Finite Wall Thickness Research Articles

The Ginzburg–Landau equation for interfacial instabilities

A coherent method for pursuing a numerical multiple scales analysis of an interface problem is presented. Finding numerical boundary conditions for the homogeneous adjoint problem and evaluation of surface terms in the inhomogeneous solvability criteria is reduced to one singular value decomposition. The method is applied to derive the complex Ginzburg–Landau equation for plane Poiseuille flow with compliant walls of finite thickness. The wall model is simple yet unprecedented in that the wall response is maintained as an independent variable throughout the wall thickness. Only small amplitude states are considered, but this type of analysis is a necessary prerequisite to the study of three-dimensional instability of finite-amplitude states in the presence of compliant walls. The effect of variations in wall thickness on the coefficients is briefly explored.

Coupling of wall conduction with natural convection in a rectangular enclosure

Conjugate heat transfer has been studied in an enclosure which consists of a conducting vertical wall of finite thickness with a uniform heat input, an insulated vertical wall and two horizontal walls at a heat sink temperature. The relative heat removal contribution by conduction in the solid wall to that by natural convection in the fluid enclosure, as well as the temperature and temperature gradient on the fluid-solid interface have been obtained for Rayleigh numbers, Ra, between 10 2 and 10 7, solid-fluid conductivity ratio, R k , between 0.5 and 50, dimensionless solid wall thickness, W, between 0.05 and 0.25 and enclosure aspect ratio, A, between 0.1 and 10. The results indicate that for low Ra, high R k and W at small and large A, the heat transfer process is dominated by the heat conduction in the solid wall. For high Ra, low R k and W at moderate A, strong interaction between conduction in the solid wall and convection in the fluid influences the heat transfer.

Domain walls of finite thickness in improper ferroelastics

Abstract The finite thickness of domain walls in improper ferroelastics leads to a temperature dependent orientation of antiphase boundaries and to the prohibition of the existence of planar ferroelastic domain walls below a certain temperature. Both effects are reviewed in a unified way. A comparison with experiments is given.

Penetration of fields through a circular hole in a wall of finite thickness

Consideration is given to a uniform, static electric field on one side of a plane metallic wall of finite thickness with a circular hole. The field induces a charge distribution on the metallic surface which behaves, at large distances from the hole, as a dipole moment, with different values for the polarizability on the inside (same side as the driving field) and outside surfaces of the hole. Two integral equations are derived for the potential in the hole and variational forms are constructed for the symmetric and asymmetric polarizabilities. Trial functions with adjustable parameters lead to accurate numerical values for the inside and outside polarizabilities. A similar approach yields corresponding values for the inside and outside magnetic susceptibilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of a transition between rectangular and circular waveguides

An analysis is presented of a transition between rectangular and circular waveguides coupled by a rectangular slot in a metallic wall of finite thickness in the common transverse cross section. Expressions for VSWR (voltage standing-wave ratio) and admittance are obtained using a moment-method formulation with entire basis and testing functions. Numerical data on the variation of input VSWR with frequency are obtained, and a comparison between the theoretical and experimental results is presented. The variations in the values of minimum VSWR with change in slot dimensions are also studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance of a Heat Exchanger Based on Enhanced Heat Diffusion in Fluids by Oscillation: Analysis

Fluid flow and heat transfer in capillary tubes (Stokes’ boundary-layer thickness nearly equal to the tube radius), subject to oscillatory flow from two reservoirs maintained at different temperatures, has been analyzed. Extension of existing analysis has been made by allowing for finite wall thickness and estimating the viscous dissipation. For a bundle of tubes connected to reservoirs of finite volume, analysis is also made of the oscillatory motion in the reservoirs (assuming a piston-type displacement within the reservoirs). The effects of various fluid and tube parameters on the heat transfer in a single tube are examined. The pathlines followed by fluid particles show that the extent of interaction between the fluid exiting the bundle and the fluid in the reservoirs (or the heat transfer surfaces in the reservoirs) depends strongly on the radial position of the exiting fluid particles. In a follow-up paper, these predictions are compared with some experimental results.

