Three-dimensional flow of a magnetohydrodynamic Casson fluid over an unsteady stretching sheet embedded into a porous medium. (English. Russian original) Zbl 1345.76115
J. Appl. Mech. Tech. Phys. 57, No. 2, 283-292 (2016); translation from Prikl. Mekh. Tekh. Fiz. 57, No. 2, 105-116 (2016).
Summary: A three-dimensional flow of a magnetohydrodynamic Casson fluid over an unsteady stretching surface placed into a porous medium is examined. Similarity transformations are used to convert time-dependent partial differential equations into nonlinear ordinary differential equations. The transformed equations are then solved analytically by the homotopy analysis method and numerically by the shooting technique combined with the Runge-Kutta-Fehlberg method. The results obtained by both methods are compared with available reported data. The effects of the Casson fluid parameter, magnetic field parameter, and unsteadiness parameter on the velocity and local skin friction coefficients are discussed in detail.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76A05 | Non-Newtonian fluids |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76S05 | Flows in porous media; filtration; seepage |
References:
| [1] | L. J. Crane, “Flow Past a Stretching Sheet,” Z. Angew. Math. Phys. 21, 645-647 (1970). · doi:10.1007/BF01587695 |
| [2] | P. S. Gupta and A. S. Gupta, “Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing,” Canad. J. Chem. Eng. 55, 744-746 (1977). · doi:10.1002/cjce.5450550619 |
| [3] | W. H. H. Banks, “Similarity Solutions of the Boundary Layer Equation for a Stretching Wall,” J. Mech. Theor. Appl. 2, 375-392 (1983). · Zbl 0538.76039 |
| [4] | B. K. Dutta, P. Roy, and A. S. Gupta, “Temperature Field in Flow over a Stretching Sheet with Uniform Heat Flux,” Int. Comm. Heat Mass Transfer 28, 1234-1237 (1985). · doi:10.1016/0017-9310(85)90132-2 |
| [5] | J. Grubka and K. M. Bobba, “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature,” Trans. ASME, J. Heat Transfer 107, 248-250 (1985). · doi:10.1115/1.3247387 |
| [6] | M. E. Ali, “On Thermal Boundary Layer on a Power Law Stretched Surface with Suction or Injection,” Int. J. Heat Mass Flow 16, 280-290 (1995). · doi:10.1016/0142-727X(95)00001-7 |
| [7] | E. M. A. Elbashbeshy, “Heat Transfer over a Stretching Surface with Variable Heat Flux,” J. Phys. D. Appl. Phys. 31, 1951-1955 (1998). · doi:10.1088/0022-3727/31/16/002 |
| [8] | A. Sriramalu, N. Kishan, and R. J. Anand, “Steady Flow and Heat Transfer of a Viscous Incompressible Fluid Flow through Porous Medium over a Stretching Sheet,” J. Energy Heat Mass Transfer 23, 483-495 (2001). |
| [9] | 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,” Int. J. Eng. Sci. 38, 1303-1314 (2000). · Zbl 1210.76205 · doi:10.1016/S0020-7225(99)00079-8 |
| [10] | E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat Transfer in a Porous Medium over a Stretching Sheet with Internal Heat Generation and Suction or Injection,” Appl. Math. Comput. 158, 799-807 (2004). · Zbl 1098.76066 |
| [11] | I. C. Liu, “Flow and Heat Transfer of Viscous Fluid Saturated in PorousMedia over a Permeable Non-Isothermal Stretching Sheet,” Trans. Porous Media 64, 375-392 (2006). · doi:10.1007/s11242-005-5235-z |
| [12] | D. Pal, “Heat and Mass Transfer in Stagnation-Point Flow Towards a Stretching Surface in the Presence of Buoyancy Force and Thermal Radiation,” Meccanica 44, 145-158 (2009). · Zbl 1254.76069 · doi:10.1007/s11012-008-9155-1 |
| [13] | C. Y. Wang, “Liquid Film on an Unsteady Stretching Surface,” Quart. Appl. Math. 48, 1234-1237 (1990). |
| [14] | H. I. Andersson, J. B. Aarseth, N. Braud, and B. S. Dandapat, “Flow of a Power-Law Fluid on an Unsteady Stretching Surface,” J. Non-Newtonian Fluid Mech. 62, 1-8 (1996). · doi:10.1016/0377-0257(95)01392-X |
| [15] | I. C. Liu and H. I. Andersson, “Heat Transfer in a Liquid Film on an Unsteady Stretching Sheet,” Int. J. Therm. Sci. 47, 766-772 (2008). · doi:10.1016/j.ijthermalsci.2007.06.001 |
| [16] | C. H. Chen, “Heat Transfer in a Power-Law Fluid over an Unsteady Stretching Sheet,” Heat Mass Transfer 39, 791-796 (2007). · doi:10.1007/s00231-002-0363-2 |
| [17] | E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat Transfer over an Unsteady Stretching Surface,” Heat Mass Transfer 41, 1-4 (2004). · Zbl 1098.76066 · doi:10.1007/s00231-004-0520-x |
