## THERMAL SCIENCE

International Scientific Journal

### PARTIAL SLIP AND THERMAL RADIATION EFFECTS ON HYDROMAGNETIC FLOW OVER AN EXPONENTIALLY STRETCHING SURFACE WITH SUCTION OR BLOWING

**ABSTRACT**

This paper is devoted to analyze computational simulation to study the partial slip and thermal radiation effects on the flow of a viscous incompressible electrically conducting fluid through an exponentially stretching surface with suction or blowing in presence of magnetic field. Using suitable similarity variables, the non-linear boundary-layer PDE are converted to ODE and solved numerically by Runge-Kutta fourth order method in association with shooting technique. Effects of suction or blowing parameter, velocity slip parameter, magnetic parameter, thermal slip parameter, thermal radiation parameter, Prandtl number, and Eckert number are demonstrated graphically on velocity and temperature profiles while skin friction coefficient and surface heat transfer rate are presented numerically. Moreover, comparison of numerical results for non-magnetic case is made with previously published work under limiting cases.

**KEYWORDS**

PAPER SUBMITTED: 2016-01-27

PAPER REVISED: 2016-06-17

PAPER ACCEPTED: 2016-06-22

PUBLISHED ONLINE: 2016-07-12

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**2**, PAGES [797 - 808]

