MHD flow of a viscous fluid over an exponentially stretching sheet in a porous medium. (English) Zbl 1437.76052

Summary: Radiation effects on magnetohydrodynamic (MHD) boundary-layer flow and heat transfer characteristic through a porous medium due to an exponentially stretching sheet have been studied. Formulation of the problem is based upon the variable thermal conductivity. The heat transfer analysis is carried out for both prescribed surface temperature (PST) and prescribed heat flux (PHF) cases. The developed system of nonlinear coupled partial differential equations is transformed to nonlinear coupled ordinary differential equations by using similarity transformations. The series solutions for the transformed of the transformed flow and heat transfer problem were constructed by homotopy analysis method (HAM). The obtained results are analyzed under the influence of various physical parameters.


76W05 Magnetohydrodynamics and electrohydrodynamics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76S05 Flows in porous media; filtration; seepage
80A21 Radiative heat transfer
Full Text: DOI


[1] Sakiadis, B. C., Boundary layer behaviour on continuous solid surfaces, AIChE Journal, 7, 1, 26-28 (1961)
[2] Sakiadis, B. C., Boundary layer behaviour on continuous solid surfaces: II, the boundary layer on a continuous flat surface, AIChE Journal, 17, 221-225 (1961)
[3] Crane, L. J., Flow past a stretching plate, Zeitschrift für Angewandte Mathematik und Physik, 21, 4, 645-647 (1970)
[4] Gupta, P. S.; Gupta, A. S., Heat and mass transfer on a stretching sheet with suction and blowing, The Canadian Journal of Chemical Engineering, 55, 6, 744-746 (1977)
[5] Brady, J. F.; Acrivos, A., Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow, Journal of Fluid Mechanics, 112, 127-150 (1981) · Zbl 0491.76037
[6] McLeod, J. B.; Rajagopal, K. R., On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary, Archive for Rational Mechanics and Analysis, 98, 4, 385-393 (1987) · Zbl 0631.76021
[7] Wang, C. Y., The three-dimensional flow due to a stretching flat surface, Physics of Fluids, 27, 8, 1915-1917 (1984) · Zbl 0545.76033
[8] Wang, C. Y., Fluid flow due to a stretching cylinder, Physics of Fluids, 31, 466-468 (1988)
[9] Cortell, R., Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing, Fluid Dynamics Research, 37, 4, 231-245 (2005) · Zbl 1153.76423
[10] Cortell, R., A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Applied Mathematics and Computation, 168, 1, 557-566 (2005) · Zbl 1081.76059
[11] Liao, S.-J., On the analytic solution of magnetohydrodynamic flows of Non-Newtonian fluids over a stretching sheet, Journal of Fluid Mechanics, 488, 189-212 (2003) · Zbl 1063.76671
[12] Ariel, P. D.; Hayat, T.; Asghar, S., The flow of an elastico-viscous fluid past a stretching sheet with partial slip, Acta Mechanica, 187, 1-4, 29-35 (2006) · Zbl 1103.76010
[13] Ariel, P. D., Axisymmetric flow of a second grade fluid past a stretching sheet, International Journal of Engineering Science, 39, 5, 529-553 (2001) · Zbl 1210.76127
[14] Hayat, T.; Sajid, M., Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, International Journal of Heat and Mass Transfer, 50, 1-2, 75-84 (2007) · Zbl 1104.80006
[15] Vajravelu, K., Flow and heat transfer in a saturated porous medium, Zeitschrift für angewandte Mathematik und Mechanik, 74, 605-614 (1994) · Zbl 0821.76078
[16] Magyari, E.; Keller, B., Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface, Journal of Physics D: Applied Physics, 32, 5, 577-585 (1999)
[17] Elbashbeshy, E. M. A., Heat transfer over an exponentially stretching continuous surface with suction, Archives of Mechanics, 53, 6, 643-651 (2001)
[18] Khan, S. K., Boundary layer vicoelastic flow over an exponential stretching sheet, International Journal of Applied Mechanics and Engineering, 11, 321-335 (2006)
[19] Raptis, A.; Perdikis, C.; Takhar, H. S., Effect of thermal radiation on MHD flow, Applied Mathematics and Computation, 153, 3, 645-649 (2004) · Zbl 1050.76061
[20] Chen, C.-H., On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation, internal heat source and thermal radiation, International Journal of Heat and Mass Transfer, 53, 19-20, 4264-4273 (2010) · Zbl 1194.80014
[21] Sajid, M.; Hayat, T., Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet, International Communications in Heat and Mass Transfer, 35, 3, 347-356 (2008)
[22] Chiam, T. C., Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet, International Communications in Heat and Mass Transfer, 23, 2, 239-248 (1996)
[23] Chiam, T. C., Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet, Acta Mechanica, 129, 1-2, 63-72 (1998)
[24] Liao, S. J., The proposed homotopy anslysis technique for the solution of non-linear problems [Ph.D. thesis] (1992), Shanghai Jiao Tong University
[25] Liao, S. J., Beyond Perturbation: Introduction to Homotopy Analysis Method (2003), Boca Raton, Fla, USA: Chapman & Hall/CRC, Boca Raton, Fla, USA
[26] Liao, S., A new branch of solutions of boundary-layer flows over an impermeable stretched plate, International Journal of Heat and Mass Transfer, 48, 12, 2529-2539 (2005) · Zbl 1189.76142
[27] Liao, S. J., An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Communications in Nonlinear Science and Numerical Simulation, 11, 3, 326-339 (2006) · Zbl 1078.76022
[28] Sajid, M.; Hayat, T.; Asghar, S., On the analytic solution of the steady flow of a fourth grade fluid, Physics Letters A: General, Atomic and Solid State Physics, 355, 1, 18-26 (2006)
[29] Abbas, Z.; Sajid, M.; Hayat, T., MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel, Theoretical and Computational Fluid Dynamics, 20, 4, 229-238 (2006) · Zbl 1109.76065
[30] Abbasbandy, S., The application of homotopy analysis method to nonlinear equations arising in heat transfer, Physics Letters A, 360, 1, 109-113 (2006) · Zbl 1236.80010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.