| [18] | A. Ishak, R. Nazar, and I. Pop, “Boundary Layer Flow and Heat Transfer over an Unsteady Stretching Vertical Surface,” Meccanica 44, 369-375 (2009). · Zbl 1241.76355 · doi:10.1007/s11012-008-9176-9 |
| [19] | M. A. E. Aziz, “Radiation Effect on the Flow and Heat Transfer over an Unsteady Stretching Sheet,” Int. Comm. Heat Mass Transfer 36, 521-524 (2009). · doi:10.1016/j.icheatmasstransfer.2009.01.016 |
| [20] | S. Shateyi and S. S. Motsa, “Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect,” Boundary Value Problems 2010 (2010); Article ID 257568; DOI: 10.1155/2010/257568. · Zbl 1195.76438 |
| [21] | D. Pal and P. S. Hiremath, “Computational Modelling of Heat Transfer over an Unsteady Stretching Surface Embedded in a Porous Medium”, Meccanica 45, 415-424 (2010). · Zbl 1258.76157 · doi:10.1007/s11012-009-9254-7 |
| [22] | D. Pal, “Hall Current and MHD Effects on Heat Transfer over an Unsteady Stretching Permeable Surface with Thermal Radiation,” Comput. Math. Appl. 66, 1161-1180 (2013). · Zbl 1381.76411 · doi:10.1016/j.camwa.2013.07.010 |
| [23] | S. Husnain, A. Mehmood, and A. Ali, “Heat and Mass Transfer Analysis in Unsteady Boundary Layer Flow through Porous Media with Variable Viscosity and Thermal Diffusivity,” J. Appl. Mech. Tech. Phys. 53 (5), 722-732 (2012). · Zbl 1298.76068 · doi:10.1134/S0021894412050112 |
| [24] | N. T. M. Eldabe and M. G. E. Salwa, “Heat Transfer of MHD Non-Newtonian Casson Fluid Flow between Two Rotating Cylinders,” J. Phys. Soc. Jpn. 64, 41-64 (1995). · doi:10.1143/JPSJ.64.4163 |
| [25] | J. Boyd, J. M. Buick, and S. Green, “Analysis of the Casson and Carreau-Yasuda non-Newtonian Blood Models in Steady and Oscillatory Flow using the Lattice Boltzmann Method,” Phys. Fluids 19, 93-103 (2007). · Zbl 1182.76081 |
| [26] | R. Bhargava, H. S. Takhar, S. Rawat, et al., “Finite Element Solutions for Non-Newtonian Pulsatile Flow in a Non-Darician Porous Medium Conduit,” Nonlinear Anal. Model. Control. 12, 317-327 (2007). · Zbl 1310.76088 |
| [27] | H. A. Attia and M. E. S. Ahmed, “Transient MHD Couette Flow of a Casson Fluid between Parallel Plates with Heat Transfer,” Italian J. Pure Appl. Math. 27, 19-38 (2010). · Zbl 1243.80004 |
| [28] | S. Mukhopadhyay, “Casson Fluid Flow and Heat Transfer over a Nonlinearly Stretching Surface,” Chinese Phys. B 27, 074701-074705 (2013). · doi:10.1088/1674-1056/22/7/074701 |
| [29] | S. K. Nandy, “Analytical Solution of MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet with Partial Slip,” ISRN. Thermodynamics 2013 (2013); Article ID 108264. · Zbl 1258.76157 |
| [30] | M. N. Tufail, A. S. Butt, and A. Ali, “Heat Source/Sink Effects on Non-Newtonian MHD Fluid Flow and Heat Transfer over a Permeable Stretching Surface: Lie Group Analysis,” Indian J. Phys. 88, 75-82 (2013); DOI: 10.1007/s12648-013-0376-3. · doi:10.1007/s12648-013-0376-3 |
| [31] | K. Vajravelu, S. Mukhopadhyay, and R. A. V. Gorder, “Casson Fluid Flow and Heat Transfer at an Exponentially Stretching Permeable Surface,” J. Appl. Mech. 80, 054502-054509 (2013). · doi:10.1115/1.4023618 |
| [32] | P. D. Ariel, “The Three-Dimensional Flow Past a Stretching Sheet and the Homotopy Perturbation Method,” Comput. Math. Appl. 54, 910-925 (2007). · Zbl 1138.76029 · doi:10.1016/j.camwa.2006.12.037 |
| [33] | M. Nakamura and T. Sawada, “Numerical Study on the Flow of a Non-Newtonian Fluid through an Axisymmetric Stenosis,” ASME, J. Biomech. Eng. 110, 137-143 (1988). · doi:10.1115/1.3108418 |
| [34] | C. Y. Wang, “The Three-Dimensional Flow due to Stretching Flat Surface,” Phys. Fluids 27, 1915-1917 (1984). · Zbl 0545.76033 · doi:10.1063/1.864868 |
| [35] | R. Kandasamy and I. Muhaimin, “Homotopy Analysis Method for Thermophoretic Particle Deposition Effect on Magnetohydrodynamic Mixed Convective Heat and Mass Transfer Past a Porous Wedge in the Presence of Suction,” J. Appl. Mech. Tech. Phys. 51 (2), 249-260 (2010). · Zbl 1272.76292 · doi:10.1007/s10808-010-0035-9 |
| [36] | H. Tabaei, M. A.Moghimi, A. Kimiaeifar, and M. A. Moghimi, “Homotopy Analysis and Differential Quadrature Solution of the Problem of Free-Convective Magnetohydrodynamic Flow over a Stretching Sheet with the Hall Effect and Mass Transfer Taken into Account,” J. Appl. Mech. Tech. Phys. 52 (4), 624-636 (2011). · Zbl 1272.76245 · doi:10.1134/S002189441104016X |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
