International Scientific Journal

External Links


In this article unsteady three dimensional MHD boundary layer flow and heat transfer analysis with constant temperature (CT) and constant heat flux (CH) in a porous medium is considered. The boundary layer flow is governed by a bidirectional stretching sheet. Similarity transformations are used to transform the governing non-linear partial differential equations to ordinary differential equations. Analytical solutions are constructed using homotopy analysis method (HAM). Convergence analysis is also presented through tabular data. The quantities of interest are the velocity, temperature, skin friction coefficient and Nusselt number. The obtained results are validated by comparisons with previously published work in special cases. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed.
PAPER REVISED: 2014-07-16
PAPER ACCEPTED: 2014-07-29
CITATION EXPORT: view in browser or download as text file
  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. Vleggaar, J., Laminar boundary layer behaviour on continuous accelerating surface, Chem. Eng. Sci., 32, (1977), pp. 1517-1525
  5. 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
  6. Crane, L., Flow past a stretching plate, Z. Angew Math. Phys., 19, (1970), pp. 744-746
  7. Banks, W. H. H., Similarity solutions of the boundary layer equations for a stretching wall, J. Mech. Theor. Appl., 2, (1983), pp. 375-392
  8. Abbasbandy, S., The application of homotopy analysis method to non-linear equation arising in heat transfer, Phys. Lett. A, 360, (2006), pp. 109-113
  9. Ahmad I., Ahmed M., Abbas Z., Sajid M., Hydromagnetic flow and heat transfer over a bidirectional stretching surface in a porous medium, Thermal Sciences, 15, (2011), pp. 205-220
  10. Wang, C. Y., The three dimensional flow due to stretching surface, Phys. Fluids, 27, (1989), pp. 1915-1917
  11. Ko, T. H., Ting, K., Optimal Reynolds number for the fully developed laminar forced convection in a helical coiled tube, Energy, 31, (2006), pp. 2142-2152.
  12. Hajmohammadi, M. R., Eskandari, H., Saffar-Avval, M., Campo, A., A new configuration of bend tubes for compound optimization of heat and fluid flow, Energy 62, (2013), pp. 418-424.
  13. Hajmohammadi, M. R., Salimpour, M. R., Saber, M., Campo, A., Detailed analysis for the cooling performance enhancement of a heat source under a thick plate, Ener. Con. Manag. 76, (2013), pp. 691-700
  14. Jiang, L., Ling, J., Jiang, L., Tang, Y., Li, Y., Zhou, W., Gao, J., Thermal performance of a novel porous crack composite wick heat pipe, Ener. Con. Manag. 81, (2014), pp. 10-18
  15. Hajmohammadi, M. R., Moulod, M., Shariatzadeh, O. J., Campo, A., Effect of a thick plate on the excess temperature of iso-heat flux heat sources cooled by laminar forced convection flow; Conjugate analysis, Numer. Heat Transf. A 66, (2014), pp. 205-216
  16. Lesage, F. J., Sempels, E. V., Bertrand, N. L., A study on heat transfer enhancement using flow channel inserts for thermoelectric power generation, Ener. Con. Manag. 75, (2013), pp. 532-541
  17. Wang, J., Wu, C., Li, K., Heat transfer enhancement through control of added perturbation velocity in flow field, Ener. Con. Manag. 70, (2013), pp. 194-201
  18. Pouzesh, A., Hajmohammadi, M. R., Poozesh, S., Investigations on the internal shape of constructal cavities intruding a heat generating body, Ther. Sci., DOI: 10.2298/TSCI120427164P 2012
  19. Hajmohammadi, M. R., Moulod, M., Shariatzadeh, O. J., Nourazar, S. S., New methods to cope with temperature elevations in heated segments of flat plates cooled by boundary layer flow, Ther. Sci., DOI: 10.2298/TSCI130128159H
  20. Hajmohammadi, M. R., Rahmani, M., Campo, A., Shariatzadeh, O. J., Optimal design of unequal heat flux elements for optimized heat transfer inside a rectangular duct, Energy 68, (2014), pp. 609-616
