Skip to main content
SpringerLink
Log in

MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

Combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained. Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.

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

Access this article

Log in via an institution

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. CRANE L J. Flow past a stretching plate [J]. Zeitschrift fur angewandte Mathematik und Physik ZAMP, 1970, 21(4): 645–647.

    Article  Google Scholar 

  2. BHATTACHARYYA K. MHD stagnation-point flow of casson fluid and heat transfer over a stretching sheet with thermal radiation [J]. Journal of Thermodynamics, 2013, doi: 1031155/2013/169674.

    Google Scholar 

  3. HAYAT T, FAROOQ M, ALSAEDI A, IQBAL Z. Melting heat transfer in the stagnation point flow of Powell-Eyring fluid [J]. Journal of Thermophysics and Heat Transfer, 2013, 27: 761–766.

    Article  Google Scholar 

  4. MUKHOPADHYAY S. MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium [J]. Alexandria Engineering Journal, 2013, 52: 259–265.

    Article  Google Scholar 

  5. IBRAHIM W, MAKINDE O D. The effect of double stratification on boundary layer flow and heat transfer of nanofluid over a vertical plate [J]. Computers & Fluids, 2013, 86: 433–441.

    Article  MATH  MathSciNet  Google Scholar 

  6. AWAIS M, HAYAT T, QAYYUM A, ALSAEDI A. Newtonian heating in a flow of thixotropic fluid [J]. European Physical Journal Plus, 2013, 128(10): 114-1–11.

    Article  Google Scholar 

  7. RASHIDI M M, ABELMAN S, MEHR N F. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid [J]. International Journal of Heat and Mass Transfer, 2013, 62: 515–525.

    Article  Google Scholar 

  8. TURKYILMAZOGLU M. The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface [J]. International Journal of Mechanical Sciences, 2013, 77: 263–268.

    Article  Google Scholar 

  9. BHATTACHARYYA K. Heat transfer analysis in unsteady boundary layer stagnation-point flow towards a shrinking/stretching sheet [J]. Ain Shams Engineering Journal, 2013, 4: 259–264.

    Article  Google Scholar 

  10. BACHOK N, ISHAK A, POP I. Stagnation point flow toward a stretching/shrinking sheet with a convective surface boundary condition [J]. Journal of the Franklin Institute, 2013, 350: 2736–2744.

    Article  MATH  MathSciNet  Google Scholar 

  11. WANG C Y. Natural convection on a vertical stretching cylinder [J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17: 1098–1103.

    Article  MathSciNet  Google Scholar 

  12. MUKHOPADHYAY S. MHD boundary layer slip flow along a stretching cylinder [J]. Ain Shams Engineering Journal, 2013, 4: 317–324.

    Article  Google Scholar 

  13. PATILP M, ROY S, POP I. Unsteady effects on mixed convection boundary layer flow from a permeable slender cylinder due to non-linearly power law stretching [J]. Computers & Fluids, 2012, 56: 17–23.

    Article  MathSciNet  Google Scholar 

  14. MUKHOPADHYAY S, GORLA R S R. Slip effects on boundary layer flow and heat transfer along a stretching cylinder [J]. International Journal of Applied Mechanics and Engineering, 2013, 18: 447–459.

    Google Scholar 

  15. MACHIREDDY G R. Chemically reactive species and radiation effects on MHD convective flow past a moving vertical cylinder [J]. Ain Shams Engineering Journal, 2013, 4: 879–888.

    Article  Google Scholar 

  16. CHIAM T C. Stagnation-point flow towards a stretching plate [J]. Journal of the Physical Society of Japan, 1994, 63: 2443–2444.

    Article  Google Scholar 

  17. MAHAPATRA T R, GUPTA A S. Magnetohydrodynamic stagnation-point flow towards a stretching sheet [J]. Acta Mech, 2001, 152: 191–196.

    Article  MATH  Google Scholar 

  18. TURKYILMAZOGLU M, POP I. Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/ shrinking sheet in a Jeffrey fluid [J]. International Journal of Heat and Mass Transfer, 2013, 57: 82–88.

    Article  Google Scholar 

  19. SHEHZAD S A, ALSAADI F E, MONAQUEL S J, HAYAT T. Soret and Dufour effects on the stagnation point flow of Jeffery fluid with convective boundary condition [J]. European Physical Journal Plus, 2013, 128(6): 56-1–15.

    Article  Google Scholar 

  20. MAKINDE O D, KHAN W A, KHAN Z H. Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet [J]. International Journal of Heat and Mass Transfer, 2013, 62: 526–533.

    Article  Google Scholar 

  21. MALVANDI A, HEDAYATI F, GANJI D D. Slip effects on unsteady stagnation point flow of ananofluid over a stretching sheet [J]. Powder Technology, 2014, 253: 377–384.

