Conjugate Effect of Radiation and Thermal Conductivity Variation on MHD Free Convection Flow for a Vertical Plate


A numerical investigation is performed to study the effect of thermal radiation on magnetohydrodynamic (MHD) free convection flow along a vertical flat plate in presence of variable thermal conductivity in this paper. The governing equations of the flow and the boundary conditions are transformed into dimensionless form using appropriate similarity transformations and then solved employing the implicit finite difference method with Keller-box scheme. Results for the details of the velocity profiles, temperature distributions as well as the skin friction, the rate of heat transfer and surface temperature distributions are shown graphically. Results reveal that the thermal radiation is more significant in MHD natural convection flow during thermal conductivity effect is considered. To illustrate the accuracy of the present results, the results for the local skin fraction and surface temperature distribution excluding the extension effects are compared with results of Merkin and Pop designed for the fixed value of Prandtl number and a good agreement were found.

Share and Cite:

R. Akhter, M. Ali, B. Hossain and M. Uddin, "Conjugate Effect of Radiation and Thermal Conductivity Variation on MHD Free Convection Flow for a Vertical Plate," American Journal of Computational Mathematics, Vol. 3 No. 3, 2013, pp. 252-259. doi: 10.4236/ajcm.2013.33035.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] V. M. Soundalgekar and H. S. Takhar, “Radiative Convective Flow Past a Semi-Infinite Vertical Plate,” Modelling Measurement and Control, Vol. 51, 1992, pp. 31-40.
[2] A. C. Cogley, W. G. Vincenti and S. E. Giles, “Differential Approximation for Radiative in a Non-Gray Gas Near Equilibrium,” American Institute of Aeronautics and Astronautics Journal, Vol. 6, No. 3, 1968, pp. 551-553.
[3] M. A. Hossain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248.
[4] A. Y. Ghaly, “Radiation Effects on a Certain MHD Free Convection Flow,” Chaos, Solitons & Fractals, Vol. 13, No. 9, 2002, pp. 1843-1850.
[5] M. A. Abd El-Naby, E. M. E. Elsayed and N. Y. Abdelazem, “Finite Difference Solution of Radiation Effect on MHD Unsteady Free Convection Flow over a Vertical Plate Variable Surface Temperature,” Journal of Applied Mathematics, Vol. 2003, No. 2, 2003, pp. 65-86.
[6] I. A. Badruddin, Z. A. Zainal, A. Zahid Khan and Z. Mallick, “Effect of Viscous Dissipation and Radiation on Natural Convection in a Porous Medium Embedded within Vertical Annulus,” International Journal of Thermal Science, Vol. 46, No. 3, 2007, pp. 221-227.
[7] S. C. Mishra, P. Talukdar, D. Trimis and F. Durst, “Two-Dimensional Transient Conduction and Radiation Heat Transfer with Temperature Dependent Thermal Conductivity,” International Communications in Heat and Mass Transfer, Vol. 32, No. 3-4, 2005, pp. 305-314.
[8] M. A. Seddeek and F. A. Salama, “The Effects of Temperatute Dependent Viscosity and Thermal Conductivity on Unsteady MHD Convective Heat Transfer Past a SemiInfinite Vertical Porous Moving Plate with Variable Suction,” Computational Material Science, Vol. 40, No. 2, 2007, pp. 186-192.
[9] P. R. Sharma and G. Singh, “Effects of Variable Thermal Conductivity, Viscous Dissipation on Steady MHD Natural Convection Flow of Low Prandtl Fluid on an Inclined Porous Plate with Ohmic Heating,” Meccanica, Vol. 45, No. 2, 2010, pp. 237-247.
[10] P. Loganathan, P. Ganesan and D. Iranian, “Effects of Thermal Conductivity on Unsteady MHD Free Convective Flow over a Semi Infinite Vertical Plate,” International Journal of Engineering Science and Technology, Vol. 2, 2010, pp. 6257-6268.
[11] H. B. Keller, “Numerical Methods in the Boundary Layer Theory,” Annual Review of Fluid Mechanics, Vol. 10, 1978, pp. 417-433.
[12] T. Cebeci and P. Bradshow, “Physical and Computational Aspects of Convective Heat Transfer,” Springer, New York, 1984.
[13] J. H. Merkin and I. Pop, “Conjugate Free Convection on a Vertical Surface,” International Journal of Heat and Mass Transfer, Vol. 39, No. 7, 1996, pp. 1527-1534.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.