MHD Slip Flow past a Shrinking Sheet
ABSTRACT
An analysis is made for the steady two-dimensional laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid near a stagnation point past a shrinking sheet with slip in the presence of a magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables and solved numerically by Shooting method. The effects of the various parameters such as velocity ratio parameter, slip parameter, Prandtl number, Eckert number and magnetic parameter for velocity and temperature distributions have been discussed in detail through graphical representation.
Cite this paper
S. Chaudhary and P. Kumar, "MHD Slip Flow past a Shrinking Sheet," Applied Mathematics, Vol. 4 No. 3, 2013, pp. 574-581. doi: 10.4236/am.2013.43081.
S. Chaudhary and P. Kumar, "MHD Slip Flow past a Shrinking Sheet," Applied Mathematics, Vol. 4 No. 3, 2013, pp. 574-581. doi: 10.4236/am.2013.43081.
References
[1] L. J. Crane, “Flow Past a Stretching Plate,” Zeitschrift für angewandte Mathematik und Physik, Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695 [2] C. K. Chen and M. I. Char, “Heat Transfer of a Continuous, Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, Vol. 135, No. 2, 1988, pp. 568-580. [3] T. C. Chiam, “Stagnation-Point Flow towards a Stretching Plate,” Journal of the Physical Society of Japan, Vol. 63, No. 6, 1994, pp. 2443-2444. doi:10.1143/JPSJ.63.2443 [4] H. I. Andersson, “Slip Flow Past a Stretching Surface,” Acta Mechanica, Vol. 158, No. 1-2, 2002, pp. 121-125. doi:10.1007/BF01463174 [5] P. D. Ariel, S. Hayat and S. Asghar, “The Flow of an Elastico-Viscous Fluid Past a Stretching Sheet with Partial Slip,” Acta Mechanica, Vol. 187, No. 1, 2006, pp. 29-35. doi:10.1007/s00707-006-0370-3 [6] R. N. Jat and S. Chaudhary, “MHD Stagnation Flows with Slip,” Il Nuovo Cimento, Vol. 122B, No. 8, 2007, pp. 823-831. [7] R. N. Jat and S. Chaudhary, “Magnetohydrodynamic Boundary Layer Flow near the Stagnation Point of a Stretching Sheet,” Il Nuovo Cimento, Vol. 123B, No. 5, 2008, pp. 555-566. [8] C. Y. Wang, “Stagnation Flow towards a Shrinking Sheet,” International Journal of Non-Linear Mechanics, Vol. 43, No. 5, 2008, pp. 377-382. doi:10.1016/j.ijnonlinmec.2007.12.021 [9] T. Fang, S. Yao, A. Zhang and A. Aziz, “Viscous Flow over a Shrinking Sheet with a Second Order Slip Flow Model,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 7, 2010, pp. 1831-1842. doi:10.1016/j.cnsns.2009.07.017 [10] S. Nadeem, A. Hussain and M. Khan, “HAM Solutions for Boundary Layer Flow in the Region of the Stagnation Point towards a Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 3, 2010, pp. 475-481. doi:10.1016/j.cnsns.2009.04.037 [11] K. Bhattacharyya and G. C. Layek, “Effects of Suction/ Blowing on Steady Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Shrinking Sheet with Thermal Radiation,” International Journal of Heat and Mass Transfer, Vol. 54, No. 1-3, 2011, pp. 302-307. doi:10.1016/j.ijheatmasstransfer.2010.09.043 [12] K. Bhattacharyya, S. Mukhopadhyay and G. C. Layek, “Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Shrinking Sheet,” International Journal of Heat and Mass Transfer, Vol. 54, No. 1, 2011, pp. 308-313. doi:10.1016/j.ijheatmasstransfer.2010.09.041
[1] L. J. Crane, “Flow Past a Stretching Plate,” Zeitschrift für angewandte Mathematik und Physik, Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695 [2] C. K. Chen and M. I. Char, “Heat Transfer of a Continuous, Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, Vol. 135, No. 2, 1988, pp. 568-580. [3] T. C. Chiam, “Stagnation-Point Flow towards a Stretching Plate,” Journal of the Physical Society of Japan, Vol. 63, No. 6, 1994, pp. 2443-2444. doi:10.1143/JPSJ.63.2443 [4] H. I. Andersson, “Slip Flow Past a Stretching Surface,” Acta Mechanica, Vol. 158, No. 1-2, 2002, pp. 121-125. doi:10.1007/BF01463174 [5] P. D. Ariel, S. Hayat and S. Asghar, “The Flow of an Elastico-Viscous Fluid Past a Stretching Sheet with Partial Slip,” Acta Mechanica, Vol. 187, No. 1, 2006, pp. 29-35. doi:10.1007/s00707-006-0370-3 [6] R. N. Jat and S. Chaudhary, “MHD Stagnation Flows with Slip,” Il Nuovo Cimento, Vol. 122B, No. 8, 2007, pp. 823-831. [7] R. N. Jat and S. Chaudhary, “Magnetohydrodynamic Boundary Layer Flow near the Stagnation Point of a Stretching Sheet,” Il Nuovo Cimento, Vol. 123B, No. 5, 2008, pp. 555-566. [8] C. Y. Wang, “Stagnation Flow towards a Shrinking Sheet,” International Journal of Non-Linear Mechanics, Vol. 43, No. 5, 2008, pp. 377-382. doi:10.1016/j.ijnonlinmec.2007.12.021 [9] T. Fang, S. Yao, A. Zhang and A. Aziz, “Viscous Flow over a Shrinking Sheet with a Second Order Slip Flow Model,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 7, 2010, pp. 1831-1842. doi:10.1016/j.cnsns.2009.07.017 [10] S. Nadeem, A. Hussain and M. Khan, “HAM Solutions for Boundary Layer Flow in the Region of the Stagnation Point towards a Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 3, 2010, pp. 475-481. doi:10.1016/j.cnsns.2009.04.037 [11] K. Bhattacharyya and G. C. Layek, “Effects of Suction/ Blowing on Steady Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Shrinking Sheet with Thermal Radiation,” International Journal of Heat and Mass Transfer, Vol. 54, No. 1-3, 2011, pp. 302-307. doi:10.1016/j.ijheatmasstransfer.2010.09.043 [12] K. Bhattacharyya, S. Mukhopadhyay and G. C. Layek, “Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Shrinking Sheet,” International Journal of Heat and Mass Transfer, Vol. 54, No. 1, 2011, pp. 308-313. doi:10.1016/j.ijheatmasstransfer.2010.09.041