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Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

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Abstract

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature, and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.

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References

  1. Crane, L. J. Flow past a stretching plate. Journal of Applied Mathematics and Physics (ZAMP), 21, 645–647 (1970)

    Article  Google Scholar 

  2. Abbasbandy, S., Hayat, T., Alsaedi, A., and Rashidi, M. M. Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 24, 390–401 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Rashidi, M. M., Bagheri, S., Momoniat, E., and Freidoonimehr, N. Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Engineering Journal, 67, 95–99 (2015)

    Google Scholar 

  4. Sheikholeslami, M., Hatami, M., and Ganji, D. D. Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. Journal of Molecular Liquids, 190, 112–120 (2014)

    Article  Google Scholar 

  5. Lin, Y., Zheng, L., and Chen, G. Unsteady flow and heat transfer of pseudoplastic nano-liquid in a finite thin film on a stretching surface with variable thermal conductivity and viscous dissipation. Powder Technology, 274, 324–332 (2015)

    Article  Google Scholar 

  6. Pourmehran, O., Rahimi-Gorji, M., and Ganji, D. D. Heat transfer and flow analysis of nanofluid flow induced by a stretching sheet in the presence of an external magnetic field. Journal of the Taiwan Institute of Chemical Engineers, 65, 162–171 (2016)

    Article  Google Scholar 

  7. Turkyilmazoglu, M. Flow of a micropolar fluid due to a porous stretching sheet and heat transfer. International Journal of Non-Linear Mechanics, 83, 59–64 (2016)

    Article  Google Scholar 

  8. Zhang, Y., Zhang, M., and Bai, Y. Flow and heat transfer of an Oldroyd-B nanofluid thin film over an unsteady stretching sheet. Journal of Molecular Liquids, 220, 665–670 (2016)

    Article  Google Scholar 

  9. Sajid, M., Ahmed, B., and Abbas, Z. Steady mixed convection stagnation point flow of MHD Oldroyd-B fluid over a stretching sheet. Journal of the Egyptian Mathematical Society, 23, 440–444 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hayat, T., Imtiaz, M., Alsaedi, A., and Almezal, S. On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 401, 296–303 (2016)

    Article  Google Scholar 

  11. Shehzad, S. A., Abdullah, Z., Abbasi, F. M., Hayat, T., and Alsaedi, A. Magnetic field effect in three-dimensional flow of an Oldroyd-B nanofluid over a radiative surface. Journal of Magnetism and Magnetic Materials, 399, 97–108 (2016)

    Article  Google Scholar 

  12. Hayat, T., Muhammad, T., Shehzad, S. A., Alhuthali, M. S., and Lu, J. Impact of magnetic field in three-dimensional flow of an Oldroyd-B nanofluid. Journal of Molecular Liquids, 212, 272–282 (2015)

    Article  Google Scholar 

  13. Niu, J., Shi, Z. H., and Tan, W. C. The viscoelastic effects on thermal convection of an Oldroyd-B fluid in open-top porous media. Journal of Hydrodynamics, Ser. B, 25, 639–642 (2013)

    Article  Google Scholar 

  14. Li, C., Zheng, L., Zhang, Y., Ma, L., and Zhang, X. Helical flows of a heated generalized Oldroyd- B fluid subject to a time-dependent shear stress in porous medium. Communications in Nonlinear Science and Numerical Simulation, 17, 5026–5041 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hayat, T., Awais, M., and Obaidat, S. Similar solution for three-dimensional flow in an Oldroyd-B fluid over a stretching surface. International Journal for Numerical Methods in Fluids, 70, 851–859 (2012)

    Article  MathSciNet  Google Scholar 

  16. Kayalvizhi, M., Kalaivanan, R., Ganesh, N. V., Ganga, B., and Hakeem, A. K. A. Velocity slip effects on heat and mass fluxes of MHD viscous-Ohmic dissipative flow over a stretching sheet with thermal radiation. Ain Shams Engineering Journal, 7, 791–797 (2016)

    Article  Google Scholar 

  17. Yasin, M. H. M., Ishak, A., and Pop, I. MHD heat and mass transfer flow over a permeable stretching/shrinking sheet with radiation effect. Journal of Magnetism and Magnetic Materials, 407, 235–240 (2016)

    Article  Google Scholar 

  18. Narayana, P. V. S. and Babu, D. H. Numerical study of MHD heat and mass transfer of a Jeffrey fluid over a stretching sheet with chemical reaction and thermal radiation. Journal of the Taiwan Institute of Chemical Engineers, 59, 18–25 (2016)

    Article  Google Scholar 

  19. Dogonchi, A. S., Divsalar, K., and Ganji, D. D. Flow and heat transfer of MHD nanofluid between parallel plates in the presence of thermal radiation. Computer Methods in Applied Mechanics and Engineering, 310, 58–76 (2016)

    Article  MathSciNet  Google Scholar 

  20. Zeeshan, A., Majeed, A., and Ellahi, R. Effect of magnetic dipole on viscous ferro-fluid past a stretching surface with thermal radiation. Journal of Molecular Liquids, 215, 549–554 (2016)

    Article  Google Scholar 

  21. Bhattacharyya, K., Mukhopadhyay, S., Layek, G. C., and Pop, I. Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet. International Journal of Heat and Mass Transfer, 55, 2945–2952 (2012)

