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Flow of Oldroyd-B Fluid over a Rotating Disk Through Porous Medium with Soret–Dufour Effects

  • Research Article-Mechanical Engineering
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Abstract

A study of Darcy flow of magnetized Oldroyd-B fluid over a rotating porous disk is analyzed. The heat and mass transport mechanism are analyzed with the significant features of thermal diffusion (Soret) and diffusion thermo (Dufour). Additionally the influence of chemical reaction is also considered on solutal field. The Von Karman transformations are used and in order to obtain the similarity equations which are then integrated numerically on \(\left[ 0,\infty \right) \) through BVP Midrich technique in Maple. The results are given through graphical structure and tabular form. A brief parametric survey is conducted against velocity fields, temperature and concentration distributions in the form of graphs. The corresponding heat transfer rate and wall concentration gradient are displayed through tables with different physical effects. The comparison tables are presented to assure the validity of our numerical scheme with the past outcomes. It is revealed that the velocity fields decline with the effect of porosity parameter. The heat transfer rate rises significantly with diminishing value of Soret number.

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Abbreviations

\(r,\varphi ,z\) :

Cylindrical coordinate

u, v, w :

Components of velocity

T :

Fluid temperature

\(T_\mathrm{w}\) :

Wall temperature

\(T_\mathrm{m}\) :

Fluid mean temperature

\(\nu \) :

Kinematic viscosity

C :

Fluid concentration

\(\phi _{1}\) :

Porosity of the medium

D :

Molecular diffusion coefficient

\(\lambda _{1}\) :

Time relaxation

M :

Magnetic field

\(\beta _{1}\) :

Relaxation time parameter

\(\Pr \) :

Prandtl number

\(k_\mathrm{T}\) :

The thermal–diffusion ratio

\(\varOmega \) :

Angular velocity rate

\(c_{s}\) :

The concentration susceptibility

\(\delta \) :

Ratio of diffusion coefficients

F :

Radial velocity

H :

Axial velocity

\(\theta \) :

Dimensionless temperature

\(\alpha \) :

Thermal diffusivity

\(c_{p}\) :

Specific heat capacity

\(T_{\infty }\) :

Ambient temperature

\(C_\mathrm{w}\) :

Wall concentration

\(\mu \) :

Dynamic viscosity

\(\rho \) :

Fluid density

\(C_{\infty }\) :

Ambient concentration

K :

Permeability of the medium

\(K_{1}\) :

The chemical reaction rate

\(\lambda _{2}\) :

Time retardation

R :

Stretching parameter

\(\beta _{2}\) :

Retardation time parameter

Sc:

Schmidt number

\(\eta \) :

Dimensionless variable

\(\theta \) :

Dimensionless temperature

\(B_{0}\) :

Strength of magnetic field

\(\mu \) :

Dynamic viscosity

G :

Azimuthal velocity

c :

Stretching rate

\(\phi \) :

Dimensionless concentration

References

  1. Von Karman, T.: Uberlaminare und turbulente Reibung. Z. Angew Math. Mech. ZAMM 1, 233–252 (1921)

    Article  Google Scholar 

  2. Cochran, W.G.: The flow due to a rotating disk. Proc Camb. Philos. Soc. 30, 365–375 (1934)

    Article  Google Scholar 

  3. Benton, E.T.: On the flow due to a rotating disk. J. Fluid Mech. 24, 781–800 (1966)

    Article  Google Scholar 

  4. Rashidi, M.M.; Kavyani, N.; Abelman, S.: Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties. Int. J. Heat Mass Transf. 70, 892–917 (2014)

    Article  Google Scholar 

  5. Khan, N.A.; Sultan, F.: Numerical analysis for the Bingham–Papanastasiou fluid flow over a rotating disk. J. Appl. Mech. Tech. Phys. 59, 638–644 (2018)

    Article  MathSciNet  Google Scholar 

  6. Ahmed, J.; Khan, M.; Ahmad, L.: Transient thin film flow of nonlinear radiative Maxwell nanofluid over a rotating disk. Phys. Lett. A 383, 1300–1305 (2019)

