Magnetohydrodynamic (MHD) Free Convective Flow past an Infinite Vertical Porous Plate with Joule Heating

Affiliation(s)

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

School of Mathematics and Statistics, The Kenya Polytechnic University College, Nairobi, Kenya.

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

School of Mathematics and Statistics, The Kenya Polytechnic University College, Nairobi, Kenya.

ABSTRACT

This work addresses the problem of Magnetohydrodynamic laminar unsteady flow of an incompressible electrically conducting fluid past an infinite vertical porous plate. It investigates how joule heating affects the velocity and temperature profiles of the fluid flow subjected to transverse magnetic field. The research examines specific equations of MHD flow which are solved numerically by finite difference approximations, using computer programme. The numerical results of this study reveal that an increase in joules heating parameter causes an increase in the velocity and temperature profiles uniformly near the plate but remain constantly distributed away from the plate, implying that the flow field of the MHD free convective flow is influenced substantially by the strength of Joules heating near the wall of the plate and at the mainstream.

Cite this paper

S. Johana, O. Jeconia, G. Francis and N. Joel, "Magnetohydrodynamic (MHD) Free Convective Flow past an Infinite Vertical Porous Plate with Joule Heating,"*Applied Mathematics*, Vol. 4 No. 5, 2013, pp. 825-833. doi: 10.4236/am.2013.45113.

S. Johana, O. Jeconia, G. Francis and N. Joel, "Magnetohydrodynamic (MHD) Free Convective Flow past an Infinite Vertical Porous Plate with Joule Heating,"

References

[1] M. Faraday, “Electricity Researches in Electricity,” 1st Series Philosophical Transactions of the Royal Society, 1831, pp. 125-162.

[2] L. Calvert and C. Santos, “Research Article on the Fundamental Principle of MHD,” Applied Mathematics and Computation, Vol. 108, 2002, pp. 11-21.

[3] G. S. Ramulu and S. K. Ghosh, “Effect of Hall Current on MHD Flow and Heat Transfer a Long a Porous Flat Plate with Mass Transfer,” International Journal for Engineering Science, Vol. 24, No. 7, 2007, pp. 1183-1193.

[4] I. C. Cooker and O. Mubo-Pepple, “Influence of Viscous Dissipation and Radiation on Unsteady MHD Free-Convection Flow past an Infinite Heated Vertical Plate in a Porous Medium with Time Independent Suction,” International Journal of Heat and Mass Transfer, Vol. 46, No. 13, 2003, pp. 2305-2311. doi:10.1016/S0017-9310(02)00544-6

[5] J. Jordan, “Network Simulation Method to Radiation and Viscous Dissipation Effect on MHD Unsteady Free Convection over Vertical Porous Plate,” Applied Mathematics Modeling, Vol. 31, No. 9, 2007, pp. 2019-2033. doi:10.1016/j.apm.2006.08.004

[6] M. E. Abo-Eldahab and A. M. El Aziz, “Viscous Dissipation and Joule Heating Effects on MHD Free Convection from a Vertical Plate with Power-Law Variation in Surface Temperature in the Presence of Hall and Ion-Slip Currents,” Applied Mathematical Modeling, Vol. 29, No. 6, 2005, pp. 579-595. doi:10.1016/j.apm.2004.10.005

[7] M. Kinyanjui and N. Chaturvedi, “MHD Stokes Problem for a Vertical Infinite Plate in a Dissipative Rotating Fluid with a Hall Current,” Energy Conversion and Management, Vol. 39, No. 5-6, 1998, pp. 541-548. doi:10.1016/S0196-8904(96)00107-0

[8] G. C. Duwahiri and D. P. Das, “Viscous and Joule Heating Effect on Forced Convection Flow of Ionized Gases along a Plane Wall with Periodic Suction and Heat Source, Model,” Simulation and Control B, Vol. 27, No. 2, 2005, pp. 47-55.

[1] M. Faraday, “Electricity Researches in Electricity,” 1st Series Philosophical Transactions of the Royal Society, 1831, pp. 125-162.

[2] L. Calvert and C. Santos, “Research Article on the Fundamental Principle of MHD,” Applied Mathematics and Computation, Vol. 108, 2002, pp. 11-21.

[3] G. S. Ramulu and S. K. Ghosh, “Effect of Hall Current on MHD Flow and Heat Transfer a Long a Porous Flat Plate with Mass Transfer,” International Journal for Engineering Science, Vol. 24, No. 7, 2007, pp. 1183-1193.

[4] I. C. Cooker and O. Mubo-Pepple, “Influence of Viscous Dissipation and Radiation on Unsteady MHD Free-Convection Flow past an Infinite Heated Vertical Plate in a Porous Medium with Time Independent Suction,” International Journal of Heat and Mass Transfer, Vol. 46, No. 13, 2003, pp. 2305-2311. doi:10.1016/S0017-9310(02)00544-6

[5] J. Jordan, “Network Simulation Method to Radiation and Viscous Dissipation Effect on MHD Unsteady Free Convection over Vertical Porous Plate,” Applied Mathematics Modeling, Vol. 31, No. 9, 2007, pp. 2019-2033. doi:10.1016/j.apm.2006.08.004

[6] M. E. Abo-Eldahab and A. M. El Aziz, “Viscous Dissipation and Joule Heating Effects on MHD Free Convection from a Vertical Plate with Power-Law Variation in Surface Temperature in the Presence of Hall and Ion-Slip Currents,” Applied Mathematical Modeling, Vol. 29, No. 6, 2005, pp. 579-595. doi:10.1016/j.apm.2004.10.005

[7] M. Kinyanjui and N. Chaturvedi, “MHD Stokes Problem for a Vertical Infinite Plate in a Dissipative Rotating Fluid with a Hall Current,” Energy Conversion and Management, Vol. 39, No. 5-6, 1998, pp. 541-548. doi:10.1016/S0196-8904(96)00107-0

[8] G. C. Duwahiri and D. P. Das, “Viscous and Joule Heating Effect on Forced Convection Flow of Ionized Gases along a Plane Wall with Periodic Suction and Heat Source, Model,” Simulation and Control B, Vol. 27, No. 2, 2005, pp. 47-55.