Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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RADIATION EFFECTS ON MHD BOUNDARY LAYER FLOW OF LIQUID METAL OVER A POROUS STRETCHING SURFACE IN POROUS MEDIUM WITH HEAT GENERATION

  • Venkateswarlu, M. (Department of Mathematics, V.R. Siddhartha Engineering College) ;
  • Reddy, G. Venkata Ramana (Department of Mathematics, K.L. University) ;
  • Lakshmi, D. Venkata (Department of Mathematics, Bapatla Women's Engineering College)
  • Received : 2014.11.03
  • Accepted : 2015.01.02
  • Published : 2015.03.25
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Abstract

The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge-Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.

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References

  1. M. Arunachalam and N. R. Rajappa: Thermal boundary layer in liquid metals with variable thermal conductivity, Appl. Sci. Res, 34(1978), pp. 179- 185. https://doi.org/10.1007/BF00418866
  2. B. Lubarsky and S. J Kaufman: Review of Experimental investigation of Liquid metal heat transfer, Report NACA TN 3336, 1995.
  3. R. N Lyon: Liquid Metal heat transfer coefficient, Chem. Eng. Progr., 47(1951), No. 2, pp. 75-79.
  4. B. C. Sakiadios: Boundary layer behaviour on continuous solid surfaces, American Institute of Chemical Engineers, 7(1961), pp. 26-28. https://doi.org/10.1002/aic.690070108
  5. L. E. Erickson, L.T. Fan, and V. G. Fox: Heat and mass transfer on a moving continuous moving surface, Industrial & Engineering Chemistry Fundamentals, 5(1966), pp. 19-25. https://doi.org/10.1021/i160017a004
  6. J. E. Danberg and K. S. Fansler: A nonsimilar moving wall boundary-layer problem, Quarterly of Applied Mathematics, 34(1979), pp. 305-309.
  7. P. S. Gupta and A. S. Gupta: Heat and mass transfer on a stretching sheet with suction or blowing, The Canadian Journal of Chemical Engineering, 55(1977), pp. 744-746. https://doi.org/10.1002/cjce.5450550619
  8. V. G. Fox, L. E. Erickson, and L.T. Fan: Heat and mass transfer on a moving continuous flat plate with suction or injection, American Institute of Chemical Engineers, 15(1969), pp. 327-333. https://doi.org/10.1002/aic.690150307
  9. K. R. Rajagopal, T. Y. Na, and A. S. Gupta: Flow of a viscoelastic fluid over a stretching sheet, RheologicaActa, 23(1984), pp. 213-215.
  10. W. C. Troy, E. A. Overman, II, G. B. Ermentrout, and J. P. Keener: Uniqueness of flow of a second order fluid past a stretching sheet, Quarterly of Applied Mathematics, 44(1987), pp. 753-755. https://doi.org/10.1090/qam/872826
  11. K. Vajravelu and T. Roper: Flow and heat transfer in a second grade fluid over a stretching sheet, International Journal of Non-Linear Mechanics, 34(1999), pp. 1031-1036. https://doi.org/10.1016/S0020-7462(98)00073-0
  12. K. Vajravel: Viscous flow over a nonlinearly stretching sheet, Applied Mathematics and Computation, 124(2001), pp. 281-288. https://doi.org/10.1016/S0096-3003(00)00062-X
  13. R. Cortell: 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, Chemical Engineering and Processing, 46(2007), pp. 721-728. https://doi.org/10.1016/j.cep.2006.09.008
  14. R. Cortell: Viscous flow and heat transfer over a nonlinearly stretching sheet, Applied Mathematics and Computation, 184(2007), pp. 864-873. https://doi.org/10.1016/j.amc.2006.06.077
  15. R. Cortell: Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, Physics Letters, Section A, 372(2008), pp. 631-636. https://doi.org/10.1016/j.physleta.2007.08.005
  16. D. A Nield and A. Bejan: Convection in Porous Media, 2nd Edition, Springer, New York, 2009.
  17. K. Vafai: Handbook of Porous Media, Marcel Dekker, New York, 2000.
  18. I. Pop and D. B Ingham: Convective Heat Transfer. Elsevier, UK, 2001.
