MHD free convection flow with fractional heat conduction law

M. A. Ezzat¹ - A. A. El-Bary²

¹ Department of Mathematics, Faculty of Education, Alexandria, Egypt
² Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt

Abstract
A new mathematical model of MHD theory has been constructed in the context of a new consideration of heat conduction with a time-fractional derivative of the order α (0 < α ≤ 1) and a time-fractional integral of the order υ (0 < υ ≤ 2). This model is applied to MHD free convection flow of a viscous conducting fluid past an infinite surface with heat sources. Laplace transforms and state-space techniques [1] are used to obtain the general solution for any set of boundary conditions. According to the numerical results and their graphs, a conclusion about the new theory has been made. Some comparisons are shown in figures to estimate the effects of the fractional order parameters α,υ on all studied fields for different theories. Figs 9, Refs 62.