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Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture

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Abstract

In this paper, the problem of unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture in an optically thin environment is presented. The dimensionless governing equations for this investigation are solved numerically by the fourth-order Runge–Kutta integration scheme along with shooting technique. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions. Graphical results for velocity, temperature and concentration profiles based on the numerical solutions are presented and discussed.

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Abbreviations

(x, y):

Cartesian coordinates

C ∞ :

Free stream concentration

(u, v):

Velocity components

C :

Concentration of the fluid

T w :

Surface temperature

C w :

Surface concentration

T ∞ :

Free stream temperature

D a :

DamkÖhler number

g :

Gravitational acceleratio

k :

Thermal conductivity

Q :

Heat generation coefficient

c p :

Specific heat at constant pressure

T :

Fluid temperature

D :

Diffusion coefficient

R A :

nth order irreversible reactio

U 0 :

Plate uniform velocity

R G :

Universal gas constant

Pr :

Prandtl number

c :

Suction parameter

E :

Activation energy

S c :

Schmidt number

b :

Heat generation parameter

G r :

Thermal Grashof number

G c :

Solutal Grashof number

θ :

Fluid temperature

φ :

Fluid concentration

η :

Similarity variable

γ :

Activation energy parameter

β :

Thermal volumetric-expansion coefficient

β c :

Concentration volumetric-expansion coefficient

σ :

Stefan-Boltzmann constant

α :

Absorption coefficient

ρ :

Fluid density

\({{\mathcal{V}}}\) :

Kinematic viscosity

References

  1. Dai F., Khonsari M.M.: A theory of hydrodynamic lubrication involving the mixture of fluids. J. Appl. Mech. 61, 634–641 (1994)

    Article  MATH  Google Scholar 

  2. Truesdell, C.: Sulle basi della thermomeccanica. Rend. Lince 22(8), 33–38, 158–166 (1957)

    Google Scholar 

  3. Mills N.: Incompressible mixtures of Newtonian fluids. Int. J. Eng. Sci. 4, 97–112 (1966)

    Article  MATH  Google Scholar 

  4. Beevers C.E., Craine R.E.: On the determination of response functions for a binary mixture of incompressible Newtonian fluids. Int. J. Eng. Sci 20, 737–745 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gögüs M.: The steady flow of a binary mixture between two rotating parallel non-coaxial disks. Int. J. Eng. Sci. 26, 665–677 (1992)

    Article  Google Scholar 

  6. Al-Sharif A., Chamniprasart K., Rajagopal K.R., Szeri A.Z.: Lubrication with binary mixtures: liquid-liquid emulsion. J. Tribol. 115, 46–55 (1993)

    Article  Google Scholar 

  7. Wang S.H., Al-Sharif A., Rajagopal K.R., Szeri A.Z.: Lubrication with binary mixtures: liquid-liquid emulsion an EHL conjunction. J. Tribol. 115, 515–522 (1993)

    Article  Google Scholar 

  8. Sparrow E.M., Cess R.D.: Radiation Heat Transfer, Augmented edition. Hemisphere Publishing Coop., Washinton (1978)

    Google Scholar 

  9. Abdus Sattar M.D., Hamid Kalim M.D.: Unsteady free-convection interaction with thermal radiation in a boundary layer flow past a vertical porous plate. J. Math. Phys. Sci. 30, 25–37 (1996)

    MATH  Google Scholar 

  10. Makinde O.D.: Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate. Int. Commun. Heat Mass Transf. 32, 1411–1419 (2005)

    Article  Google Scholar 

  11. Kamel M.H.: Unsteady MHD convection through porous medium with combined heat and mass transfer with heat source/sink. Energy Convers. Manag. 42, 393–405 (2001)

    Article  Google Scholar 

  12. Kandasamy R., Periasamy K., Sivagnana Prabhu K.K.: Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection. Int. J. Heat Mass Transf. 48, 1388–1394 (2005)

    Article  MATH  Google Scholar 

  13. Makinde, O.D., Moitshek, R.J.: On non-perturbative techniques for thermal radiation effect on natural convection past a vertical plate embedded in a saturated porous medium. Math. Probl. Eng. 2008, 689074 (2008)

  14. Makinde O.D.: On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux. Int. J. Num. Methods Heat Fluid Flow 19(3/4), 546–554 (2009)

    Article  Google Scholar 

  15. Ogulu A., Makinde O.D.: Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. Chem. Eng. Commun. 196(4), 454–462 (2009)

    Article  Google Scholar 

  16. Makinde, O.D., Olanrewaju, P.O.: Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition. Trans. ASME J. Fluid Eng. 132, 044502(1–4) (2010)

  17. Sibanda P., Makinde O.D.: On steady MHD flow and heat transfer due to a rotating disk in a porous medium with Ohmic heating and viscous dissipation. Int. J. Num. Methods Heat Fluid Flow 20(3), 269–285 (2010)

    Article  Google Scholar 

  18. Cheng P.: Two dimensional radiation gas flow by moment method. AIAA J 2, 1662–1664 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  19. Heck A.: Introduction to Maple, 3rd edn. Springer-Verlag, New York (2003)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering, Cape Peninsula University of Technology, P.O. Box 1906, Bellville, 7535, South Africa

    O. D. Makinde

  2. Department of Mathematics, Covenant University, Km. 10 Idiroko Road, Canaanland, P.M.B. 1023, Ota, Nigeria

    P. O. Olanrewaju

  3. Department of Mathematics, College of Natural and Applied Sciences (CoNAS), University of Dar-es-salaam, P.O. Box 35062, Dar-es-salaam, Tanzania

    W. M. Charles

Authors
  1. O. D. Makinde
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  2. P. O. Olanrewaju
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  3. W. M. Charles
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Correspondence to O. D. Makinde.

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Makinde, O.D., Olanrewaju, P.O. & Charles, W.M. Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture. Afr. Mat. 22, 65–78 (2011). https://doi.org/10.1007/s13370-011-0008-z

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  • DOI: https://doi.org/10.1007/s13370-011-0008-z

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