of Fourier transform and Adomian decomposition method for the solution of nonlinear Cauchy problems of the reaction-diffusion equation. Z Naturforschung A 67:355–362Google Scholar
- 22.Zhou JK (1986) Differential transformation and its applications for electrical circuits. Huazhong University Press, WuhanGoogle Scholar
- 31.Boyd JP (2002) Chebyshev and Fourier spectral methods, 2nd edn. Courier Corporation, New YorkGoogle Scholar