Integration of the Magnetohydrodynamic Boundary‐Layer Equations by Meksyn's Method

Abstract

Es wird das nichtlineare Randwertproblem formuliert, das die räumliche Entwicklung der Grenzschicht in einer leitenden Flüssigkeit beschreibt, die bei Vorhandensein eines äußeren Druckgradienten quer zu einem inhomogenen Magnetfeld entlang einer ebenen Platte strömt. Mit Hilfe von Transformationen, Reihenentwicklungen und Integrationsverfahren (Sattelpunkt‐Methode), wie sie von Meksyn in die Analysis hydrodynamischer Grenzschichten eingeführt worden sind, werden analytische Lösungen für das Geschwindigkeitsfeld sowohl in Punkten der anliegenden als auch der abgelösten magnetohydrodynamischen Strömung gewonnen. Der Anwendung auf magnetohydrodynamische Diffusor‐Strömungen wird besondere Aufmerksamkeit geschenkt. Es wird gezeigt, daß ein inhomogenes Magnetfeld die Grenzschichtablösung unterdrücken kann.

Analytical treatment on magnetohydrodynamic (MHD) flow and heat transfer due to a stretching hollow cylinder

“…According to the definition in Equation (7), the governing equation and the corresponding initial condition of u m ( ) can be deduced from zero-order deformation equation (1). Differentiating Equation (1) for m times with respect to the embedding parameter p and setting p = 0 and finally dividing by m!, we will have the so-called mth-order deformation equation in the form:…”

“…MHD boundary layers are observed in various technical systems employing liquid metal and plasma flow transverse of magnetic fields [1].…”

Thermophoresis and Brownian motion effects on MHD bioconvection of nanofluid with nonlinear thermal radiation and quartic chemical reaction past an upper horizontal surface of a paraboloid of revolution

“…Since chemical reactant B is of higher concentration than that of cubic schemes described in [35] and [12], hence the suitable schemes can be described as isothermal quartic autocatalytic reaction and first order reaction. The concentration of chemical reactant A is "a".…”

Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source in a nanofluid

“…We consider the case of a short circuit problem in which the applied electric field E = 0, and also assume that the induced magnetic field is small compared to the external magnetic field B 0 . This implies a small magnetic Reynolds number for the oscillating plate (see Liron and Wilhelm [28]). The surface temperature is assumed to have the constant value T w while the ambient temperature has the constant value T ?…”