2-D Electrical Modeling over Undulated Topography

The electrical response of a cylindrical inclusion in topographic relief has been treated analytically for a uniform electric field. The undulated topography has been conveniently defined by a smoothly connected mathematical surface defining a hump or bump. A Born approximation of Laplace’s equation in a bipolar coordinate system has been derived by solving for the mixed‐boundary conditions, namely Neumann and Dirichlet conditions, respectively. The topographic relief causes focusing and defocusing at the transition zones of flat and topographic relief and the central zone of the hump. Consequently, the electric field is weakly linear within the flat zone and entirely nonlinear within the hump. The inclusion of a cylindrical target aggravates the field nonlinearity. The electric field and induced polarization (IP) response over the cylindrical target embedded in topographic relief are strongly dependent on the width and height of the hump and a steady function of increase in resistivity ([Formula: see text]) as well as chargeability ([Formula: see text]) contrasts. The electrical field and IP response over the cylindrical target embedded in the topographic relief, after correcting for topographic effect, resembles most closely the field measured on an equivalent flat half‐space of a particular elevation. The areas of the topographic surface above and below this unique datum bisecting the topographic relief are exactly equal.

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Enhanced Passive Thermal Management of Grid-Scale Power Routers Utilizing Ionic Wind

Volume 8A: Heat Transfer and Thermal Engineering ◽

10.1115/imece2014-38713 ◽

2014 ◽

Cited By ~ 1

Author(s):

Noris Gallandat ◽

J. Rhett Mayor

Keyword(s):

Heat Transfer ◽

Electric Field ◽

Mixed Boundary ◽

Control Volume ◽

Vertical Channel ◽

Mixed Boundary Conditions ◽

Thermal Design ◽

Finite Difference Approximation ◽

Difference Approximation ◽

Ionic Wind

This paper presents a numerical model assessing the potential of ionic wind as a heat transfer enhancement method for the cooling of grid distribution assets. Distribution scale power routers (13–37 kV, 1–10 MW) have stringent requirements regarding lifetime and reliability, so that any cooling technique involving moving parts such as fans or pumps are not viable. Increasing the air flow — and thereby enhancing heat transfer — through Corona discharge could be an attractive solution to the thermal design of such devices. In this work, the geometry of a rectangular, vertical channel with a corona electrode at the entrance is considered. The multiphysics problem is characterized by a set of four differential equations: the Poisson equation for the electric field and conservation equations for electric charges, momentum and energy. The electrodynamics part of the problem is solved using a finite difference approximation (FDA). Solutions for the potential, electric field and free charge density are presented for a rectangular control volume with mixed boundary conditions.

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Study on the electrical response of small ethanol‐air diffusion flame under the uniform electric field

International Journal of Energy Research ◽

10.1002/er.5828 ◽

2020 ◽

Vol 44 (14) ◽

pp. 11872-11882

Author(s):

Yanlai Luo ◽

Yunhua Gan ◽

Zhengwei Jiang

Keyword(s):

Electric Field ◽

Diffusion Flame ◽

Electrical Response ◽

Uniform Electric Field ◽

Air Diffusion

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Stable finite element approximation of a Cahn–Hilliard–Stokes system coupled to an electric field

European Journal of Applied Mathematics ◽

10.1017/s0956792516000395 ◽

2016 ◽

Vol 28 (3) ◽

pp. 470-498

Author(s):

ROBERT NÜRNBERG ◽

EDWARD J. W. TUCKER

Keyword(s):

Finite Element ◽

Electric Field ◽

Organic Solar Cells ◽

Stokes System ◽

Chemical Potential ◽

Mixed Boundary ◽

Mixed Boundary Conditions ◽

Finite Element Approximation ◽

Strength Parameter ◽

Element Approximation

We consider a fully practical finite element approximation of the Cahn–Hilliard–Stokes system: $$\begin{align*} \gamma \tfrac{\partial u}{\partial t} + \beta v \cdot \nabla u - \nabla \cdot \left( \nabla w \right) & = 0 \,, \quad w= -\gamma \Delta u + \gamma ^{-1} \Psi ' (u) - \tfrac12 \alpha c'(\cdot,u) | \nabla \phi |^2\,, \\ \nabla \cdot (c(\cdot,u) \nabla \phi) & = 0\,,\quad \begin{cases} -\Delta v + \nabla p = \varsigma w \nabla u, \\ \nabla \cdot v = 0, \end{cases} \end{align*}$$ subject to an initial condition u0(.) ∈ [−1, 1] on the conserved order parameter u ∈ [−1, 1], and mixed boundary conditions. Here, γ ∈ $\mathbb{R}_{>0}$ is the interfacial parameter, α ∈ $\mathbb{R}_{\geq0}$ is the field strength parameter, Ψ is the obstacle potential, c(⋅, u) is the diffusion coefficient, and c′(⋅, u) denotes differentiation with respect to the second argument. Furthermore, w is the chemical potential, φ is the electro-static potential, and (v, p) are the velocity and pressure. The system has been proposed to model the manipulation of morphologies in organic solar cells with the help of an applied electric field and kinetics.

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