    Article  Google Scholar 

  7. Ellahi, R.; Tariq, M.H.; Hassan, M.; Vafaia, K.: On boundary layer nano-ferroliquid flow under the influence of low oscillating stretchable rotating disk. J. Mol. Liq. 229, 339–345 (2017)

    Article  Google Scholar 

  8. Mahanthesh, B.; Gireesha, B.J.; Shehzad, S.A.; Rauf, A.; Kumar, P.B.S.: Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition. Phys. B Cond. Matt. 537, 98–104 (2018)

    Article  Google Scholar 

  9. Gholinia, M.; Hosseinzadeh, K.; Mehrzadi, H.; Ganji, D.D.; Ranjbar, A.A.: Investigation of MHD Eyring–Powell fluid flow over a rotating disk under effect of homogeneous–heterogeneous reactions. Case Stud. Ther. Eng. 13, 100356 (2019)

    Article  Google Scholar 

  10. Ahmed, J.; Khan, M.; Ahmad, L.: Stagnation point flow of Maxwell nanofluid over a permeable rotating disk with heat source/sink. J. Mol. Liq. 287, 110853 (2019)

    Article  Google Scholar 

  11. Khan, M.; Hafeez, A.; Ahmed, J.: Impacts of non-linear radiation and activation energy on the axisymmetric rotating flow of Oldroyd-B fluid. Phys. A Stat. Mech. Appl. (2020). https://doi.org/10.1016/j.physa.2019.124085

  12. Hafeez, A.; Khan, M.; Ahmed, J.: Stagnation point flow of radiative Oldroyd-B nanofluid over a rotating disk. Comp. Methods Prog. Biomed. 191, 105342 (2020)

    Article  Google Scholar 

  13. Hafeez, A.; Khan, M.; Ahmed, J.: Thermal aspects of chemically reactive Oldroyd-B fluid flow over a rotating disk with Cattaneo–Christov heat flux theory. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09421-4

  14. Hafeez, A.; Khan, M.; Ahmed, J.: Flow of Oldroyd-B fluid over a rotating disk with Cattaneo–Christov theory for heat and mass fluxes. Comp. Methods Prog. Biomed. 191, 105374 (2020)

    Article  Google Scholar 

  15. Cheng, P.; Minkowycz, W.J.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040–2044 (1977)

    Article  Google Scholar 

  16. Kou, H.S.; Huang, D.K.: Some transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall temperature. Int. Commun. Heat Mass Transf. 23, 273–286 (1996)

    Article  Google Scholar 

  17. Kou, H.S.; Huang, D.K.: Possible transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall heat flux. Int. Commun. Heat Mass Transf. 23, 1031–1042 (1996)

    Article  Google Scholar 

  18. Chamkha, A.J.: Solar radiation assisted natural convection in uniform porous medium supported by a vertical flat plate. ASME J. Heat Transf. 119, 89–96 (1997)

    Article  Google Scholar 

  19. Chamkha, A.J.; Khaled, A.R.A.: Hydromagnetic combined heat and mass transfer by natural convection from a permeable surface embedded in a fluid-saturated porous medium. Int. J. Numer. Methods Heat Fluid Flow 10, 455–477 (2000)

    Article  Google Scholar 

  20. Chamkha, A.J.; Al-Mudhaf, A.F.; Pop, I.: Effect of heat generation or absorption on thermophoretic free convection boundary layer from a vertical flat plate embedded in a porous medium. Int. Commun. Heat Mass Transf. 33, 1096–1102 (2006)

    Article  Google Scholar 

  21. Modather, M.; Chamkha, A.J.: An analytical study of MHD heat and mass transfer oscillatory flow of a micropolar fluid over a vertical permeable plate in a porous medium. Turk. J. Eng. Environ. Sci. 33, 245–258 (2010)

    Google Scholar 

  22. Gorla, R.S.R.; Chamkha, A.J.: Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid. Nanoscale Microscale Thermophys. Eng. 15, 81–94 (2011)

    Article  Google Scholar 

  23. Chamkha, A.J.; Abbasbandy, S.; Rashad, A.M.; Vajravelu, K.: Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid. Meccanica 48, 275–285 (2013)

    Article  MathSciNet  Google Scholar 

  24. Ghalambaz, M.; Behseresht, A.; Behseresht, J.; Chamkha, A.J.: Effects of nanoparticles diameter and concentration on natural convection of the Al2O3–water nanofluids considering variable thermal conductivity around a vertical cone in porous media. Adv. Powder Technol. 26, 224–235 (2015)

