Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 804719, 27 pages
http://dx.doi.org/10.1155/2010/804719
Research Article

Thermal Radiation and MHD Effects on Free Convective Flow of a Polar Fluid through a Porous Medium in the Presence of Internal Heat Generation and Chemical Reaction

1Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
2Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia

Received 27 July 2010; Revised 20 October 2010; Accepted 19 November 2010

Academic Editor: Saad A. Ragab

Copyright © 2010 R. A. Mohamed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. U. N. Das, R. Deka, and V. M. Soundalgekar, “Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction,” Forschung im Ingenieurwesen, vol. 60, no. 10, pp. 284–287, 1994. View at Google Scholar
  2. H. I. Andersson, O. R. Hansen, and B. Holmedal, “Diffusion of a chemically reactive species from a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 37, no. 4, pp. 659–664, 1994. View at Google Scholar · View at Scopus
  3. S. P. Anjali Devi and R. Kandasamy, “Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate,” Warme- und Stoffubertragung Zeitschrift, vol. 35, no. 6, pp. 465–467, 1999. View at Google Scholar · View at Scopus
  4. R. Muthucumaraswamy and P. Ganesan, “On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species,” Forschung im Ingenieurwesen, vol. 66, no. 1, pp. 17–23, 2000. View at Google Scholar · View at Scopus
  5. R. Muthucumaraswamy and P. Ganesan, “First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux,” Acta Mechanica, vol. 147, no. 1–4, pp. 45–57, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. R. Muthucumaraswamy, “Effects of suction on heat and mass transfer along a moving vertical surface in the presence of chemical reaction,” Forschung im Ingenieurwesen, vol. 67, no. 3, pp. 129–132, 2002. View at Publisher · View at Google Scholar
  7. R. Muthucumaraswamy, “Effects of a chemical reaction on a moving isothermal vertical surface with suction,” Acta Mechanica, vol. 155, no. 1-2, pp. 65–70, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Y. Ghaly and M. A. Seddeek, “Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate with temperature dependent viscosity,” Chaos, Solitons and Fractals, vol. 19, no. 1, pp. 61–70, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Kandasamy, K. Periasamy, and K. K. S. Prabhu, “Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection,” International Journal of Heat and Mass Transfer, vol. 48, no. 7, pp. 1388–1394, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Kandasamy, K. Periasamy, and K. K. Sivagnana Prabhu, “Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects,” International Journal of Heat and Mass Transfer, vol. 48, no. 21-22, pp. 4557–4561, 2005. View at Publisher · View at Google Scholar
  11. R. A. Mohamed, I. A. Abbas, and S. M. Abo-Dahab, “Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1385–1395, 2009. View at Publisher · View at Google Scholar
  12. K. Vajravelu and A. Hadjinicolaou, “Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation,” International Communications in Heat and Mass Transfer, vol. 20, no. 3, pp. 417–430, 1993. View at Google Scholar · View at Scopus
  13. A. J. Chamkha and I. Camille, “Effects of heat generation/absorption and thermophoresis on hydromagnetic flow with heat and mass transfer over a flat surface,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 10, no. 4, pp. 432–448, 2000. View at Google Scholar · View at Scopus
  14. A. J. Chamkha, “Effects of heat generation on g-jitter induced natural convection flow in a channel with isothermal or isoflux walls,” Heat and Mass Transfer, vol. 39, no. 7, pp. 553–560, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. M. A. El-Hakiem, “Natural convection in a micropolar fluid with thermal dispersion and internal heat generation,” International Communications in Heat and Mass Transfer, vol. 31, no. 8, pp. 1177–1186, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Bagai, “Effect of variable viscosity on free convection over a non-isothermal axisymmetric body in a porous medium with internal