Skip to main content
Log in

Effect of Variable Fluid Properties on MHD Mixed Convection Flow of Second-Grade Fluid Over a Linear Heated Stretching Sheet with a Convective Boundary Condition

  • Research Article
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

An analysis has been carried out to study the effect of variable fluid properties on MHD mixed convection flow of second-grade fluid flowing along an infinite stretching sheet with convective boundary condition. The fluid is placed on an infinite heated elastic surface with linear stretching rate and a vertical velocity component due to suction at the sheet is considered. The combined effects of inertia, viscous, visco-elastic, and magnetic forces are analyzed. The basic equations governing the flow, heat transfer, and mass transfer are reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformations for velocity, temperature, and concentration. The fluid viscosity is assumed to vary as an inverse linear function of temperature, whereas the thermal conductivity as a linear function of temperature. These equations are solved numerically and the results for velocity, temperature, concentration, skin friction, local Nusselt number, and local Sherwood number are discussed using flow parameters. The investigation reveals that Joule heating and viscous dissipation enhance the temperature profile, and there are considerable effects in the presence of variable fluid properties. Comparison with previous studies shows good agreement as a special case of the problem.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. Bird RB, Stewart WE, Lightfoot EN (2007) Transport phenomena. Wiley, Hoboken

    Google Scholar 

  2. Apelblat A (1982) Mass transfer with a chemical reaction of the first order. Effect of axial diffusion. Chem Eng J 23(2):193–203

    Article  Google Scholar 

  3. Chamkha AJ (2003) MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction. Int Commun Heat Mass Transf 30(3):413–422

    Article  Google Scholar 

  4. Rout BR, Parida SK, Panda S (2013) MHD heat and mass transfer of chemical reaction fluid flow over a moving vertical plate in presence of heat source with convective surface boundary condition. Int J Chem Eng 2013:1–10

    Article  Google Scholar 

  5. Andersson HI, Hansen OR, HOlmedal B (1994) Diffusion of a chemically reactive species from a stretching sheet. Int J Heat Mass Transf 37(4):659–664

    Article  MATH  Google Scholar 

  6. Akyildiz FT, Bellout H, Vajravelu K (2006) Diffusion of chemically reactive species in a porous medium over a stretching sheet. J Math Anal Appl 320(1):322–339

    Article  MathSciNet  MATH  Google Scholar 

  7. Cortell R (2007) MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species. Chem Eng Process Process Intensif 46(8):721–728

    Article  Google Scholar 

  8. Lai FC, Kulacki FA (1990) The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium. Int J Heat Mass Transf 33(5):1028–1031

    Article  Google Scholar 

  9. Pop I, Gorla RSR, Rashidi M (1992) The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate. Int J Eng Sci 30(1):1–6

    Article  Google Scholar 

  10. Hassanien IA (1997) The effect of variable viscosity on flow and heat transfer on a continuous stretching surface. ZAMM J Appl Math Mech 77(11):876–880

    Article  MathSciNet  MATH  Google Scholar 

  11. Abel MS, Khan SK, Prasad KV (2002) Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity. Int J Nonlinear Mech 37(1):81–88

    Article  MATH  Google Scholar 

  12. Mukhopadhyay S, Layek GC (2008) Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface. Int J Heat Mass Transf 51(9):2167–2178

    Article  MATH  Google Scholar 

  13. Prasad KV, Pal D, Umesh V, Rao NS (2010) The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet. Commun Nonlinear Sci Numer Simul 15(2):331–344

    Article  ADS  MATH  Google Scholar 

  14. Magyari E, Pop I, Keller B (2002) Mixed convection boundary-layer flow past a horizontal permeable flat plate. Fluid Dyn Res 31(3):215–225

    Article  ADS  MATH  Google Scholar 

  15. Goren SL (1977) Thermophoresis of aerosol particles in the laminar boundary layer on a flat plate. J Colloid Interface Sci 61(1):77–85

    Article  ADS  Google Scholar 

  16. Tsai R (1999) A simple approach for evaluating the effect of wall suction and thermophoresis on aerosol particle deposition from a laminar flow over a flat plate. Int Commun Heat Mass Transf 26(2):249–257

    Article  Google Scholar 

  17. Chamkha AJ, Pop I (2004) Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium. Int Commun Heat Mass Transf 31(3):421–430

    Article  Google Scholar 

  18. Hayat T, Ashraf B, Shehzad SA, Alsaedi A, Bayomi N (2015) Three-dimensional mixed convection flow of viscoelastic nanofluid over an exponentially stretching surface. Int J Numer Methods Heat Fluid Flow 25(2):333–357