    Article  Google Scholar 

  22. Sheikholeslami, M., Ganji, D. D., Javed, M. Y., and Ellahi, R. Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model. Journal of Magnetism and Magnetic Materials, 374, 36–43 (2015)

    Article  Google Scholar 

  23. Epstein, M. and Cho, D. H. Melting heat transfer in steady laminar flow over a flat plate. Journal of Heat Transfer, 98, 531–533 (1976)

    Article  Google Scholar 

  24. Ahmad, S. and Pop, I. Melting effect on mixed convection boundary layer flow about a vertical surface embedded in a porous medium. Transport in Porous Media, 102, 317–323 (2014)

    Article  Google Scholar 

  25. Awais, M., Hayat, T., and Alsaedi, A. Investigation of heat transfer in flow of Burgers’ fluid during a melting process. Journal of the Egyptian Mathematical Society, 23, 410–415 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hayat, T., Imtiaz, M., and Alsaedi, A. Melting heat transfer in the MHD flow of Cu-water nanofluid with viscous dissipation and Joule heating. Advanced Powder Technology, 27, 1301–1308 (2016)

    Article  Google Scholar 

  27. Hayat, T., Hussain, Z., Alsaedi, A., and Ahmad, B. Heterogeneous-homogeneous reactions and melting heat transfer effects in flow with carbon nanotubes. Journal of Molecular Liquids, 220, 200–207 (2016)

    Article  Google Scholar 

  28. Rashidi, M. M., Nasiri, M., Khezerloo, M., and Laraqi, N. Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls. Journal of Magnetism and Magnetic Materials, 401, 159–168 (2016)

    Article  Google Scholar 

  29. Hayat, T., Qayyum, S., Imtiaz, M., and Alsaedi, A. Comparative study of silver and copper water nanofluids with mixed convection and nonlinear thermal radiation. International Journal of Heat and Mass Transfer, 102, 723–732 (2016)

    Article  Google Scholar 

  30. Sajid, M., Ahmed, B., and Abbas, Z. Steady mixed convection stagnation point flow of MHD Oldroyd-B fluid over a stretching sheet. Journal of the Egyptian Mathematical Society, 23, 440–444 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  31. Hayat, T., Abbasi, F. M., Yami, M. A., and Monaquel, S. Slip and Joule heating effects in mixed convection peristaltic transport of nanofluid with Soret and Dufour effects. Journal of Molecular Liquids, 194, 93–99 (2014)

    Article  Google Scholar 

  32. Abbasi, F. M., Shehzad, S. A., Hayat, T., and Ahmad, B. Doubly stratified mixed convection flow of Maxwell nanofluid with heat generation/absorption. Journal of Magnetism and Magnetic Materials, 404, 159–165 (2016)

    Article  Google Scholar 

  33. Liao, S. J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall/CRC, Boca Raton (2003)

    Book  Google Scholar 

  34. Turkyilmazoglu, M. Solution of the Thomas-Fermi equation with a convergent approach. Communications in Nonlinear Science and Numerical Simulation, 17, 4097–4103 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  35. Arqub, O. A. and Ajou, A. E. Solution of the frictional epidemic model by homotopy analysis method. Journal of King Saud University-Science, 25, 73–81 (2013)

    Article  Google Scholar 

  36. Hayat, T., Khan, M. I., Farooq, M., Yasmeen, T., and Alsaedi, A. Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. Journal of Molecular Liquids, 220, 49–55 (2016)

    Article  Google Scholar 

  37. Abbasbandy, S., Yurusoy, M., and Gulluce, H. Analytical solutions of non-linear equations of power-law fluids of second grade over an infinite porous plate. Mathematical and Computational Applications, 19, 124–133 (2014)

    Article  MathSciNet  Google Scholar 

  38. Farooq, U., Zhao, Y. L., Hayat, T., Alsaedi, A., and Liao, S. J. Application of the HAM-based mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nanofluid. Computers & Fluids, 111, 69–75 (2015)

    Article  MathSciNet  Google Scholar 

  39. Ellahi, R., Hassan, M., and Zeeshan, A. Shape effects of nanosize particles in Cu-H2O nanofluid on entropy generation. International Journal of Heat and Mass Transfer, 81, 449–456 (2015)

    Article  Google Scholar 

  40. Hayat, T., Asad, S., Mustafa, M., and Alsaedi, A. MHD stagnation-point flow of Jeffrey fluid over a convectively heated stretching sheet. Computers & Fluids, 108, 179–185 (2015)

    Article  MathSciNet  Google Scholar 

  41. Sui, J., Zheng, L., Zhang, X., and Chen, G. Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate. International Journal of Heat and Mass Transfer, 85, 1023–1033 (2015)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    T. Hayat, A. Kiran & M. Imtiaz

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

Authors
  1. T. Hayat
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  2. A. Kiran
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  3. M. Imtiaz
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  4. A. Alsaedi
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Correspondence to M. Imtiaz.

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Hayat, T., Kiran, A., Imtiaz, M. et al. Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid. Appl. Math. Mech.-Engl. Ed. 38, 957–968 (2017). https://doi.org/10.1007/s10483-017-2218-6

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  • DOI: https://doi.org/10.1007/s10483-017-2218-6

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