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Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating

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Abstract

An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic parameter M, the viscosity/temperature parameter θ r , the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number are presented graphically and in tabulated form.

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References

  1. Sakiadis BC (1961) Boundary layer behavior on continuous solid surfaces: I. Boundary layer equations for two dimensional and axi-symmetric flow. AIChE J 7:26–28

    Article  Google Scholar 

  2. Sakiadis BC (1961) Boundary layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE J 7:221–225

    Article  Google Scholar 

  3. Tsou FK, Sparrow FK, Goldstein RJ (1967) Flow and heat transfer in the boundary layer on a continuous moving surface. Int J Heat Mass Transfer 10:219–223

    Article  Google Scholar 

  4. Erickson LE, Fan LT, Fox VG (1966) Heat and mass transfer on a moving continuous flat plate with suction or injection. Ind Eng Chem Fund 5:19–25

    Article  Google Scholar 

  5. Soundalgekar VM, Murthy TVR (1980) Heat transfer past a continuous moving plate with variable temperature. Warme Stoffubertragung 14:91–93

    Article  ADS  Google Scholar 

  6. Ishak A, Nazar R, Pop I (2006) Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 41(5):509–518

    Article  MATH  Google Scholar 

  7. Gebhart B, Pera L (1971) The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Int J Heat Mass Tranfer 14(12):2025–2050

    Article  MATH  Google Scholar 

  8. Pera L, Gebhart B (1973) Natural convection boundary layer flow over horizontal and slightly inclined surfaces. Int J Heat Mass Tranfer 16(6):1131–1136

    Article  Google Scholar 

  9. Chen TS, Yuh CF (1980) Combined heat and mass transfer in mixed convection along vertical and inclined plates. Int J Heat Mass Transfer 23:527–537

    Article  MATH  ADS  Google Scholar 

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

    Article  Google Scholar 

  11. Vajravelu K, Hadjinicolaou A (1997) Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream. Int J Eng Sci 35:1237–1244

    Article  MATH  Google Scholar 

  12. Chiam TC (1995) Hydromagnetic flow over a surface stretching with a power-law velocity. Int J Eng Sci 33:429–435

    Article  MATH  Google Scholar 

  13. Abo-Eldahab EM, Abd El-Aziz M (2004) Blowing/suction effect on hydromagnetic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation /absorption. Int J Therm Sci 43:709–719

    Article  Google Scholar 

  14. Abo-Eldahab EM, Abd El-Aziz M (2005) Flow and heat transfer in a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream. Appl Math Comput 162:881–899

    Article  MATH  MathSciNet  Google Scholar 

  15. Wang CY (1984) The three-dimensional flow due to a stretching flat surface. Phys Fluids 27(8):1915–1917

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Surma Devi CD, Takhar HS, Nath G (1996) Unsteady three-dimensional flow due to a stretching surface. Int J Heat Mass Transfer 29:1996–1999

    Article  Google Scholar 

  17. Lakshmisha KN, Venkateswaran S, Nath G (1988) Three dimensional unsteady flow with heat and mass transfer. J Heat Transfer 110:590–595

    Article  Google Scholar 

  18. Gorla RSR, Sidawi I (1994) Free convection on a vertical stretching surface with suction and blowing. Appl Sci Res 52:247–257

    Article  MATH  Google Scholar 

  19. Chamkha AJ (1999) Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption. Int J Heat Fluid Flow 20:84–92

    Article  Google Scholar 

  20. Abo-Eldahab EM (2005) Hydromagnetic three-dimentional flow over a stretching surface with heat and mass transfer. Heat Mass Transfer 41:734–743

    Article  ADS  Google Scholar 

  21. Abo-Eldahab EM, Abd El-Aziz M (2005) Hydromagnetic three-dimensional free convective heat transfer over a stretching surface embedded in a non-Darcian porous medium in the presence of heat generation or absorption. Can J Phys 83:739–751

