Journal of Applied Mathematics

Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature

M. A. Abd El-Naby, Elsayed M. E. Elbarbary, and Nader Y. Abdelazem

Full-text: Open access

Abstract

An analysis is performed to study radiation effects on magnetohydrodynamic (MHD) unsteady free-convection flow past a semi-infinite vertical plate with variable surface temperature in the presence of transversal uniform magnetic field. The boundary layer equations are transformed into a linear algebraic system by an implicit finite-difference method. A parametric study is performed to illustrate the influence of radiation parameter, magnetic parameter, and Prandtl number on the velocity and temperature profiles. The numerical results reveal that the radiation has significant influences on the velocity and temperature profiles, skin friction, and Nusselt number. The results indicate that the velocity, temperature, and local and average skin friction increase as the radiation parameter increases, while the local and average Nusselt numbers decrease as the radiation parameter increases.

Article information

Source
J. Appl. Math., Volume 2003, Number 2 (2003), 65-86.

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.jam/1049725709

Digital Object Identifier
doi:10.1155/S1110757X0320509X

Mathematical Reviews number (MathSciNet)
MR1980385

Zentralblatt MATH identifier
1064.76101

Subjects
Primary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects 76R10
Secondary: 76W05

Citation

Abd El-Naby, M. A.; Elbarbary, Elsayed M. E.; Abdelazem, Nader Y. Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature. J. Appl. Math. 2003 (2003), no. 2, 65--86. doi:10.1155/S1110757X0320509X. https://projecteuclid.org/euclid.jam/1049725709


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References

  • A. C. Cogley, W. G. Vincenti, and S. E. Gilles, Differential approximation for radiation transfer in a nongray near equilibrium, AIAA J. 6 (1968), 551--553.
  • E. M. A. Elbashbeshy, Radiation effect on heat transfer over a stretching surface, Canad. J. Phys. 78 (2000), 1107--1112.
  • P. Ganesan and H. P. Rani, Transient natural convection flow over vertical cylinder with variable surface temperatures, Forsch. Ingenieurwesen 66 (2000), 11--16.
  • A. Y. Ghaly and E. M. E. Elbarbary, Radiation effect on MHD free-convection flow of a gas at a stretching surface with a uniform free stream, J. Appl. Math. 2 (2002), no. 2, 93--103. \CMP1+908+3431 908 343
  • M. Y. Gokhale, Magnetohydrodynamic transient-free convection past a semi-infinite vertical plate with constant heat flux, Canad. J. Phys. 69 (1991), 1451--1453.
  • J. D. Hoffman, Numerical Methods for Engineers and Scientists, McGraw-Hill, New York, 1992.
  • S. Kakac and Y. Yener, Convective Heat Transfer, CRC Press, Florida, 1995.
  • R. Muthukumaraswamy and P. Ganesan, Unsteady flow past an impulsive by started vertical plate with heat and mass transfer, Heat and Mass Transfer 34 (1998), 187--193.
  • W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho (eds.), Handbook of Heat Transfer, McGraw-Hill, New York, 1998.
  • M. F. Roming, The influence of electric and magnetic fields on heat transfer to electrically conducting fluid, Advances in Heat Transfer (T. F. Irvine and J. P. Hartnett, eds.), vol. 1, Academic Press, 1964, pp. 286--354.
  • M. A. Seddeek, Thermal radiation and buoyancy effects on MHD free convective heat generating flow over an accelerating permeable surface with temperature-dependent viscosity, Canad. J. Phys. 79 (2001), 725--732.
  • T. M. Shih, Numerical Heat Transfer, Series in Computational Methods in Mechanics and Thermal Sciences, Hemisphere, Washington, DC, 1984.
  • V. M. Soundalgekar, Finite difference analysis of transient free convection with mass transfer on an isothermal vertical flat plate, Internat. J. Engrg. Sci. 19 (1981), 757--770.
  • H. S. Takhar, P. Ganesan, K. Ekambavahar, and V. M. Soundalgekar, Transient free convection past a semi-infinite vertical plate with variable surface temperature, Internat. J. Numer. Methods Heat Fluid Flow 7 (1997), 280--296.
  • H. S. Takhar, R. S. R. Gorla, and V. M. Soundalgekar, Radiation effects on MHD free convection flow of a gas past a semi-infinite vertical plate, Internat. J. Numer. Methods Heat Fluid Flow 6 (1996), 77--83.