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Melting heat transfer in an axisymmetric stagnation-point flow of the Jeffrey fluid

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Abstract

This investigation explores the characteristics of melting heat transfer in a boundary layer flow of the Jeffrey fluid near the stagnation point on a stretching sheet subject to an applied magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by similarity transformations. Resulting nonlinear problems are solved analytically by the homotopy analysis method. It is noticed that an increase in the melting parameter decreases the dimensionless velocity and temperature, while an increase in the Deborah number increases the velocity and momentum boundary layer thickness.

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References

  1. L. J. Crane, “Flow Past a Stretching Plate,” Z Angew. Math. Phys. 21, 645–647 (1970).

    Article  Google Scholar 

  2. P. D. Ariel, “Axisymmetric Flow of a Second Grade Fluid Past a Stretching Sheet,” Int. J. Eng. Sci. 39, 529–553 (2001).

    Article  MATH  Google Scholar 

  3. P. D. Ariel, “Axisymmetric Flow due to a Stretching Sheet with Partial Slip,” Comput. Math. Appl. 54, 1169–1183 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. T. Hayat, M. Nawaz, S. Asghar, and S. Mesloub, “Thermal-Diffusion and Diffusion Thermo Effects on Axisymmetric Flow of a Second Grade Fluid,” Int. J. Heat Mass Transfer 54 (13/14), 3031–3041 (2011).

    Article  MATH  Google Scholar 

  5. T. Hayat, M. Nawaz, and S. Obaidat, “Axisymmetric Magnetohydrodynamic Flow of a Micropolar Fluid between Unsteady Stretching Surfaces,” Appl. Math. Mech. 32 (3), 361–374 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  6. T. C. Chiam, “Stagnation-Point Flow Towards a Stretching Plate,” J. Phys. Soc. Jpn. 63, 2443–2444 (1994).

    Article  ADS  Google Scholar 

  7. T. R.Mahapatra, S. K. Nandy, and A. S. Gupta, “Magnetohydrodynamic Stagnation Point Flow of a Power-Law Fluid Towards a Stretching Surface,” Int. J. Non-Linear Mech. 44, 124–129 (2009).

    Article  MATH  Google Scholar 

  8. F. Lapropulu and D. Li, “Stagnation-Point Flow of a Second Grade Fluid with Slip,” Int. J. Non-Linear Mech. 43, 941–947 (2008).

    Article  ADS  Google Scholar 

  9. H. A. Attia, “Axisymmetric Stagnation Point Flow Towards a Stretching Surface in the Presence of a Uniform Magnetic Field with Heat Generation,” Tamkang J. Sci. Eng. 10 (1), 11–16 (2007).

    Google Scholar 

  10. A. Ishak, R. Nazar, N. Amin, et al., “Mixed Convection in the Stagnation Point Flow Towards a Stretching Vertical Permeable Sheet,” Malaysian J. Math. Sci. 2, 217–226 (2007).

    Google Scholar 

  11. T. Hayat and M. Nawaz, “Unsteady Stagnation Point Flow of Viscous Fluid Caused by an Impulsively Rotating Disk,” J. Taiwan Inst. Chem. Eng. 42 (1), 41–49 (2011).

    Article  Google Scholar 

  12. M. Epstein and D. H. Cho, “Melting Heat Transfer in Steady Laminar Flow over a Flat Plate,” J. Heat Transfer 98, 531–533 (1976).

    Article  Google Scholar 

  13. A. Ishak, R. Nazar, N. Bachok, and I. Pop, “Melting Heat Transfer in Steady Laminar Flow over a Moving Surface,” Heat Mass Transfer 46, 463–468 (2010).

    Article  ADS  Google Scholar 

  14. N. Bachok, A. Ishak, and I. Pop, “Melting Heat Transfer in Boundary Layer Stagnation Point Flow Towards a Stretching/Shrinking Sheet,” Phys. Lett. A 374, 4075–4079 (2010).

    Article  ADS  MATH  Google Scholar 

  15. S. J. Liao, “Notes on the Homotopy Analysis Method: Some Definitions and Theorems,” Comm. Non-linear Sci. Numer. Simulat. 14, 983–997 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. H. Xu, S. J. Liao, and X. C. You, “Analysis of Nonlinear Fractional Partial Differential Equations with Homotopy Analysis Method,” Comm. Non-linear Sci. Numer. Simulat. 14, 1152–1156 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. H. Xu, S. J. Liao, and I. Pop, “Series Solution of Unsteady Boundary Layer Flows of non Newtonian Fluids near a Forward Stagnation Point,” J. Non-Newtonian Fluid Mech. 139, 31–43 (2006).

    Article  MATH  Google Scholar 

  18. S. J. Liao, “Comparison between the Homotopy Analysis Method and Homotopy Perturbation Method,” Appl. Math. Comput. 169, 1186–1194 (2005).

    MathSciNet  MATH  Google Scholar 

  19. S. Abbasbandy, “Approximate Solution for the Nonlinear Model of Diffusion and Reaction in Porous Catalysts by Means of the Homotopy Analysis Method,” Chem. Eng. J. 136, 144–150 (2008).

    Article  Google Scholar 

  20. S. Abbasbandy, “The Application of Homotopy Analysis Method to Solve a Generalized Hirota–Satsuma Coupled KdV Equation,” Phys. Lett. A 372, 613–618 (2008).

    Article  MathSciNet  Google Scholar 

  21. S. Abbasbandy and F. S. Zakaria, “Soliton Solution for the Fifth-Order KdV Equation with Homotopy Analysis Method,” Non-Linear Dynamics 51, 83–87 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Kechil and I. Hashim, “Approximate Analytical Solution for MHD Stagnation-Point Flow in Porous Media,” Comm. Non-linear Sci. Numer. Simulat. 14, 1346–1354 (2009).

    Article  ADS  Google Scholar 

  23. I. Hashim, O. Abdulaziz, and S. Momani, “Homotopy Analysis Method for Fractional IVPs,” Comm. Non-linear Sci. Numer. Simulat. 14, 674–684 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. M. S. H. Chowdhry, I. Hashim, and O. Abdulaziz, “Comparison of Homotopy Analysis Method and Homotopy-Perturbation Method for Purely Nonlinear Fin-Type Problems,” Comm. Non-linear Sci. Numer. Simulat. 14, 371–378 (2009).

    Article  ADS  MATH  Google Scholar 

  25. T. Hayat and M. Nawaz, “Magnetohydrodynamics Three-Dimensional Flow of a Second Grade Fluid with Heat Transfer in the Presence of Hall and Ion Slip Currents,” Z. Naturforsch 65a, 683–691 (2010).

    ADS  Google Scholar 

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Correspondence to M. Nawaz.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 2, pp. 132–141, March–April, 2016.

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Nawaz, M., Hayat, T. & Zeeshan, A. Melting heat transfer in an axisymmetric stagnation-point flow of the Jeffrey fluid. J Appl Mech Tech Phy 57, 308–316 (2016). https://doi.org/10.1134/S0021894416020140

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  • DOI: https://doi.org/10.1134/S0021894416020140

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