Skip to main content
Log in

Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. J. Crane, “Flow past a stretching plate,” Z. Angew. Math. Phys. 21, 645–647 (1970).

    Article  Google Scholar 

  2. M. M. Rashidi, A. J. Chamkha, and M. Keimanesh, “Application of multi-step differential transform method on flow of a second-grade fluid over a stretching or shrinking sheet,” Am. J. Comput. Math. 6, 119–128 (2011).

    Article  Google Scholar 

  3. A. Ahmad and S. Asghar, “Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field,” Appl. Math. Lett. 24, 1905–1909 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Hayat, S. A. Shehzad, M. Qasim, and S. Obaidat, “Flow of a second grade fluid with convective boundary conditions,” Thermal Sci. S 15, 253–261 (2011).

    Article  Google Scholar 

  5. M. Nazar, C. Fetecau, D. Vieru, and C. Fetecau, “New exact solutions corresponding to the second problem of Stokes for second grade fluids,” Nonlinear Anal. Real World Appl. 11, 584–591 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Nazar and N. A. Latip, “Numerical investigation of three-dimensional boundary layer flow due to a stretching surface in a viscoelastic fluid,” Eur. J. Sci. Res. 29, 509–517 (2009).

    Google Scholar 

  7. K. Bhattacharyya, M. S. Uddin, G. C. Layek, and M. A. Malek, “Effect of chemically reactive solute diffusion on boundary layer flow past a stretching surface with suction or blowing,” J. Math. Math. Sci. 25, 41–48 (2010).

    Google Scholar 

  8. R. Cortell, “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Appl. Math. Comput. 184, 864–873 (2007).

    MathSciNet  MATH  Google Scholar 

  9. S. Abbasbandy, H. R. Ghehsareh, and I. Hashim, “An approximate solution of the MHD flow over a nonlinearly stretching sheet by rational Chebyshev collocation method,” UPB. Sci. Bull. 74 (2012).

    Google Scholar 

  10. S. Mukhopadhyay, “Casson fluid flow and heat transfer over a nonlinearly stretching surface,” Chin. Phys. B 22, 074701 (2013).

    Article  Google Scholar 

  11. M. Turkyilmazoglu and I. Pop, “Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a Jeffrey fluid,” Int. J. Heat Mass Transf. 57, 82–88 (2013).

    Article  Google Scholar 

  12. M. Q. Al-Odat, R. A. Damesh, and T. A. Al-Azab, “Thermal boundary layer on an exponentially stretching continuous surface in the presence of magnetic field,” Int. J. Appl. Mech. Eng. 11, 289–299 (2006).

    MATH  Google Scholar 

  13. M. Sajid and T. Hayat, “Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet,” Int. Commun. Heat Mass Transfer 35, 347–356 (2008).

    Article  Google Scholar 

  14. S. Nadeem and C. Lee, “Boundary layer flow of nanofluid over an exponentially stretching surface,” Nanoscale Res. Lett. 7, 94 (2012).

    Article  Google Scholar 

  15. K. Bhattacharyya, “Boundary layer flow and heat transfer over an exponentially shrinking sheet,” Chin. Phys. Lett. 28, 074701 (2011).

    Article  Google Scholar 

  16. S. Mukhopadhyay, K. Vajravelu, and R. A. V. Gorder, “Casson fluid flow and heat transfer at an exponentially stretching permeable surface,” J. Appl. Mech. 80, 054502 (2013).

    Article  Google Scholar 

  17. M. Mustafa, T. Hayat, and S. Obaidat, “Boundary layer flow of a nanofluid over an exponentially stretching sheet with convective boundary conditions,” Int. J. Numer. Meth. Heat Fluid Flow 23, 945–959 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  18. I. C. Liu, H. H. Wang, and Y. F. Peng, “Flow and heat transfer for three dimensional flow over an exponentially stretching surface,” Chem. Eng. Commun. 200, 253–268 (2013).

    Article  Google Scholar 

  19. S. Mukhopadhyay, G. C. Layek, and S. K. A. Samad, “Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity,” Int. J. Heat Mass Transf. 48, 4460–4466 (2005).

    Article  MATH  Google Scholar 

  20. S. S. Motsa, T. Hayat, and O. M. Aldossary, “MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method,” Appl. Math. Mech., 975–990 (2012).

    Google Scholar 

  21. M. M. Rashidi and E. Erfani, “A new analytical study of MHD stagnation-point flow in porous media with heat transfer,” Comput. Fluids 40, 172–178 (2011).