- Crane, L. J., Flow Past a Stretching Plate, Z. Angew. Math. Phys., 21 (1970), 4, pp. 645-647
- Chakrabarti, A., Gupta, A. S., Hydromagnetic Flow and Heat Transfer over a Stretching Sheet, Q. Appl. Math. 37 (1979), 1, pp. 73-78
- Carragher, P., Crane, L. J., Heat Transfer on a Continuous Stretching Sheet, J. Appl. Math. Mech., 62 (1982), 10, pp. 564-565
- Kumaran, V., Ramanaiah, G., A Note on the Flow over a Stretching Sheet, Acta Mechanica, 116 (1996), 1-4, pp. 229-233
- Ishak, A., et al., Mixed Convection Boundary Layers in the Stagnation-Point Flow toward a Stretching Vertical Sheet, Meccanica, 41 (2006), 5, pp. 509-518
- Liu, I. C., Andersson, H. I., Heat Transfer in a Liquid Film on an Unsteady Stretching Sheet, Int. J. Therm. Sci., 47, (2008), 6, pp. 766-772
- Jat, R. N., Chaudhary, S., Magnetohydrodynamic Boundary Layer Flow near the Stagnation Point of a Stretching Sheet, Il Nuovo Cimento 123 B (2008), 5, pp. 555-566
- Sahoo, B., Do, Y., Effects of Slip on Sheet-Driven Flow and Heat Transfer of a Third Grade Fluid past a Stretching Sheet, Int. Commun. Heat Mass Transf., 37 (2010), 8, pp. 1064-1071
- Mahapatra, T. R., et al., Stability Analysis of the Dual Solutions for Stagnation-Point Flow over a Non-Linearly Stretching Surface, Meccanica, 47 (2012), 7, pp. 1623-1632
- Makinde, O. D., et al., Buoyancy Effects on MHD Stagnation Point Flow and Heat Transfer of a Nanofluid past a Convectively Heated Stretching/Shrinking Sheet, Int. J. Heat Mass Transf., 62 (2013), pp. 526-533
- Elbashbeshy, E. M. A., Heat Transfer over an Exponentially Stretching Continuous Surface with Suction, Arch. Mech. 53 (2001), 6, pp. 643-651
- Parhta, M. K., et al., Effect of Viscous Dissipation on the Mixed Convection Heat Transfer from an Exponentially Stretching Surface, Heat Mass Transf., 41 (2005), 4, pp. 360-366
- Sanjayanand, E., Khan, S. K., On Heat and Mass Transfer in a Viscoelastic Boundary Layer Flow over an Exponentially Stretching Sheet, Int. J. Therm. Sci. 45 (2006), 8, pp. 819-828
- Sajid, M., Hayat, T., Influence of Thermal Radiation on the Boundary Layer Flow Due to an Exponentially Stretching Sheet, Int. Commun. Heat Mass Transf., 35 (2008), 3, pp.347-356
- Bidin, B., Nazar, R., Numerical Solution of the Boundary Layer Flow over an Exponentially Stretching Sheet with Thermal Radiation, Eur. J. Sci. Res., 33 (2009), 4, pp. 710-717
- Nadeem, S., et al., Effects of Thermal Radiation on the Boundary Layer Flow of a Jeffrey Fluid over an Exponentially Stretching Surface, Numer. Algor.,57 (2011), 2, pp. 187-205
- Mukhopadhyay, S., Gorla, R. S. R., Effects of Partial Slip on Boundary Layer Flow past a Permeable Exponential Stretching Sheet in Presence of Thermal Radiation, Heat Mass Transf., 48 (2012), 10, pp. 1773-1781
- Raju, C. S. K., et al., Dual Solutions of MHD Boundary Layer Flow past an Exponentially Stretching Sheet with Non-Uniform Heat Source/Sink, J. Appl. Fluid Mech., 9 (2016), 2, pp. 555-563
- Hasimoto, H., Boundary-Layer Slip Solutions for a Flat Plate, J. Aeronaut. Sci., 25 (1958), 1, pp. 68-69
- Wang, C. Y., Stagnation Flows with Slip: Exact Solutions of the Navier-Stoke equations, Z. Angew. Math. Phys., 54 (2003), 1, pp. 184-189
- Ariel, P. D., Axisymmetric Flow Due to a Stretching Sheet with Partial Slip, Comput. Math. Appl., 54 (2007), 7-8, pp. 1169-1183
- Hron, J., et al., Flows of Incompressible Fluids Subject to Navier's Slip on the Boundary, Comput. Math. Appl. 56 (2008), 8, pp. 2128-2143
- Fang, T., et al., Viscous Flow over a Shrinking Sheet with a Second Order Slip Flow Model, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 7, pp. 1831-1842
- Sajid, M., et al., Stretching Flows with General Slip Boundary Condition, Int. J. Mod. Phys. B, 24 (2010), 30, pp. 5939-5947
- Das K., A Mathematical Model on Magnetohydrodynamic Slip Flow and Heat Transfer over a Non-Linear Stretching Sheet, Therm. Sci., 18 (2014), 2, pp. S475-S488
- Gupta, P. S., Gupta, A. S., Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing, Can. J. Chem. Engg., 55 (1977), 6, pp. 744-746
- Chen, C. K., Char, M. I., Heat Transfer of a Continuous, Stretching Surface with Suction or Blowing, J. Math. Anal. Appl., 135 (1988), 2, pp. 568-580
- Ali, M. E., On Thermal Boundary Layer on a Power-Law Stretched Surface with Suction or Injection, Int. J. Heat Fluid Flow, 16 (1995), 4, pp. 280-290
- Seddeek, M. A., Effects of Magnetic Field and Variable Viscosity on Forced Non-Darcy Flow about a Flat Plate with Variable Wall Temperature in Porous Media in the Presence of Suction and Blowing, J. Appl. Mech. Tech. Phys., 43 (2002), 1, pp. 13-17
- Pantokratoras, A., Laminar Free-Convection over a Vertical Isothermal Plate with Uniform Blowing or Suction in Water with Variable Physical Properties, Int. J. Heat Mass Transf., 45 (2002), 5, pp. 963-977
- 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 Dyn. Res., 37 (2005), 4, pp. 231-245
- Bestman, A. R., Adjepong, S. K., Unsteady Hydromagnetic Free-Convection Flow with Radiative Heat Transfer in a Rotating Fluid, Astrophys. Space Sci., 143 (1988), 1, pp. 73-80
- Naroua, H., et al., Finite Element Analysis of Natural Convection Flow in a Rotating Fluid with Radiative Heat Transfer, J. Magnetohydrodyn. Plasma Res., 7 (1998), 4, pp. 257-274
- Ouaf, M. E. M., Exact Solution of Thermal Radiation on MHD Flow over a Stretching Porous Sheet, Appl. Math. Comput., 170 (2005), 2, pp. 1117-1125
- Makinde, O. D., Ogulu, A., The Effect of Thermal Radiation on the Heat and Mass Transfer Flow of a Variable Viscosity Fluid past a Vertical Porous Plate Permeated by a Transverse Magnetic Field, Chem. Eng. Commun., 195 (2008), 12, pp. 1575-1584
- Pal, D., Mondal, H., Radiation Effects on Combined Convection over a Vertical Flat Plate Embedded in a Porous Medium of Variable Porosity, Meccanica, 44 (2009), 2, pp. 133-144
- Jat, R. N., Chaudhary, S., Radiation Effects on the MHD Flow near the Stagnation Point of a Stretching Sheet, Z. Angew. Math. Phys., 61 (2010), 6, pp. 1151-1154
- Elbashbeshy, E. M. A., Emam, T. G., Effects of Thermal Radiation and Heat Transfer over an Unsteady Stretching Surface Embedded in a Porous Medium in the Presence of Heat Source or Sink, Therm. Sci., 15 (2011), 5, pp. 477-485
- Khan, Y., et al., On the Study of Viscous Fluid due To Exponentially Shrinking Sheet in the Presence of Thermal Radiation, Therm. Sci., 19 (2015), 1, pp. S191-S196
- Chaudhary, S., et al., Effects of Thermal Radiation on Hydromagnetic Flow over an Unsteady Stretching Sheet Embedded in a Porous Medium in the Presence of Heat Source or Sink, Meccanica, 50 (2015), 8, pp. 1977-1987
- Sandeep N., et al., Unsteady MHD Radiative Flow and Heat Transfer of a Dusty Nanofluid over an Exponentially Stretching Surface, Engg. Sci. Tech., An Int. J., 19 (2016), 1, pp. 227-240
- Brewster, M. Q., Thermal Radiative Transfer and Properties, John Wiley and Sons Inc., New York, USA, 1992