heat generation,” Acta Mechanica, vol. 169, no. 1–4, pp. 187–194, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. M. M. Molla, M. A. Hossain, and L. S. Yao, “Natural convection flow along a vertical wavy surface with uniform surface temperature in presence of heat generation/absorption,” International Journal of Thermal Sciences, vol. 43, no. 2, pp. 157–163, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. F. M. Hady, R. A. Mohamed, and A. Mahdy, “MHD free convection flow along a vertical wavy surface with heat generation or absorption effect,” International Communications in Heat and Mass Transfer, vol. 33, no. 10, pp. 1253–1263, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. M. M. Molla, M. A. Hossain, and M. C. Paul, “Natural convection flow from an isothermal horizontal circular cylinder in presence of heat generation,” International Journal of Engineering Science, vol. 44, no. 13-14, pp. 949–958, 2006. View at Publisher · View at Google Scholar
  20. A. J. Chamkha, A. F. Al-Mudhaf, and I. Pop, “Effect of heat generation or absorption on thermophoretic free convection boundary layer from a vertical flat plate embedded in a porous medium,” International Communications in Heat and Mass Transfer, vol. 33, no. 9, pp. 1096–1102, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. M. E. Ali, “The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation,” International Journal of Thermal Sciences, vol. 46, no. 2, pp. 157–163, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. P. M. Patil and P. S. Kulkarni, “Effects of chemical reaction on free convective flow of a polar fluid through a porous medium in the presence of internal heat generation,” International Journal of Thermal Sciences, vol. 47, no. 8, pp. 1043–1054, 2008. View at Publisher · View at Google Scholar
  23. V. M. Soundalgekar and H. S. Takhar, “MHD forced and free convection flow past a semi infinite plate,” AIAA Journal, pp. 457–458, 1977. View at Google Scholar
  24. E. L. Aero, A. N. Bulygin, and E. V. Kuvshinskiio, “Asymmetric hydromechanics,” Journal of Applied Mathematics and Mechanics, vol. 29, no. 2, pp. 333–346, 1965. View at Google Scholar · View at Scopus
  25. N. van D'ep, “Equations of a fluid boundary layer with couple stresses,” Journal of Applied Mathematics and Mechanics, vol. 32, no. 4, pp. 777–783, 1968. View at Google Scholar · View at Scopus
  26. G. Łukaszewicz, Micropolar Fluids: Theory and Applications, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston, Mass, USA, 1999.
  27. F. S. Ibrahim, I. A. Hassanien, and A. A. Bakr, “Unsteady magnetohydrodynamic micropolar fluid flow and heat transfer over a vertical porous plate through a porous medium in the presence of thermal and mass diffusion with a constant heat source,” Canadian Journal of Physics, vol. 82, no. 10, pp. 775–790, 2004. View at Publisher · View at Google Scholar · View at Scopus
  28. M. M. Rahman and M. A. Sattar, “Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption,” Journal of Heat Transfer, vol. 128, no. 2, pp. 142–152, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. J. Kim, “Unsteady MHD convection flow of polar fluids past a vertical moving porous plate in a porous medium,” International Journal of Heat and Mass Transfer, vol. 44, no. 15, pp. 2791–2799, 2001. View at Publisher · View at Google Scholar · View at Scopus
  30. K. A. Helmy, “MHD unsteady free convection flow past a vertical porous plate,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 78, no. 4, pp. 255–270, 1998. View at Google Scholar · View at Zentralblatt MATH
  31. A. Ogulu, “The influence of radiation absorption on unsteady free convection and mass transfer flow of a polar fluid in the presence of a uniform magnetic field,” International Journal of Heat and Mass Transfer, vol. 48, no. 23-24, pp. 5078–5080, 2005. View at Publisher · View at Google Scholar · View at Scopus
  32. S. P. Anjali Devi and R. Kandasamy, “Effects of chemical reaction, heat and mass transfer on MHD flow past a semi infinite plate,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 80, no. 10, pp. 697–701, 2000. View at Google Scholar · View at Scopus