    Article  Google Scholar 

  25. Reddy, P.S.; Sreedevi, P.; Chamkha, A.J.: MHD boundary layer flow, heat and mass transfer analysis over a rotating disk through porous medium saturated by Cu–water and Ag–water nanofluid with chemical reaction. Powder Technol. 307, 46–55 (2017)

    Article  Google Scholar 

  26. Eckert, E.R.G.; Drake, R.M.: Analysis of Heat and Mass Transfer. McGraw Hill, New York (1987)

    MATH  Google Scholar 

  27. Jha, B.K.; Singh, A.K.: Soret effects on free-convection and mass transfer flow in the Stokes problem for an infinite vertical plate. Astrophys. Space Sci. 173, 251–255 (1990)

    Article  Google Scholar 

  28. Kafoussias, N.G.: MHD thermal-diffusion effects on free-convective and mass-transfer flow over an infinite vertical moving plate. Astrophys. Space Sci. 192, 11–19 (1992)

    Article  Google Scholar 

  29. Alam, M.M.; Sattar, M.A.: Unsteady MHD free convection and mass transfer flow in a rotating system with thermal diffusion. J. Energy Heat Mass Transf. 20, 77–87 (1998)

    Google Scholar 

  30. Postelnicu, A.: Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Int. J. Heat Mass Transf. 47, 1467–1472 (2004)

    Article  Google Scholar 

  31. Tsai, R.; Huang, J.S.: 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, 2399–2406 (2009)

    Article  Google Scholar 

  32. Partha, M.K.; Murthy, P.V.S.N.; Sekhar, G.P.R.: Soret and Dufour effects in a non-Darcy porous medium. J. Heat Transf. 128, 605–610 (2006)

    Article  Google Scholar 

  33. RamReddy, C.; Murthy, P.V.S.N.; Chamkha, A.J.; Rashad, A.M.: Soret effect on mixed convection flow in a nanofluid under convective boundary condition. Int. J. Heat Mass Transf. 64, 384–392 (2013)

    Article  Google Scholar 

  34. Reddy, P.S.; Chamkha, A.J.: Soret and Dufour effects on MHD convective flow of Al2O3–water and TiO2–water nanofluids past a stretching sheet in porous media with heat generation/absorption. Adv. Powder Technol. 27, 1207–1218 (2016)

    Article  Google Scholar 

  35. Shojaei, A.; Amiri, A.J.; Ardahaie, S.S.; Hosseinzadeh, K.; Ganji, D.D.: Hydrothermal analysis of Non-Newtonian second grade fluid flow on radiative stretching cylinder with Soret and Dufour effects. Case Stud. Ther. Eng. 13, 100384 (2019)

    Article  Google Scholar 

  36. Gregg, J.L.; Sparrow, E.M.: Heat transfer from a rotating disk to fluids of any Prandtl number. ASME J. Heat Transf. 81, 249–251 (1959)

    Article  Google Scholar 

  37. Bachok, N.; Ishak, A.; Pop, I.: Flow and heat transfer over a rotating porous disk in a nanofluid. Phys. B Cond. Matt. 406, 1767–1772 (2011)

    Article  Google Scholar 

  38. Turkyilmazoglu, M.: Nanofluid flow and heat transfer due to a rotating disk. Comput. Fluids 94, 139–146 (2014)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    Abdul Hafeez, Masood Khan, Jawad Ahmed, Awais Ahmed & Zahoor Iqbal

  2. Department of Basic Sciences, University of Engineering and Technology, Taxila, 47050, Pakistan

    Jawad Ahmed

Authors
  1. Abdul Hafeez
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  2. Masood Khan
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  4. Awais Ahmed
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  5. Zahoor Iqbal
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Correspondence to Abdul Hafeez.

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Hafeez, A., Khan, M., Ahmed, J. et al. Flow of Oldroyd-B Fluid over a Rotating Disk Through Porous Medium with Soret–Dufour Effects. Arab J Sci Eng 45, 5949–5957 (2020). https://doi.org/10.1007/s13369-020-04575-7

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