    Article  Google Scholar 

  22. ROSCA N C, POP I. Mixed convection stagnation point flow past a vertical flat plate with a second order slip: Heat flux case [J]. International Journal of Heat and Mass Transfer. 2013, 65: 102–109.

    Article  Google Scholar 

  23. KHALILIS, DINARVAND S, HOSSEINIR, DEHKORDIIR, TAMIM H. Stagnation-point flow and heat transfer of a nanofluid adjacent to linearly stretching/shrinking sheet: A numerical study [J]. Research Journal of Applied Sciences, Engineering and Technology, 2014, 7: 83–90.

    Google Scholar 

  24. ALSAEDI A, ALSAADI F E, ALI S, HAYAT T. Stagnation point flow of Burgers’ fluid and mass transfer with chemical reaction and porosity [J]. Journal of Mechanics, 2013, 29: 453–460.

    Article  Google Scholar 

  25. JAFARI M, RAHIMI A B. Axisymmetric stagntion-point flow and heat transfer of a viscous fluid on a moving plate with time-dependent axial velocity and uniform transpiration [J]. Scientia Iranica, 2013, 20: 152–161.

    Google Scholar 

  26. ECKERT E R G, DRAKE R M. Analysis of heat and mass transfer [M]. New York: McGraw Hill, 1972: 715–722.

    Google Scholar 

  27. PAL D, MONDAL H. Influence of chemical reaction and thermal radiation on mixed convection heat and mass transfer over a stretching sheet in Darcian porous medium with Soret and Dufour effects [J]. Energy Conversion and Management, 2012, 62: 102–108.

    Article  Google Scholar 

  28. CHENG C Y. Soret and Dufour effects on free convection heat and mass transfer from an arbitrarily inclined plate in a porous medium with constant wall temperature and concentration [J]. International Communications in Heat and Mass Transfer, 2012, 39: 72–77.

    Article  Google Scholar 

  29. ALTAWALLBEHA A A, BHADAURIAB B S, HASHIM I. Linear and nonlinear double-diffusive convection in a saturated anisotropic porous layer with Soret effect and internal heat source [J]. International Journal of Heat and Mass Transfer, 2013, 59: 103–111.

    Article  Google Scholar 

  30. CHENG C Y. Soret and Dufour effects on free convection boundary layers over an inclined wavy surface in a porous medium [J]. International Communications in Heat and Mass Transfer, 2011, 38: 1050–1055.

    Article  Google Scholar 

  31. HAYAT T, NAZ R, ASGHAR S, MESLOUB S. Soret-Dufour effects on three-dimensional flow of third grade fluid [J]. Nuclear Engineering and Design, 2012, 243: 1–14.

    Article  Google Scholar 

  32. LIAO S J. Homotopy analysis method in non-linear differential equations [M]. Heidelberg: Springer and Higher Education Press, 2012: 15–78.

    Book  Google Scholar 

  33. MOTSA S S. On the practical use of the spectral homotopy analysis method and local linearisation method for unsteady boundary-layer flows caused by an impulsively stretching plate [J]. Numer Algor, 2013, DOI 10.1007/s11075-013-9766-z.

    Google Scholar 

  34. HAYAT T, FAROOQ M, ALSAEDI A, IQBAL Z. Melting heat transfer in the stagnation point flow of Powell-Eyring fluid [J]. Journal of Thermo physics and Heat Transfer, 2013, 27: 761–766.

    Article  Google Scholar 

  35. HAYAT T, QAYYUM A, ALSAEDI F, AWAIS M, DOBAIE A M. Thermal radiation effects in squeezing flow of a Jeffery fluid [J]. European Physical Journal Plus, 2013, 128: 85-1–7.

    Google Scholar 

  36. HASSAN H N, RASHIDI M M. An analytical solution of micropolar fluidinaporous channel with mass injection using homotopy analysis method [J]. International Journal of Numerical Methods For Heat and Fluid Flow, 2014, 24: 419–437.

    Article  MathSciNet  Google Scholar 

  37. TURKYILMAZOGLU M. Solution of the Thomas-Fermi equation with a convergent approach [J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17: 4097–4103.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Computing, Mohammad Ali Jinnah University, Islamabad Campus, Islamabad, 44000, Pakistan

    M. Ramzan

  2. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    M. Farooq & T. Hayat

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    T. Hayat, A. Alsaedi & J. Cao

  4. Department of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, China

    J. Cao

Authors
  1. M. Ramzan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Farooq
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Farooq.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramzan, M., Farooq, M., Hayat, T. et al. MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects. J. Cent. South Univ. 22, 707–716 (2015). https://doi.org/10.1007/s11771-015-2574-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-015-2574-y

Key words

Search

Navigation