  19. E.M.A. Elbashbesh: Free convection flow with variable viscosity and thermal diffusivity along a vertical plate in the presence of magnetic field, International Journal of Engineering Science, 38(2000), pp. 207-213. https://doi.org/10.1016/S0020-7225(99)00021-X
  20. A. Raptis and C. Perdikis: Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field, International Journal of Non-Linear Mechanics, 41(2006), pp. 527-529. https://doi.org/10.1016/j.ijnonlinmec.2005.12.003
  21. S. Awang Kechil and I. Hashim: Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field, Physics Letters, Section A, 372(2008) pp. 2258-2263. https://doi.org/10.1016/j.physleta.2007.11.027
  22. Z. Abbas and T. Hayat: Radiation effects on MHD flow in a porous space, International Journal of Heat and Mass Transfer, 51(2008), pp. 1024-1033. https://doi.org/10.1016/j.ijheatmasstransfer.2007.05.031
  23. E. M. Ouaf Mahmoud: Exact solution of thermal radiation on MHD flow over a stretching porous sheet, Applied Mathematics and Computation., 170(2005), pp. 1117-1125. https://doi.org/10.1016/j.amc.2005.01.010
  24. S. Mukhopadhyay, G. C. Layek and R. S. R. Gorla: MHD combined convective flow and heat transfer past a porous stretching surface, International Journal of Fluid Mechanics Research, 34(2007), pp. 244-257. https://doi.org/10.1615/InterJFluidMechRes.v34.i3.40
  25. A.D.M Gururaj and C. Pavithra: Nonlinear MHD boundary layer of a liquid metal with heat transfer over a porous stretching surface with nonlinear radiation effects, Advances in Applied Science Research, 4(2013), No. 2, pp. 77-92.
  26. S. P Anjali Devi and A. D. M. Gururaj: Effects of variable viscosity and nonlinear radiation on MHD flow with heat transfer over a surface with a power-law velocity, Advances in Applied Science Research, 3(2012), pp. 319-334.
  27. M.A. Samad, M. Mohebujjaman: MHD heat and mass transfer free convection flow along a vertical stretching sheet in presence of magnetic field with heat generation, Res. J. of Appl. Sc., Engg. and Technology, 1(2009) , pp. 98-106.
  28. A. K Singh: MHD free convection and mass transfer flow with heat source and thermal diffusion, Journal of Energy Heat and Mass Transfer, 23(2001), pp. 167-178.
  29. D. ChKesavaiah, P. V Satyanarayana and S. Venkataramana: Effects of the chemical reaction and radiation absorption on unsteady MHD convective heat and mass transfer flow past a semi-infinite vertical permeable moving plate embedded in porous medium with heat source and suction, Int. J. of Appl. Math and Mech., 7(2011), pp52-69.
  30. S Mohammed Ibrahim and N Bhaskar Reddy: Radiation and mass transfer effects on MHD free convection flow along a stretching surface with viscous dissipation and heat generation, Int. J. of Appl. Math and Mech. 8(2011), pp. 1-21.
  31. M.A Samad and M Mobebujjama: MHD heat and mass transfer free convection flow along a vertical stretching sheet in presence of magnetic field with heat generation, Research Journal of Applied Sciences, Engineering and Technology, 1(2009),pp.98-106.
  32. T. C. Chaim: Hydromagnetic flow over a surface stretching with a power law velocity, International Jour- nal of Engineering Science, 33(1995), pp. 429-435. https://doi.org/10.1016/0020-7225(94)00066-S
  33. M. E. Ali: Heat transfer characteristics of a continuous stretching surface, Heat and Mass Transfer, 29(1994), pp. 227-234.
  34. Michael Modest: Radiative Heat Transfer, 2nd ed. McGraw-Hill, New York, 2003.
  35. M. A. Hossain and I Pop: Effect of heat transfer on compressible boundary layer flow past a sphere, Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), 79(1999), pp. 715-720. https://doi.org/10.1002/(SICI)1521-4001(199910)79:10<715::AID-ZAMM715>3.0.CO;2-K
  36. M. K Jain., S. R. K Iyengar and R. K Jain: Numerical methods for scientific and engineering computations, Wiley Eastern Ltd., New Delhi, India, 1985.

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