  33. H. S. Takhar, A. J. Chamkha, and G. Nath, “Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species,” International Journal of Engineering Science, vol. 38, no. 12, pp. 1303–1314, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  34. 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, vol. 41, no. 4, pp. 527–529, 2006. View at Publisher · View at Google Scholar · View at Scopus
  35. M. A. Seddeek, “Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydromagnetic flow with heat and mass transfer over a heat surface,” Acta Mechanica, vol. 177, no. 1–4, pp. 1–18, 2005. View at Publisher · View at Google Scholar · View at Scopus
  36. R. C. Sharma and K. D. Thakur, “On couple-stress fluid heated from below in porous medium in hydromagnetics,” Czechoslovak Journal of Physics, vol. 50, no. 6, pp. 753–758, 2000. View at Google Scholar · View at Scopus
  37. V. Sharma and S. Sharma, “Thermosolutal convection of micropolar fluids in hydromagnetics in porous medium,” Indian Journal of Pure and Applied Mathematics, vol. 31, no. 10, pp. 1353–1367, 2000. View at Google Scholar · View at Scopus
  38. Y. J. Kim, “Heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium,” Transport in Porous Media, vol. 56, no. 1, pp. 17–37, 2004. View at Publisher · View at Google Scholar · View at Scopus
  39. A. Sunil, A. Sharma, P. K. Bharti, and R. G. Shandil, “Effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium,” International Journal of Engineering Science, vol. 44, no. 11-12, pp. 683–698, 2006. View at Publisher · View at Google Scholar · View at Scopus
  40. V. M. Soundalgekar, “Free convection effects on stokes problem for a vertical plate,” Journal of Heat Transfer, vol. 99, no. 3, pp. 499–501, 1977. View at Google Scholar · View at Scopus
  41. A. Raptis, “Flow of a micropolar fluid past a continuously moving plate by the presence of radiation,” International Journal of Heat and Mass Transfer, vol. 41, no. 18, pp. 2865–2866, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  42. Y. J. Kim and A. G. Fedorov, “Transient mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate,” International Journal of Heat and Mass Transfer, vol. 46, no. 10, pp. 1751–1758, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  43. H. A. M. El-Arabawy, “Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation,” International Journal of Heat and Mass Transfer, vol. 46, no. 8, pp. 1471–1477, 2003. View at Publisher · View at Google Scholar · View at Scopus
  44. M. A. Rahman and M. A. Sattar, “Transient convective flow of micropolar fluid past a continuously moving vertical porous plate in the presence of radiation,” International Journal of Applied Mechanics and Engineering, vol. 12, no. 2, pp. 497–513, 2007. View at Google Scholar
  45. E. M. Abo-Eldahab and A. F. Ghonaim, “Radiation effect on heat transfer of a micropolar fluid through a porous medium,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 500–510, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  46. A. Ogulu, “On the oscillating plate-temperature flow of a polar fluid past a vertical porous plate in the presence of couple stresses and radiation,” International Communications in Heat and Mass Transfer, vol. 32, no. 9, pp. 1231–1243, 2005. View at Publisher · View at Google Scholar · View at Scopus
  47. M. A. Rahman and T. Sultan, “Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium,” Nonlinear Analysis Modeling and Control, vol. 13, no. 1, pp. 71–87, 2008. View at Google Scholar
  48. R. A. Mohamed and S. M. Abo-Dahab, “Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation,” International Journal of Thermal Sciences, vol. 48, pp. 1800–1813, 2009. View at Google Scholar
  49. R. Bayron Bird, W. E. Strwart, and E. N. Lightfoot, Transfer Phenomena, John Wiley and Sons, New York, NY, USA, 1992.
  50. S. Whitakar, “Advances in theory of fluid motion in porous media,” Industrial and Engineering Chemistry, vol. 61, no. 12, pp. 14–28, 1969. View at Google Scholar
  51. E. M. Sparrow and R. D. Cess, Radiation Heat Transfer, chapters 7, 10 and 19, Hemisphere, Washington, DC, USA, 1978.