RADIATIVE HEAT TRANSFER WITH HYDROMAGNETIC FLOW AND VISCOUS DISSIPATION OVER A STRETCHING SURFACE IN THE PRESENCE OF VARIABLE HEAT FLUX
Abstract
The boundary layer steady flow and heat transfer of a viscous incompressible fluid due to a stretching plate with viscous dissipation effect in the presence of a transverse magnetic field is studied. The equations of motion and heat transfer are reduced to non-linear ordinary differential equations and the exact solutions are obtained using properties of confluent hypergeometric function. It is assumed that the prescribed heat flux at the stretching porous wall varies as the square of the distance from origin. The effects of the various parameters entering into the problem on the velocity field and temperature distribution are discussed.
Dates
- Submission Date2008-04-16
- Revision Date2008-06-17
- Acceptance Date2008-06-12
References
- Sakiadis, B. C., Boundary Layer Behavior on Continuous Solid Surface, American Institute of Chemical Engineers Journal, 7 (1961), 1, pp. 26-28
- Erickson, L. E., Fan, L. T., Fox, V. G., Heat and Mass Transfer of a Moving Continuous Flat Plate with Suction or Injection, Ind. Engng. Chem. Fundam., 5 (1966), 1, pp. 19-25
- Gupta, P. S., Gupta, A. S., Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing, Canad. J. of Chem. Eng., 55 (1977), 6, pp. 744-746
- Crane, L. J., Flow Past a Stretching Plate, ZAMP, 21 (1970), 4, pp. 645-647
- Mc Cormack, P. D., Crane, L. J., Physical Fluid Dynamics, Academic Press, New York, USA, 1973
- McLeod, J. B., Rajagopal, K. R., On the Uniqueness of Flow of a Navier- Stokes Fluid Due to a Stretching Boundary, Arch. Rational Mech. Anal., 98 (1987), 4, pp. 385-393
- Troy, W. C., et al., Uniqueness of Flow of a Second Order Fluid Past a Stretching Surface, Q. Appl. Math., 44 (1987), 4, pp. 753-755
- Vleggaar, J., Laminar Boundary-Layer Behaviour on Continuous Accelerating Surfaces, Chem. Eng. Sci.,32 (1977), 12, pp. 1517-1525
- Soundalgekar, V. M., Murty, T. V. R., Heat Transfer Past a Continuous Moving Plate with Variable Temperature, Wärme- und Stoffübertragung, 14 (1980), 2, pp. 91-93
- Carragher, P., Crane, L., Heat Transfer on Continuous Stretching Sheet, ZAMM, 62 (1982), 10, pp. 564-565
- Dutta, B. K., Heat Transfer from a Stretching Sheet in a Viscous Flow with Suction or Blowing, ZAMM, 68 (1988), 6, pp. 231-236
- 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
- Afzal, N., Varshney, I. S., The Cooling of Low Heat Resistance Stretching Sheet Moving through a Fluid, Wärme- und Stoffübertragung, 14 (1980), 4, pp. 289-293
- Kuiken, H. K., On the Boundary Layer in Fluid Mechanics that Decay Algebraically Along Stretches on Wall that Are not Vanishingly Small, I. M. A. J. Appl. Math., 27 (1981), 4, pp. 387-405
- Banks, W. H. H., Similarity Solutions of the Boundary Layer Equations for Stretching Wall, J. Mec. Theo. Appl., 2 (1983), 3, pp. 375-392
- Banks, W. H. H., Zaturska, M. B., Eigen Solutions in Boundary-Layer Flow Adjacent to a Stretching Wall, I. M. A. J. Appl. Math., 36 (1986), 3, pp. 263-273
- Chiam, T. C., Hydromagnetic Flow Over a Surface Stretching with a Power Law Velocity, Int. J. Engng. Sci., 33 (1995), 3, pp. 429-435
- Abo-Eldahab, E. M., Salem, A. M., Hall Effect on MHD Free Convection Flow of a Non Newtonian Power Law Fluid at a Stretching Surface, Int. Comm. Heat Mass Transfer, 31 (2004), 3, pp. 343-354
- Shafie, S., Amin, N., Pop, I., Unsteady Boundary Layer Due to a Stretching Sheet in a Porous Medium Using Brinkman Equation Model, Int. J. of Heat and Technology, 24 (2006), 2, pp. 111-117
- Kechil, S. A., Hashim, I., Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate, Chinese Physics Letters, 24 (2007), 1, pp. 139-142
- Liao, S. J., Series Solutions of Unsteady Boundary-Layer Flows over a Stretching Flat Plate, Studies in Applied Mathematics, 117 (2006), 3, pp. 239-263
- Cess, R. D., Interaction of Thermal Radiation with Free Convection Heat Transfer, Int. J. Heat Mass Transfer, 9 (1966), 11, pp. 1269-1277
- Arpaci, V. S., Effects of Thermal Radiation on the Laminar Free Convection from a Heated Vertical Plate, Int. J. Heat Mass Transfer, 11 (1968), 11, pp. 871-881
- Cheng, E. H., Ozisik, M. N., Radiation with Free Convection in an Absorbing Emitting and Scattering Medium, Int. J. Heat Mass Transfer, 15 (1972), 6, pp. 1243-1252
- Hossain, M. A., Takhar, H. S., Radiation Effects on Mixed Convection along a Vertical Plate with Uniform Surface Temperature, Heat and Mass Transfer, 31 (1996), 4, pp. 243-248
- Hossain, M. A., Takhar, H. S., Radiation-Conduction Interaction in Mixed Convection along Rotating Bodies, Heat and Mass Transfer, 33 (1997), 3, pp. 201-208
- Hossain, M. A., Pop, I., Rees, D. A. S., Free Convection-Radiation Interaction from an Isothermal Plate Inclined at a Small Angle to the Horizontal, Acta Mechanica, 127 (1998), 1, pp. 63-73
- Ganeshan, P., Loganathan, P., Soundalgekar, V. M., Radiation Effects on Flow Past an Impulsively Started Infinite Vertical Plate, Int. J. of Applied Mechanics and Engineering, 6 (2001), 3, pp. 719-730
- Brewster, M. Q., Thermal Radiative Transfer and Properties, John Wiley and Sons Inc., New York, USA, 1992
- Rashad, A. M., Radiative Effect on Heat Transfer from a Stretching Surface in a Porous Medium, Int. J. of Appl. Math. and Mech., 3 (2007), 4, pp.14-23
- Abramowitz, M., Stegan, L. A., Handbook of Mathematical Functions, 55, National Bureau of Standards/ Amer. Math. Soc., Providence, RI, 1972
Volume
13,
Issue
2,
Pages163 -169