HYDROMAGNETIC FLOW AND HEAT TRANSFER ADJACENT TO A STRETCHING VERTICAL SHEET IN A MICROPOLAR FLUID

Abstract

An analysis is carried out for the steady two-dimensional mixed convection flow adjacent to a stretching vertical sheet immersed in an incompressible electrically conducting micropolar fluid. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the leading edge. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically using a finite difference scheme known as the Keller box method. The effects of magnetic and material parameters on the flow and heat transfer characteristics are discussed. It is found that the magnetic field reduces both the skin friction coefficient and the heat transfer rate at the surface for any given K and λ. Conversely, both of them increase as the material parameter increases for fixed values of M and λ.

Keywords

Dates

  • Submission Date2010-03-08
  • Revision Date2011-10-16
  • Acceptance Date2012-08-14

DOI Reference

10.2298/TSCI100308198Y

References

  1. Sakiadis, B. C., Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow, AIChE J., 7 (1961), pp. 26-28
  2. Sakiadis, B. C, Boundary-layer behavior on continuous solid surfaces: II. Boundary-layer equations on a continuous flat surface, AIChE J., 7 (1961), pp. 221-225
  3. Tsou, F. K, Sparrow, E. M., Goldstein, R. J., Flow and heat transfer in the boundary layer on a continuous moving surface, International Journal of Heat and Mass Transfer, 10 (1967), pp. 219-235
  4. Crane, L. J., Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, 21 (1970), pp. 645-647
  5. Dutta, B. K., Roy, P., Gupta, A. S., Temperature field in flow over a stretching sheet with uniform heat flux, International Communications Heat and Mass Transfer, 12 (1985), pp. 89-94
  6. Grubka, L. J., Bobba, K. M., Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME Journal of Heat Transfer, 107 (1985), pp. 248-250
  7. Chen, C. K., Char, M. I., Heat transfer of a continuous stretching surface with suction and blowing, Journal of Mathematical Analysis and Applications, 135 (1988), pp. 568-580
  8. Ali, M. E., On thermal boundary layer on a power law stretched surface with suction or injection, International Journal of Heat and Fluid Flow, 16 (1995), pp. 280-290
  9. Elbashbeshy, E.M.A., Heat transfer over a stretching surface with variable surface heat flux, Journal of Physics D: Applied Physics, 31 (1998), pp. 1951-1954
  10. Ishak, A., Nazar, R., Pop, I., Unsteady mixed convection boundary layer flow due to a stretching vertical surface, The Arabian Journal for Science and Engineering, 31 (2006), pp. 165-182
  11. Vajravelu, K., Hadjinicolaou, A., Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream, International Journal of Engineering Science, 35 (1997), pp. 1237-1244
  12. Chiam, T. C., Hydromagnetic flow over a surface stretching with a power-law velocity, International Journal of Engineering Science, 33 (1995), pp. 429-435
  13. Pop, I., Na, T. Y., A note on MHD flow over a stretching permeable surface, Mechanics Research Communications, 25 (1998), pp. 263-269
  14. Chamkha, A. J., Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption, International Journal of Heat and Fluid Flow, 20 (1999), 84-92
  15. Chandran, P., Sacheti, N. C., Singh, A. K., Hydromagnetic flow and heat transfer past a continuously moving porous boundary, International Communications Heat and Mass Transfer, 23 (1996), pp. 889-898
  16. Mukhopadhyay, S., Layek, G. C., Samad, Sk. A., Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity, International Journal of Heat and Mass Transfer, 48 (2005), pp. 4460-4466
  17. Ishak, A., Nazar, R., Pop, I., MHD boundary-layer flow due to a moving extensible surface, Journal of Engineering Mathematics, 62 (2008), pp. 23-33
  18. Chen, C.H., Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption, International Journal of Non-Linear Mechanics, 44 (2009), pp. 596-603
