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On Comparison of Homotopy Analysis Method and Finite Difference Method for Two Dimensional Steady Compressible Flow with Pressure Gradients

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Abstract

In this paper we analyse the effect of suction/injection on steady compressible fluid flow in boundary layer region. Falkner–Skan transformations will reduce the governing partial differential equations (pde’s) into two nonlinear pde’s. Finite difference method is applied to the system of equations to compare with the semi analytical results obtained by homotopy analysis method, which shows good agreement for the velocity and temperature profiles with suction, injection and no suction effects. The effect of injection, suction are studied for velocity and temperature distribution which are depicted in a graph. It is observed that the flow separation exists for large values of suction and injection in boundary layer region. The error estimates of \(l_1\), \(l_2\) and \(l_{\infty }\) for all the three cases are listed for velocity and temperature which are the indications of the obtained numerical solutions is close to HAM solution.

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References

  1. Rauf, A., Abbas, Z., Shehzad, S.A., Mushtaq, T.: Characterization of temperature-dependent fluid properties in compressible viscous fluid flow induced by oscillation of disk. Chaos Solitons Fractals 132, 109573 (2020)

    Article  MathSciNet  Google Scholar 

  2. T. Mushtaq, S. A., Shehzad, Abbas Z., Rauf, A.: Effects of injection and suction on time dependent flow across oscillatory disk, Author Submitted Manuscript - PHYSSCR-110746.R1

  3. Shehzad, S.A., Abbas, Z., Raufa, A., Mushtaq, T.: Effectiveness of Hall current and thermophysical properties in compressible flow of viscous fluid thorough spinning oscillatory disk. Int. Commun. Heat Mass Trans. 116, 104678 (2020)

    Article  Google Scholar 

  4. Oosthuizen, P.H., Carscallen, W.E.: Compressible Fluid Flow. McGraw-Hill, New York (1997)

    Google Scholar 

  5. Liao, S.J.: The proposed homotopy analysis techniques for the solution of nonlinear problems, Ph.D. dissertation, Shanghai Jiao Tong University, Shanghai, China, (1992)

  6. Achala, L.N., Madhusudhan, R., Sathyanarayana, S.B.: Study of Compressible Fluid Flow in Boundary Layer Region by Homotopy Analysis Method, International Journal of Latest Trends in Engineering and Technology, 9(1), (2018), e-ISSN:2278-621X

  7. Achala, L.N., Sathyanarayana, S.B.: Approximate analytical solution of compressible boundary layer flow with an adverse pressure gradient by homotopy analysis method. Theor. Math. Appl. 5(1), 15–31 (2015)

    MATH  Google Scholar 

  8. Curle, N.: The Laminar Boundary Layer Equations. Clarendon Press, Oxford (1962)

    MATH  Google Scholar 

  9. Cebecci, T.: The laminar boundary layer on a circular cylinder started impulsively from rest. J. Comput. Phys. 31, 153–172 (1979)

    Article  MathSciNet  Google Scholar 

  10. Kafoussias, N., Karabis, A., Xenos, M.: Numerical study of two dimensional laminar boundary layer compressible flow with pressure gradient and heat and mass transfer. Int. J. Eng. Sci. 37, 1795–1812 (1999)

    Article  Google Scholar 

  11. Kuerti, G.: The laminar boundary layer in compressible Flow, Adv. Appl. Mech. 2, 21(92) (1951)

  12. Young, A.D.: Section on boundary layers, Int. J. Howarth (Ed.), Modern Developments in Fluid Mechanics High Speed Flow, Clarendon Press, Oxford, 1:375-475 (1953)

  13. Anderson, J.D.: Hypersonic and High-Temperature Gas Dynamics. McGraw-Hill, New York (1989)

    Google Scholar 

  14. Howarth, L.: Proc. Roy. Soc. Lond. A 164, 547–579 (1938)

    Google Scholar 

  15. Cebeci, T., Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer. Springer, Berlin (1984)

    Book  Google Scholar 

  16. Schreier, S.: Compressible flow. Wiley, New York (1982)

    Book  Google Scholar 

  17. Xenos, M., Tzirtzilakis, E., Kafoussias, N.: Compressible Turbulent Boundary-Layer Flow Control Over a Wedge, 2nd International Conference From Scientific Computing to Computational Engineering, 2nd IC-SCCE Athens, 5-8 July, (2006)

  18. Riley, N.: Unsteady Laminar Boundary Layers, 17(2) (1975)

  19. Sau, A., Nath, G.: Unsteady compressible boundary layer flow stagnation line of an infinite swept cylinder. Acta Mech. 108, 143–156 (1995)

    Article  Google Scholar 

  20. Liao, S.J.: Homotopy analysis method in nonlinear differential equations. Springer, Berlin (2011)

    Google Scholar 

  21. Bender, C.M., Orszag, S.A.: Advanced mathematical methods for scientists and engineers. Springer, Berlin (1999)

    Book  Google Scholar 

  22. Hinch, E.J.: “Perturbation Methods”, Cambridge Texts in Applied Mathematics, vol. 6. Cambridge University Press, Cambridge (1991)

    Google Scholar 

  23. Siddheshwar, P.G.: A series solution for the Ginzburg-Landau equation with a time-periodic coefficient. Appl. Math. 3, 542–554 (2010)

    Article  Google Scholar 

  24. Liao, S.J.: A kind of approximate solution technique which does not depend upon small parameters (II), an application in fluid mechanics. Int. J. Nonlin. Mech. 32, 815–822 (1997)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Government College (Autonomous), Kalaburagi, 585105, Karnataka, India

    Mahantesh M. Nandeppanavar

  2. Jyothy Institute of Technology, Centre for Incubation, Innovation Research and Consultancy, Bangalore, 560082, Karnataka, India

    R. Madhusudhan, M. C. Kemparaju & R. Latha

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  1. Mahantesh M. Nandeppanavar
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  2. R. Madhusudhan
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  3. M. C. Kemparaju
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  4. R. Latha
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Correspondence to Mahantesh M. Nandeppanavar.

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Nandeppanavar, M.M., Madhusudhan, R., Kemparaju, M.C. et al. On Comparison of Homotopy Analysis Method and Finite Difference Method for Two Dimensional Steady Compressible Flow with Pressure Gradients. Int. J. Appl. Comput. Math 7, 20 (2021). https://doi.org/10.1007/s40819-021-00952-4

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