    Article  MATH  Google Scholar 

  22. S. Mukhopadhyay, “Effects of slip on unsteady mixed convective flow and heat transfer past a stretching surface,” Chin. Phys. Lett. 27, 124401 (2010).

    Article  Google Scholar 

  23. T. Hayat, Z. Abbas, I. Pop, and S. Asghar, “Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium,” Int. J. Heat Mass Transf. 53, 466–474 (2010).

    Article  MATH  Google Scholar 

  24. M. Turkyilmazoglu, “The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface,” Int. J. Mech. Sci. 77, 263–268 (2013).

    Article  Google Scholar 

  25. E. M. A. Elbashbeshy and D. A. Aldawody, “Heat transfer over an unsteady stretching surface with variable heat flux in the presence of a heat source or sink,” Comput. Math. Appl. 60, 2806–2811 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  26. R. Kandasamy, T. Hayat, and S. Obaidat, “Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink,” Nuclear Eng. Design 241, 2155–2161 (2011).

    Article  Google Scholar 

  27. A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Commun. Nonlinear Sci. Numer. Simul. 14, 1064–1068 (2009).

    Article  Google Scholar 

  28. O. D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition,” Int. J. Therm. Sci. 50, 1326–1332 (2011).

    Article  Google Scholar 

  29. S. A. Shehzad, T. Hayat, and A. Alsaedi, “Three-dimensional flow of Jeffery fluid with convective surface boundary conditions,” Int. J. Heat Mass Transf. 55, 3971–3976 (2012).

    Article  Google Scholar 

  30. M. M. Rashidi, N. F. Mehr, A. Hosseini, O. A. Bég, and T. K. Hung, “Homotopy simulation of nanofluid dynamics from a nonlinearly stretching isothermal permeable sheet with transpiration,” Meccanica. doi 10.1007/s11012-013-9805-9

  31. Y.P. Liu, S. J. Liao, and Z. B. Li, “Symbolic computation of strongly nonlinear periodic oscillations,” J. Symb. Comput. 55, 72–95 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  32. S. Abbasbandy, M. S. Hashemi, and I. Hashim, “On convergence of homotopy analysis method and its application to fractional integro-differential equations,” Quaestiones Math. 36, 93–105 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  33. L. Zheng, J. Niu, X. Zhang, and Y. Gao, “MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump,” Math. Comput. Model. 56, 133–144 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  34. M. M. Rashidi, S.C. Rajvanshi, and M. Keimanesh, “Study of Pulsatile flow in a porous annulus with the homotopy analysis method,” Int. J. Numer. Methods Heat Fluid Flow 22, 971–989 (2012).

    Article  MATH  Google Scholar 

  35. M. Turkyilmazoglu, “Solution of Thomas–Fermi equation with a convergent approach,” Commun. Nonlinear Sci. Numer. Simul. 17, 4097–4103 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  36. T. Hayat, M. B. Ashraf, H. H. Alsulami, and M. S. Alhuthali, “Three dimensional mixed convection flow of viscoelastic fluid with thermal radiation and convective conditions,” Plos One 9, e90038 (2014).

    Article  Google Scholar 

  37. H. N. Hassan and M. M. Rashidi, “An analytic solution of micropolar flow in a porous channel with mass injection using homotopy analysis method,” Int. J. Numer. Methods Heat Fluid Flow 24 (2), 419–437 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  38. T. Hayat, S. A. Shehzad, M. B. Ashraf, and A. Alsaedi, “Magnetohydrodynamic mixed convection flow of thixotropic fluid with thermophoresis and Joule heating,” J. Thermophys. Heat Transf. 27, 733–740 (2013).

    Article  Google Scholar 

  39. T. Hayat, M. B. Ashraf, and A. Alsaedi, “Small-time solutions for the thin-film flow of a Casson fluid due to a suddenly moved plate,” J. Aerosp. Eng. 27, 04014034 (2014).

    Article  Google Scholar 

  40. T. Hayat, M. Farooq, and A. Alsaedi, “Melting heat transfer in the stagnation point flow of Maxwell fluid with double-diffusive convection,” Int. J. Numer. Methods Heat Fluid Flow 24, 760–774 (2014).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Bilal Ashraf.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bilal Ashraf, M., Alsaedi, A., Hayat, T. et al. Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink. Comput. Math. and Math. Phys. 57, 1066–1079 (2017). https://doi.org/10.1134/S0965542517060021

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542517060021

Keywords

Navigation