  21. Hajmohammadi, M. R., Campo, A., Nourazar, S. S., Ostad, A. M., Improvement of forced convection cooling due to the attachment of heat sources to a conducting thick plate, ASME J. Heat Transf. 135, (2013), pp. 124504-1
  22. Hajmohammadi, M. R., Nourazar, S. S., Conjugate forced convection heat transfer from a heated flat plate of finite thickness and temperature-dependent thermal conductivity, Heat Transf. Eng. 35, (2014), pp. 863-874
  23. Hajmohammadi, M. R., Nourazar, S. S., On the insertion of a thin gas layer in micro cylindrical Couette flows involving power-law liquids, Int. J. Heat Mass Transf. 75, (2014), pp. 97-108
  24. Dessie, H., Kishan, N., MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink, Ain Shams Eng. J. (in press)
  25. Rashad, A. M., Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium, J. Egyp. Math. Soc. 22, (2014), pp. 134-142
  26. Nadeem, S., Haq, R. U., Akbar, N. S., Khan, Z. H., MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet, Alex. Eng. J. 52, (2013), pp. 577-582
  27. Pahlavan, A. A., Aliakbar, V., Farahani, F. V., Sadeghy, K., MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method, Commun. Nonlinear Sci. Numer. Simul. 14, (2009), pp. 473-488
  28. Aly, E. H., Vajravelu, K., Exact and numerical solutions of MHD nano boundary-layer flows over stretching surfaces in a porous medium, Appl. Math. Comput. 232, (2014), pp. 191-204
  29. Cortell, R., 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, Chem. Eng. Proces.: Process Intensification 46, (2007), pp. 721-728
  30. Turkyilmazoglu, M., The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface, Int. J. Mech. Sci. 77, (2013), pp. 263-268
  31. Ariel, P. D., Generalized three dimensional flow due to stretching surface. Z. Angew. Math. Mech., 83, (2003), pp. 844-852
  32. Abdullah, I. A., Analytic solution of heat and mass transfer over a permeable stretching plate, Thermal Sciences, 13, (2009), pp. 183-197
  33. Liu, I. C, Andersson, H. I., Heat transfer over a bidirectional stretching sheet with variable thermal conditions, Int. J. Heat Mass Transfer, 51, (2008), pp. 4018-4024
  34. Ahmad, I, Sajid, M., Awan, W., Rafique, M., Aziz, W., Ahmed, M., Abbasi, A., Taj, M., MHD flow of a viscous fluid over an exponentially stretching sheet in a porous medium, J. Appl. Math., 2014, (2014), pp. 256761
  35. Nazar, R., Amin, N., Pop, I., Unsteady boundary layer flow due to stretching surface in a rotating fluid, Mech. Res. Commun., 31, (2009), pp. 121-128
  36. Liao, S. J., An analytic solution of unsteady boundary layer flows caused by an impulsively stretching plate, Commun. Non-linear Sci, Num. Simulation, 11, (2006), pp. 326-339
  37. Hayat, T., Mustafa, M., Asghar, S., Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction, Non Linear Analysis Real World Application, 11, (2010), pp. 3186-3199
  38. Elbashbeshy, E. M. A., Basid, M. A. A., Heat transfer over an unsteady stretching surface, Heat and Mass Transfer, 41, (2004), pp. 1-4
  39. Ahmad, I., On unsteady boundary layer flow of a second grade fluid over a stretching sheet, Add. Theor. Appl. Mech., 6, (2013), pp. 95-105.
  40. Mukhopadhyay, S., Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous medium, Int. J. Heat Mass Transf., 52, (2009), pp. 3261-3265
  41. Seshadri, R., Sreeshlan, N., Noth, G., Unsteady three dimensional stagnation point flow of a viscoelastic fluid, Int. J. Eng. Sci., 35, (1997), pp. 445-454
  42. Hayat, T., Mustafa, M., Hendi, A. A., Time dependent three dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet, App. Math. Mech., 32, (2011), pp. 167-178
  43. Liao, S. J., The proposed homotopy analysis method for the solution of nonlinear problems, PhD thesis, Shangai Jiao Tong University, China, 1992
  44. Liao, S. J., Beyond perturbation: Introduction to Homotopy Analysis Method, Chapman & Hall, CRC Press, Boca Raton 2003

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence