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Series solutions for steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder with sinusoidal radius variation

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Abstract

This article deals with the study of the steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder that has a sinusoidal radius variation. By means of similarity transformation, the governing partial differential equations are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique namely homotopy analysis method (HAM). Expressions for velocity and temperature fields are developed in series form. In this study, three different types of nanoparticles are considered, namely alumina (Al2O3), titania (TiO2), and copper (Cu) with water as the base fluid. For alumina–water nanofluid, graphical results are presented to describe the influence of the nanoparticle volume fraction φ and the ratio of the gradient of velocities c on the velocity and temperature fields. Moreover, the features of the flow and heat transfer characteristics are analyzed and discussed for foregoing nanofluids. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper–water nanofluid compared to the alumina–water and titania–water nanofluids.

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References

  1. Liao SJ (1992) The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University

  2. Liao SJ (2003) Beyond perturbation: introduction to homotopy analysis method. Chapman and Hall/CRC Press, Boca Raton

    Book  Google Scholar 

  3. Liao SJ (1997) A kind of approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics. Int J Non-Linear Mech 32:815–822

    Article  MATH  Google Scholar 

  4. Liao SJ (1999) An explicit, totally analytic approximation of Blasius viscous flow problems. Int J Non-Linear Mech 34:759–778

    Article  MATH  Google Scholar 

  5. Liao SJ (2004) On the homotopy analysis method for nonlinear problems. Appl Math Comput 147:499–513

    Article  MathSciNet  MATH  Google Scholar 

  6. Xu A, Liao SJ (2006) Series solutions of unsteady MHD flows above a rotating disk. Meccanica 41:599–609

    Article  MathSciNet  MATH  Google Scholar 

  7. Liao SJ, Tan Y (2007) A general approach to obtain series solutions of nonlinear differential equations. Stud Appl Math 119:297–355

    Article  MathSciNet  Google Scholar 

  8. Aziz RC, Hashim I, Alomari AK (2011) Thin film flow and heat transfer on an unsteady stretching sheet with internal heating. Meccanica 46:349–357

    Article  MathSciNet  Google Scholar 

  9. Abbasbandy S (2006) The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A 360:109–113

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Abbasbandy S (2008) Approximate solution for the non-linear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem Eng J 136:144–150

    Article  Google Scholar 

  11. Allan FM, Syam MI (2005) On the analytic solution of non-homogeneous Blasius problem. J Comput Appl Math 182:362–371

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Hayat T, Javed T (2007) On analytic solution for generalized three-dimensional MHD flow over a porous stretching sheet. Phys Lett A 370:243–250

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Joneidi AA, Domairry G, Babaelahi M (2010) Homotopy analysis method to Walter’s B fluid in a vertical channel with porous wall. Meccanica 45:857–868

    Article  MathSciNet  Google Scholar 

  14. Dinarvand S (2009) A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field. Cent Eur J Phys 7(1):114–122

    Article  Google Scholar 

  15. Dinarvand S (2010) On explicit, purely analytic solutions of off-centered stagnation flow towards a rotating disc by means of HAM. Nonlinear Anal, Real World Appl 11:3389–3398

    Article  MathSciNet  MATH  Google Scholar 

  16. Cheng J, Liao SJ, Mohapatra RN, Vajravelu K (2008) Series solutions of nano boundary layer flows by means of the homotopy analysis method. J Math Anal Appl 343:233–245

    Article  MathSciNet  MATH  Google Scholar 

  17. Dinarvand S (2011) The laminar free-convection boundary-layer flow about a heated and rotating down-pointing vertical cone in the presence of a transverse magnetic field. Int J Numer Methods Fluids 67:2141–2156

    Article  MATH  Google Scholar 

  18. Dinarvand S, Rashidi MM (2010) A reliable treatment of homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls. Nonlinear Anal, Real World Appl 11:1502–1512

    Article  MathSciNet  MATH  Google Scholar 

  19. Dinarvand S, Doosthoseini A, Doosthoseini E, Rashidi MM (2010) Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces. Nonlinear Anal, Real World Appl 11:1159–1169

    Article  MathSciNet  MATH  Google Scholar 

  20. Hiemenz K (1911) Die grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech J 326:321–331

    Google Scholar 

  21. Homann F (1936) Der Einfluss grosser Zähigkeit bei der Strömung um den Zylinder und um die Kugel. Z Angew Math Mech 16:153–164

    Article  MATH  Google Scholar 

  22. Garg WK, Rajagopal KR (1990) Stagnation-point flow of a non-Newtonian fluid. Mech Res Commun 17:415–421

    Article  MathSciNet  MATH  Google Scholar 

  23. Seshadri R, Sreeshylan N, Nat G (1997) Unsteady three-dimensional stagnation point flow of a viscoelastic fluid. Int J Eng Sci 35:445–454

    Article  MATH  Google Scholar 

  24. Domairry G, Ziabakhsh Z (2012) Solution of boundary layer flow and heat transfer of an electrically conducting micropolar fluid in a non-Darcian porous medium. Meccanica 47:195–202

    Article  MathSciNet  Google Scholar 

  25. Howarth L (1951) the boundary-layer in three-dimensional flow. Part II. The flow near a stagnation point. Philos Mag 42:1433–1440

    MathSciNet  MATH  Google Scholar 

  26. Davey A (1961) A boundary layer flow at a saddle point of attachment. J Fluid Mech 10:593–610

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Bhattacharyya S, Gupta AS (1998) MHD flow and heat transfer at a general three-dimensional stagnation point. Int J Non-Linear Mech 33:125–134

    Article  MATH  Google Scholar 

  28. Tiwari RK, Das MS (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018

    Article  MATH  Google Scholar 

  29. Bachok N, Ishak A, Nazar R, Pop I (2010) Flow and heat transfer at a general three-dimensional stagnation point in a nanofluid. Physica B 405:4914–4918

    Article  ADS  Google Scholar 

  30. Xu H, Liao SJ, Pop I (2007) Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Eur J Mech B, Fluids 26(1):15–27

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu H, Liao SJ, Pop I (2008) Series solutions of unsteady free convection flow in the stagnation-point region of a three-dimensional body. Int J Therm Sci 47(5):600–608

    Article  Google Scholar 

  32. Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336

    Article  Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Department, Amirkabir University of Technology, 424 Hafez Avenue, Tehran, Iran

    Saeed Dinarvand, Reza Hosseini & Ebrahim Damangir

  2. Mathematics Department, University of Cluj, 3400, Cluj, CP 253, Romania

    Ioan Pop

Authors
  1. Saeed Dinarvand
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  2. Reza Hosseini
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  3. Ebrahim Damangir
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  4. Ioan Pop
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Correspondence to Saeed Dinarvand.

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Dinarvand, S., Hosseini, R., Damangir, E. et al. Series solutions for steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder with sinusoidal radius variation. Meccanica 48, 643–652 (2013). https://doi.org/10.1007/s11012-012-9621-7

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  • DOI: https://doi.org/10.1007/s11012-012-9621-7

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