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FALKNER-SKAN EQUATION FOR FLOW PAST A MOVING WEDGE WITH SUCTION OR INJECTION
Ishak, Anuar,Nazar, Roslinda,Pop, Ioan 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
The characteristics of steady two-dimensional laminar boundary layer flow of a viscous and incompressible fluid past a moving wedge with suction or injection are theoretically investigated. The transformed boundary layer equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of Falkner-Skan power-law parameter (m), suction/injection parameter ($f_0$) and the ratio of free stream velocity to boundary velocity parameter (${\lambda}$) are discussed in detail. The numerical results for velocity distribution and skin friction coefficient are given for several values of these parameters. Comparisons with the existing results obtained by other researchers under certain conditions are made. The critical values of $f_0$, m and ${\lambda}$ are obtained numerically and their significance on the skin friction and velocity profiles is discussed. The numerical evidence would seem to indicate the onset of reverse flow as it has been found by Riley and Weidman in 1989 for the Falkner-Skan equation for flow past an impermeable stretching boundary.
Fluid flow effects on diffusion layer and current density for electrochemical systems
Behzad Ebad,Morteza Behbahani-Nejad,Maziar Changizian,Ioan Pop 한국화학공학회 2020 Korean Journal of Chemical Engineering Vol.37 No.9
The effects of flow field upon the distribution of ionic concentration, electric potential, concentration boundary layer thickness, and electric current density were investigated. A modified numerical scheme is proposed to simulate the corresponding electrochemical system which is governed by nonlinear partial differential equations. Seven types of geometries and various flow fields with Reynolds numbers up to 2100 are considered. The obtained results indicate the current numerical method can successfully simulate the increase of current density on the cathode as the applied potential cell increases, and that rise will continue until the limiting current density is reached. To predict the effect of fluid flow, the proposed scheme is applied for various Peclet numbers. The increase of current density for Peclet numbers between 1 and 104 is quite evident. But for large Peclet numbers between 104 and 107 , the current density increases gradually. The results also show that as the anode size is doubled, the maximum current density occurs at the leading and trailing edges. However, if the cathode size is doubled, the maximum current density occurs at the center regions of it. Knowing the regions where current density is extremum helps electochemical system designers to control the parameters of the corresponding process.