  19. Subhas Abel, M., Siddheshwar, P. G., Mahesha, N., Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source, International Journal of Non-Linear Mechanics, 44 (2009), pp. 1-12
  20. Eringen, A. C., Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16 (1966), pp. 1-18
  21. Eringen, A. C., Theory of thermomicropolar fluids, Journal of Mathematical Analysis and Applications, 38 (1972), pp. 480-496
  22. Ishak, A., Nazar, R., Pop, I., Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface, Canadian Journal of Physics 84 (2006). Pp. 399-410
  23. Ishak, A., Nazar, R., Pop, I., MHD boundary-layer flow of a micropolar fluid past a wedge with variable wall temperature, Acta Mechanica., 196 (2008), pp. 75-86
  24. Ishak, A., Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect, Meccanica, 45 (2010), pp. 367-373
  25. Ishak, A., Nazar, R., Pop, I., Stagnation flow of a micropolar fluid towards a vertical permeable surface, International Communications in Heat and Mass Transfer, 35 (2008), pp. 276-281
  26. Ishak, A., Nazar, R., Pop, I., Moving wedge and flat plate in a micropolar fluid, International Journal of Engineering Science, 44 (2006), pp. 1225-1236
  27. Yacob, N. A., Ishak, A., Pop, I., Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid, Computers & Fluids 47 (2011), pp. 16-21
  28. Rahman, M. M., Eltayeb, I. A., Mujibur Rahman, S. M., Thermo-micropolar fluid flow along a vertical permeable plate with uniform surface heat flux in the presence of heat generation, Thermal Science, 13 (2009), 1, pp. 23-36
  29. Rahman, M. M., Rahman, M. A., Samad, M. A., Alam, M. S., Heat transfer in micropolar fluid along a non-linear stretching sheet with temperature dependent viscosity and variable surface temperature, International Journal of Thermophysics, 30 (2009), 5, pp. 1649-1670
  30. Rahman, M. M., Al-Lawatia, M., Effects of higher order chemical reaction on micropolar fluid flow on a power law permeable stretched sheet with variable concentration in a porous medium, The Canadian Journal of Chemical Engineering, 88 (2010), pp. 23-32
  31. Lok, Y.Y., Pop, I., Ingham, D.B., Steady two-dimensional periodic motion of a micropolar fluid near an infinite array of moving walls, Journal of Applied Mathematics and Mechanics (ZAMM), 89 (2009), pp., 570-586
  32. Ariman, T., Turk, M.A., Sylvester, N.D., Microcontinuum fluid mechanics - a review, International Journal of Engineering. Science, 11 (1973), pp. 905-930
  33. Ariman, T., Turk, M.A., Sylvester, N.D., Application of microcontinuum fluid mechanics, International Journal of Engineering Science, 11 (11974), pp. 273-293
  34. Łukaszewicz, G., Micropolar Fluids: Theory and Application, Birkhauser, Basel, 1999
  35. Eringen, A.C., Microcontinuum Field Theories. II: Fluent Media, Springer, New York, 2001
  36. Rahman, M. M., and Sattar, M. A., MHD convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption, ASME Journal of Heat Transfer, 128 (2006), 2, pp. 142-152
  37. Eldabe, N. T., Ouaf, M. E. M., Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation, Applied Mathematics and Computation., 177 (2006), pp. 561-571
  38. Chen, C. H., Effects of magnetic field and suction/injection on convective heat transfer of non-Newtonian power-law fluids past a power-law stretched sheet with surface heat flux, International Journal of Thermal Sciences, 47 (2008), pp. 954-961
  39. Ishak, A., Jafar, K., Nazar, R., Pop, I., MHD stagnation point flow towards a stretching sheet, Physica A, 388 (2009), pp. 3377-3383
  40. Nazar, R., Amin, N., Filip, D., Pop, I., Stagnation point flow of a micropolar fluid towards a stretching sheet, International Journal of Non-Linear Mechanics,39 (2004), pp. 1227-1235
  41. Ahmadi, G., Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, International Journal of Engineering Science, 14 (1976), pp. 639-646
  42. Abramowitz, M., Stegun, I. A., Handbook of Mathematical Functions, Dover, New York, 1965.
  43. Cebeci, T., Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1988.
Volume 17, Issue 2, Pages525 -532