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Numerical study of thermodiffusion effects on boundary layer flow of nanofluids over a power law stretching sheet

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Abstract

This paper deals with the triple-diffusive boundary layer flow of nanofluid over a nonlinear stretching sheet. In this model, where binary nanofluid is used, the Brownian motion, thermophoresis, and cross-diffusion are classified as the main mechanisms, which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations, which is introduced by Blasius (The boundary layers in fluids with little friction, 1950). The variational finite element method is used to solve these ordinary differential equations. We have examined the effects of different controlling parameters, namely the Brownian motion parameter, the thermophoresis parameter, modified Dufour number, nonlinear stretching parameter, Prandtl number, regular Lewis number, Dufour Lewis number, and nanofluid Lewis number on the flow field and heat transfer characteristics. The physics of the problem is well explored for the embedded material parameters through tables and graphs. The present study has many applications in coating and suspensions, movement of biological fluids, cooling of metallic plate, melt-spinning, heat exchangers technology, and oceanography.

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References

  • Awad FG, Sibanda P, Khidir AA (2013) Thermodiffusion effects on magneto-nanofluid flow over a stretching sheet. Boundary Value Probl. doi:10.1186/1687-2770-2013-136

  • Bg OA, Bakier A, Prasad V (2009) Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects. Comput Mater Sci 46(1):57–65

    Article  Google Scholar 

  • Blasius H (1950) The boundary layers in fluids with little friction, UNT digital library. http://digital.library.unt.edu/ark:/67531/metadc64584/

  • Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128(3):240–250

    Article  Google Scholar 

  • Chen CK, Char MI (1988) Heat transfer of a continuous, stretching surface with suction or blowing. J Math Anal Appl 135(2):568–580

    Article  MATH  MathSciNet  Google Scholar 

  • Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-newtonian flows, ASME FED-vol. 231/MD-vol. 66:99–105

  • Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA (2001) Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett 79(14):2252–2254

    Article  Google Scholar 

  • Cortell R (2007) Viscous flow and heat transfer over a nonlinearly stretching sheet. Appl Math Comput 184(2):864–873

    Article  MATH  MathSciNet  Google Scholar 

  • Cortell R (2011) Heat and fluid flow due to non-linearly stretching surfaces. Appl Math Comput 217(19):7564–7572

    Article  MATH  MathSciNet  Google Scholar 

  • Dettmer W, Peric D (2006) A computational framework for fluid-rigid body interaction: finite element formulation and applications. Comput Methods Appl Mech Eng 195(13–16):1633–1666

    Article  MATH  MathSciNet  Google Scholar 

  • Dutta B, Roy P, Gupta A (1985) Temperature field in flow over a stretching sheet with uniform heat flux. Int Commun Heat Mass Transf 12:89–94

    Article  Google Scholar 

  • Elbashbeshy E (2001) Heat transfer over an exponentially stretching continuous surface with suction. Arch Mech 53(6):643–651

    MATH  Google Scholar 

  • Goyal M, Bhargava R (2013) Boundary layer flow and heat transfer of viscoelastic nanofluids past a stretching sheet with partial slip conditions. Appl Nanosci 1–7. doi:10.1007/s13204-013-0254-5

  • Gupta PS, Gupta AS (1977) Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng 55(6):744–746

    Article  Google Scholar 

  • Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 193(33–35):3523–3540

    Article  MATH  MathSciNet  Google Scholar 

  • Khan W, Aziz A (2011) Double-diffusive natural convective boundary layer flow in a porous medium saturated with a nanofluid over a vertical plate: prescribed surface heat, solute and nanoparticle fluxes. Int J Therm Sci 50(11):2154–2160

    Article  Google Scholar 

  • Khan W, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53(11–12):2477–2483

    Article  MATH  Google Scholar 

  • Khan WA, Uddin MJ, Ismail AIM (2012) Effect of momentum slip on double-diffusive free convective boundary layer flow of a nanofluid past a convectively heated vertical plate, proceedings of the Institution of Mechanical Engineers. Part N J Nanoeng Nanosyst 226(3):99–109

    MathSciNet  Google Scholar 

  • Kumaran V, Ramanaiah G (1996) A note on the flow over a stretching sheet. Acta Mech 116(1–4):229–233

    Article  MATH  Google Scholar 

  • Kuznetsov A, Nield D (2010) Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49(2):243–247

    Article  MathSciNet  Google Scholar 

  • Kuznetsov A, Nield D (2011) Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 50(5):712–717

    Article  Google Scholar 

  • Lin YY, Lo SP (2003) Finite element modeling for chemical mechanical polishing process under different back pressures. J Mater Process Technol 140(1–3):646–652

    Article  Google Scholar 

  • Makinde O, 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 

  • Mansour M, Anssary NE, Aly A (2008) Effects of chemical reaction and thermal stratification on mhd free convective heat and mass transfer over a vertical stretching surface embedded in a porous media considering Soret and Dufour numbers. Chem Eng J 145(2):340–345

    Article  Google Scholar 

  • Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7(4):227–233

    Article  Google Scholar 

  • McCormack PD, Crane L (1973) Physical fluid dynamics. Academic Press, New York

    MATH  Google Scholar 

  • Nandeppanavar MM, Vajravelu K, Abel MS, Ng CO (2011) Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature. Int J Heat Mass Transf 54(23–24):4960–4965

    Article  MATH  Google Scholar 

  • Pop I, Ingham D (2001) Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media. Elsevier, Oxford

    Google Scholar 

  • Prasad K, Vajravelu K, Datti P (2010) Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties. Int J Non Linear Mech 45(3):320–330

    Google Scholar 

  • Rana P, Bhargava R (2012) Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study. Commun Nonlinear Sci Numer Simul 17(1):212–226

    Article  MathSciNet  Google Scholar 

  • Reddy JN (1985) An introduction to the finite element method. McGraw-Hill Book Co, New York

    Google Scholar 

  • Sajid M, Hayat T (2008) Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. Int Commun Heat Mass Transf 35(3):347–356

    Article  MathSciNet  Google Scholar 

  • Tsai R, Huang J (2009) Heat and mass transfer for Soret and Dufour’s effects on Hiemenz flow through porous medium onto a stretching surface. Int J Heat Mass Transf 52(9–10):2399–2406

    Article  MATH  Google Scholar 

  • Vajravelu K, Cannon JR (2006) Fluid flow over a nonlinearly stretching sheet. Appl Math Comput 181:609–618

    Article  MATH  MathSciNet  Google Scholar 

  • Weaver JA, Viskanta R (1991) Natural convection due to horizontal temperature and concentration gradients. Species interdiffusion, Soret and Dufour effects. Int J Heat Mass Transf 34(12):3121–3133

    Google Scholar 

Download references

Acknowledgments

The first author would like to thank Council of Scientific and Industrial Research for providing PhD scholarship.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, Uttarakhand, India

    Mania Goyal & Rama Bhargava

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  1. Mania Goyal
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  2. Rama Bhargava
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Correspondence to Mania Goyal.

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Goyal, M., Bhargava, R. Numerical study of thermodiffusion effects on boundary layer flow of nanofluids over a power law stretching sheet. Microfluid Nanofluid 17, 591–604 (2014). https://doi.org/10.1007/s10404-013-1326-2

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  • DOI: https://doi.org/10.1007/s10404-013-1326-2

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