Solving MHD Falkner-Skan Boundary-Layer Equation Using Collocation Method Based On Rational Legendre Function With Transformed Hermite-Gauss Nodes

The Falkner-Skan equation arises in the study of laminar boundary layers exhibiting similarity. The MHD systems are used effectively in many applications including power generators, pumps, accelerators, electrostatic filters, droplet filters, the design of heat exchangers, the cooling of reactors, etc. For the MHD Falkner-Skan equation, we have developed a new numerical technique transforming the governing partial differential equation into a nonlinear third-order boundary value problem by similarity variables and then solve it by the rational Legendre collocation method. In this paper we use transformed Hermite-Gauss nodes as interpolation points. The solutions obtained thus are in excellent agreement with those obtained by previous papers. In this work we concentrated on the boundary conditions of ƒ(0) = ƒ′ (0) = 0, ƒ′(+∞) = 1, which is corresponding to a fixed and impermeable wedge flow. The physical quantities of interest which is represented by the value of ƒ′′(0) is the skin friction coefficient. PACS: 34B16 • 34B40 • 65L60 • 65M70