Modeling of fluid dynamics and the associated heat transfer induced by plasma between two parallel electrodes is investigated. In particular, we consider a capacitvely coupled radio frequency discharge plasma generator, where the plasma is generated on the surface of a dielectric circuit board with electrode strips on the top and bottom. The electrodes have a thickness of 100 μm, which is comparable to the height of the boundary layer. The regime considered is that the electron component is in the non-equilibrium state, and the plasma is nonthermal. Overall, due to the ion and large fluid particle interaction, the pressure is higher in the downstream of the electrode, causing the velocity structure to resemble that of a wall jet. Parameters related to the electrode operation, including the voltage, frequency, and free stream speed are varied to investigate the characteristics of the plasma-induced flow. Consistent with the experimental observation, the model shows a clear dependence of the induced jet velocity on the applied voltage and frequency. The heat flux exhibited a similar dependence on the strength of the plasma. The present plasma-induced flow concept can be useful for thermal management and active flow control.

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A method where polygon corners in Schwarz-Christoffel mappings are rounded, is used to construct mappings from the upper half-plane to regions bounded by arbitrary piecewise smooth curves. From a given curve, a polygon is constructed by taking tangents to the curve in a number of carefully chosen so-called tangent points. The Schwarz-Christoffel mapping for that polygon is then constructed and modified to round the corners.Since such a modification causes effects on the polygon outside the rounded corners, the parameters in the mapping have to be redetermined. This is done by comparing side-lengths in tangent polygons to the given curve and the curve produced by the modified Schwarz-Christoffel mapping. The set of equations that this comparison gives, can normally be solved using a quasi-Newton method.The resulting function maps the upper half-plane on a region bounded by a curve that apart from possible vertices is smooth, i.e., one time continuously differentiable, that passes through the tangent points on the given curve, has the same direction as the given curve in these points and changes direction monotonically between them. Furthermore, where the original curve has a vertex, the constructed curve has a vertex with the same inner angle.The method is especially useful for unbounded regions with smooth boundary curves that pass infinity as straight lines, such as channels with parallel walls at the ends. These properties are kept in the region produced by the constructed mapping.

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a b s t r a c tThe Schwarz-Christoffel mapping from the upper half-plane to a polygonal region in the complex plane is an integral of a product with several factors, where each factor corresponds to a certain vertex in the polygon. Different modifications of the Schwarz-Christoffel mapping in which factors are replaced with the so-called curve factors to achieve polygons with rounded corners are known since long times. Among other requisites, the arguments of a curve factor and its correspondent scl factor must be equal outside some closed interval on the real axis.In this paper, the term approximate curve factor is defined such that many of the already known curve factors are included as special cases. Additionally, by alleviating the requisite on the argument from exact to asymptotic equality, new types of curve factors are introduced. While traditional curve factors have a C 1 regularity, C ∞ regular approximate curve factors can be constructed, resulting in smooth boundary curves when used in conformal mappings.Applications include modelling of wave scattering in waveguides. When using approximate curve factors in modified Schwarz-Christoffel mappings, numerical conformal mappings can be constructed that preserve two important properties in the waveguides. First, the direction of the boundary curve can be well controlled, especially towards infinity, where the application requires two straight parallel walls. Second, a smooth (C ∞ ) boundary curve can be achieved.