    Article  ADS  Google Scholar 

  22. Gary J, Kassory DR, Tadjeran H, Zebib A (1982) The effect of significant viscosity variation on convective heat transport in water-saturated porous media. J Fluid Mech 117:233–249

    Article  MATH  ADS  Google Scholar 

  23. Mehta KN, Sood S (1992) Transient free convection flow with temperature dependent viscosity in a fluid saturated porous medium. Int J Eng Sci 30:1083–1087

    Article  MATH  Google Scholar 

  24. Kafoussius NG, Williams EW (1995) The effect of temperature-dependent viscosity on the free convective laminar boundary layer flow past a vertical isothermal flat plate. Acta Mechanica 110:123–137

    Article  Google Scholar 

  25. Kafoussius NG, Rees DAS, Daskalakis JE (1998) Numerical study of the combined free-forced convective laminar boundary layer flow past a vertical isothermal flat plate with temperature-dependent viscosity. Acta Mechanica 127:39–50

    Article  Google Scholar 

  26. Hossain MA, Khanafer K, Vafai K (2000) The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate. Int J Therm Sci 40:115–124

    Article  Google Scholar 

  27. Hossain MA, Takhar HS (1996) Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transfer 31:243–248

    ADS  Google Scholar 

  28. Hossain MA, Munir MS, Hafiz MZ, Takhar HS (2000) Flow of a viscous incompressible fluid with temperature dependent viscosity past a permeable wedge with uniform surface heat flux. Heat Mass Transfer 36(4):333–341

    Article  ADS  Google Scholar 

  29. Hady FM, Bakier AY, Gorla RSR (1996) Mixed convection boundary layer flow on a continuous flat plate with variable viscosity. Heat Mass Transfer 31: 169–172

    ADS  Google Scholar 

  30. Abo-Eldahab EM, Elgendy MS (2000) Radiation effect on convective heat transfer in an ellectically conducting fluid at a stretching surface with variable viscosity and uniform free stream. Physica Scripta 62:321–325

    Article  ADS  Google Scholar 

  31. Kays WM (1966) Convective Heat and Mass Transfer. McGraw-Hill, New York, p 362

    Google Scholar 

  32. Arunachalam M, Rajappa NR (1978) Thermal boundary layer in liquid metals with variable thermal conductivity. Appl Sci Res 34:179–187

    Article  MATH  Google Scholar 

  33. Chiam TC (1998) Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta Mechanica 129:63–72

    Article  MATH  Google Scholar 

  34. Abo-Eldahab EM (2004) The effect of temperature-dependent fluid properties on free convective flow along a semi-infinite vertical plate by the presence of radiation. Heat Mass Transfer 41:163–169

    ADS  Google Scholar 

  35. Abo-Eldahab EM, Abd El-Aziz M (2004) Hall current and Ohmic heating effects on mixed convection boundary layer flow of a micropolar fluid from a rotating cone with power-law variation in surface temperature. Int Comm Heat Mass Transfer 31(5):751–762

    Article  Google Scholar 

  36. Abo-Eldahab EM, Abd El-Aziz M (2005) Viscous dissipation and Joule heating effects on MHD-free con- vection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents. Appl Math Model 29:579–595

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  38. Slattery JC (1972) Momentum energy and mass transfer in continua. McGraw-Hill, New York

    Google Scholar 

  39. Schilichting H (1972) Boundary Layer Theory. McGraw-Hill, New York, p 266

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Helwan University, P.O. Box 11795, Cairo, Egypt

    Mohamed Abd El-Aziz

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  1. Mohamed Abd El-Aziz
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Correspondence to Mohamed Abd El-Aziz.

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Abd El-Aziz, M. Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating. Meccanica 42, 375–386 (2007). https://doi.org/10.1007/s11012-006-9051-5

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  • DOI: https://doi.org/10.1007/s11012-006-9051-5

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