    Article  MathSciNet  MATH  Google Scholar 

  19. Eckert ERG, Drake RM (1971) Analysis of heat and mass transfer. McGrawHill, New York

    MATH  Google Scholar 

  20. Hayat T, Abbas Z, Pop I, Asghar S (2010) 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(1):466–474

    Article  MATH  Google Scholar 

  21. Seddeek MA (2002) Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow. Int J Heat Mass Transf 45(4):931–935

    Article  MATH  Google Scholar 

  22. Raptis A, Perdikis C (1998) Viscoelastic flow by the presence of radiation. ZAMM J Appl Math Mech 78(4):277–279

    Article  MathSciNet  MATH  Google Scholar 

  23. Bataller RC (2007) Viscoelastic fluid flow and heat transfer over a stretching sheet under the effects of a non-uniform heat source, viscous dissipation and thermal radiation. Int J Heat Mass Transf 50(15):3152–3162

    Article  MATH  Google Scholar 

  24. Hayat T, Muhammad T, Shehzad SA, Alsaedi A (2015) Temperature and concentration stratification effects in mixed convection flow of an Oldroyd-B fluid with thermal radiation and chemical reaction. PloS ONE 10(6):e0127646

    Article  Google Scholar 

  25. Makinde OD (2010) On MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition. Can J Chem Eng 88(6):983–990

    Article  Google Scholar 

  26. Makinde OD, Aziz A (2011) Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int J Therm Sci 50(7):1326–1332

    Article  Google Scholar 

  27. Rahman MM (2011) Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition. Meccanica 46(5):1127–1143

    Article  MathSciNet  MATH  Google Scholar 

  28. Bachok N, Ishak A, Pop I (2013) Stagnation point flow toward a stretching/shrinking sheet with a convective surface boundary condition. J Frankl Inst 350(9):2736–2744

    Article  MathSciNet  MATH  Google Scholar 

  29. Singh V, Agarwal S (2014) Heat transfer for two types of viscoelastic fluid over an exponentially stretching sheet with variable thermal conductivity and radiation in porous medium. Therm Sci 18(4):1079–1093

    Article  Google Scholar 

  30. Hayat T, Shehzad SA, Qasim M, Obaidat S (2011) Flow of a second grade fluid with convective boundary conditions. Therm Sci 15(suppl. 2):253–261

    Article  Google Scholar 

  31. Astarita G, Marrucci G (1974) Principles of non-Newtonian fluid mechanics, vol 28. McGraw-Hill, New York

    MATH  Google Scholar 

  32. Dunn JE, Fosdick RL (1974) Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade. Arch Ration Mech Anal 56(3):191–252

    Article  MathSciNet  MATH  Google Scholar 

  33. Chiam TC (1996) Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet. Int Commun Heat Mass Transf 23(2):239–248

    Article  Google Scholar 

  34. Beard DW, Walters K (1964) Elastico-viscous boundary-layer flows. I. Two-dimensional flow near a stagnation point. In: Proceedings of Cambridge Philosophical Society, vol 60, pp 667–674. Cambridge University Press

  35. Sparrow EM, Cess RD (1978) Radiation heat transfer. Series in thermal and fluids engineering. Augmented edition, vol 1. McGraw-Hill, New York

    Google Scholar 

  36. Talbot L, Cheng RK, Schefer RW, Willis DR (1980) Thermophoresis of particles in a heated boundary layer. J Fluid Mech 101(04):737–758

    Article  ADS  Google Scholar 

  37. Hayat T, Mustafa M, Sajid M (2009) Influence of thermal radiation on blasius flow of a second grade fluid. Z Naturforsch A 64a:827–833

    Article  ADS  Google Scholar 

  38. Liu I-Chung (2004) Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse magnetic field. Int J Heat Mass Transf 47(19):4427–4437

    Article  MATH  Google Scholar 

  39. Hayat T, Qasim M (2010) Influence of thermal radiation and joule heating on MHD flow of a Maxwell fluid in the presence of thermophoresis. Int J Heat Mass Transf 53(21):4780–4788

    Article  MATH  Google Scholar 

  40. Makinde OD, Olanrewaju PO, Charles WM (2011) Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture. Afr Mat 22(1):65–78

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. P. Priyadarsan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Priyadarsan, K.P., Panda, S. Effect of Variable Fluid Properties on MHD Mixed Convection Flow of Second-Grade Fluid Over a Linear Heated Stretching Sheet with a Convective Boundary Condition. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 225–237 (2020). https://doi.org/10.1007/s40010-018-0559-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-018-0559-6

Keywords

Navigation