International Scientific Journal


In this study, we present a steady three-dimensional magnetohydrodynamic (MHD) flow and heat transfer characteristics of a viscous fluid due to a bidirectional stretching sheet in a porous medium. The heat transfer analysis has been carried out for two heating processes namely (i) the prescribed surface temperature (PST) and (ii) prescribed surface heat flux (PHF). In addition the heat transfer rate varies along the surface. The similarity solution of the governing boundary layer partial differential equations is developed by employing homotopy analysis method (HAM). The quantities of interest are velocity, temperature, skin-friction and wall heat flux. The results obtained are presented through graphs and tabular data. It is observed that both velocity and boundary layer thickness decreases by increasing the porosity and magnetic field. This shows that application of magnetic and porous medium cause a control on the boundary layer thickness. Moreover, the results are also compared with the existing values in the literature and found in excellent agreement.
PAPER REVISED: 2011-01-11
PAPER ACCEPTED: 2011-01-23
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THERMAL SCIENCE YEAR 2011, VOLUME 15, ISSUE Supplement 2, PAGES [S205 - S220]
  1. Sakiadis, B. C., Boundary layer behavior on continuous solid surface. I. Boundary layer equation for two-dimensional and axisymmetric flow, AIChE J. 7 (1961) pp. 26-28.
  2. Sakiadis, B. C., Boundary layer behavior on continuous solid surface. II. Boundary layer equations on continuous solid surface, AIChE J. 7 (1961) pp. 221-225.
  3. McCormack, P. D., Crane, L., Physical Fluid Dynamics Academic press, New York 1973
  4. Gupta, P. S., Gupta, A. S., Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng. 55 (1977) pp. 744-756.
  5. Cortell, R., Similarity solutions for flow and heat transfer in a viscoelastic fluid over a stretching sheet, Int. J. Non-Linear Mech.29 (1994) pp. 155-161.
  6. Vleggaar, J., Laminar boundary layer behaviour on continuous accelerating surface, Chem. Eng. Sci. 32 (1977) pp. 1517-1525.
  7. Dutta, B. K., Roy, P., Gupta. A. S., Temperature field in a flow over a stretching sheet with uniform heat flux, Int. Commun. Heat Mass Transfer 12 (1985) pp. 89-94.
  8. Magyari, E., Keller, B., Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls, Eur. J. Mech.B-Fluids 19 (2000) pp. 109-122.
  9. Crane, L., Flow past a stretching plate, Z. Angew Math. Phys. 19 (1970) pp. 744-746.
  10. Banks, W. H. H., Similarity solutions of the boundary layer equations for a stretching wall, J. Mech Theor. Appl. 2 (1983) pp. 375-392.
  11. Ali, M. E., Heat transfer characteristics of a continuous stretching surface, Warme Stoffubertag 29 (1944) pp. 227-234
  12. Hayat, T., Sajid, M., Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, Int. J. Heat Mass Transfer 50 (2007) pp. 75-84.
  13. Kumar, H., Radiation heat transfer with hydromagnetic flow and viscous dissipation over a stetching surface in the presence of variable heat flux, Thermal Science, 13 (2009) pp. 163-169.
  14. Wang, C. Y., The three dimensional flow due to stretching surface, Phys. Fluids 27 (1984) pp. 1915-1917.
  15. Laha, M. K. Gupta, P. S., Gupta, A. S., Heat transfer characteristics of the flow of an incompressible viscous fluid over a stretching sheet, Warme Stoffubertrag 24 (1989) pp. 151-153.
  16. Ariel P. D, Generalized three dimensional flow due to stretching surface. Z. Angew. Math. Mech . 83 (2003) pp. 844-852.
  17. Chung, I., Andersson, H.. I. , Heat transfer over a bidirectional stretching sheet with variable thermal conditions, Int. J. Heat Mass Transfer 51 (2008) pp. 4018-4024.
  18. Abdullah, I. A., Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, Dofour-Soret effect and Hall effect, Thermal Science, 13 (2009) pp. 183-197.
  19. Liao, S. J., Beyond perturbation: Introduction to Homotopy Analysis Method, chapman & Hall, Boca Raton, 2003.
  20. Liao, S. J., On the homotopy analysis method for nonlinear problems, Appl. Math. Comput. 147 (2004) pp. 499-513.
  21. Sajid, M., Hayat, T., Asghar, S., On the analytic solution of the steady flow of a fourth grade fluid, Phys. Lett. A 355 (2008) pp. 18-24.
  22. Abbas, Z., Sajid, M., Hayat, T., MHD boundary layer flow of an upper -convected Maxwell fluid in a channel Theor. Comput. Fluid. Dyn. 20 (2006) pp. 229-238.
  23. Liao, S. J., A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate, J. Fluid Mech. 385 (1999) pp. 101-128.
  24. Liao, S. J., Campo, A., Analytic solutions of the temperature distribution in Blasius viscous flow problems, J. Fluid Mech. 453 (2002) pp. 411-425.
  25. Cheng, J., Liao, S. J. and Pop, I., Analytic series solution for unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium, Transport in Porous Media, pp. 61(2005)365-379.
  26. Yang, C., Liao, S. J., On the explicit purely analytic solution of Von Karman swirling viscous flow, Comm. Non-linear Sci. Numer. Simm. 11 (2006) pp. 83-93.
  27. Abbasbandy, S., Homotopy analysis method for heat radiation equations, Int. Comm. Heat and Mass Transfer 34 (2007) pp. 380-387.
  28. Hayat, T., Sajid, M., Ayub, M., A note on series solution for generalized Couette flow, Comm. Non-linear Sci. Numer. Simm. 12 (2007) pp. 1481-1487.

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