Slotted waveguide directional coupler characteristics

A moment method (MoM) solution for slotted waveguide directional couplers which is sufficiently accurate for predicting the couplers' characteristics is demonstrated. The slot length in the waveguide directional couplers considered is about four wavelengths and the wall thickness is about 0.27 lambda . To simplify the numerical computation, the formulation assumes a uniform field across the slot aperture and utilizes Galerkin's method with the entire domain sinusoidal basis. A self-consistent method taking the finite wall thickness into account avoids an additional matrix equation, as in other MoM formulations. The final solution forms the basis for an efficient computer code applicable to dielectric-loaded slotted waveguide directional couplers. The uniform field assumption restricts the present solution to narrow slots. Numerical results verify, by comparisons with published analytical and experimental data, that this solution is valid for slot lengths as long as 4 lambda . A detailed discussion of the characteristics of narrow-wall and broad-wall slotted waveguide directional couplers is presented. >

Compound coupling slots for arbitrary excitation of waveguide-fed planar slot arrays

A resonant coupling slot cut in the common broad wall of two crossed rectangular waveguides is analyzed. The slot is offset from the center line and tilted with respect to the longitudinal axis of the main waveguide, whereas it is centered-tiled in the branch waveguide. It is shown that the slot offset and tilt control the branch waveguide excitation amplitude with a phase variability of 360 degrees . Pertinent integral equations are developed, taking into account finite wall thickness. The integral equations are solved for the slot aperture electric field using the method of moments. Dominant mode scattering by the slot in both waveguides is obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of a centered-inclined waveguide slot coupler

Integral equations are developed for a centered-inclined coupling slot (including the effect of finite wall-thickness of the common broad-wall) and the slot-aperture electric intensity field is found using the method of moments. Numerical results for resonant length, backscattered wave amplitude, and phase variation off-resonance are presented over a range of values of the waveguide b dimension, wall thickness, slot width, and frequency. It is shown that the resonant length is relatively insensitive to slot tilt, theta , for a standard-height X-band waveguide, whereas its dependence on theta is significant for reduced-height waveguides. The phase variation of scattered TE/sub 10/ waves in both waveguides off-resonance is less for wider slots and smaller b dimensions. Shunt-series coupling slots exhibit greater phase variation off resonance when compared to a centred-inclined coupling slot. Also, the former has a longer resonant length for a smaller b dimension and for a wider slot. Thus the centred-inclined slot coupler possesses superior characteristics. The higher-order mode coupling between a centred-inclined slot coupler and a pair of straddling radiating slots in the branch waveguide is significant. >

Compound radiating slots in a broad wall of a rectangular waveguide

An analysis is presented of the characteristics of a broad wall radiating slot, offset from the center line and tilted with respect to the longitudinal axis of a rectangular waveguide. Pertinent integral equations are developed, taking into account finite wall thickness, and are solved for the slot aperture E-field using the method of moments. Compound slot characteristics are then deduced, including resonant length and dominant mode scattering. Numerical results for the scattering from resonant slots are presented over a range of offsets, tilt angles, frequencies and waveguide dimensions. For resonant compound slots, offset and tilt are shown to control the aperture electric-field amplitude with a phase variability of 360 degrees . The results have significant applications in the design of compound slot arrays.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Characteristics of a longitudinal/transverse coupling slot in crossed rectangular waveguides

A rigorous analysis of a broad-wall slot coupler between two crossed rectangular waveguides is presented. The slot is longitudinal and offset from the center line in the main guide and is centered transverse in the branch guide. Integral equations are developed, taking into account finite wall thickness. The integral equations are then solved for the aperture electric field. Coupling slot characteristics are obtained, including the resonant length and dominant mode scattering. Numerical results for resonant length and scattering parameters are presented over a range of offsets, waveguide dimensions, and frequencies. >

Vector fourier transform analysis of dielectric‐covered slot in the broad wall of a waveguide

AbstractThe resonant length versus offset of a dielectric‐covered narrow square ended slot is studied. The slot, located in the broad wall of a rectangular waveguide, is excited by a single mode. The external field is matched to the internal field by the Galerkin method concept. Corrections due to finite wall thickness are also included.

Radiation from cone-shape flanged open-ended thin-wall circular waveguide

The performance of an open-ended circular waveguide with a very sharp cone-shaped flanged termination was measured. These measured results were found to approach those calculated for a semi-infinite open-ended circular waveguide with infinitesimal wall thickness. This analysis is based on L.A. Weinstein's (1969) theory (Wiener-Hopf solution) and sufficient accuracy was obtained to compare results with other methods. Measured results are included for a practical model of this type of antenna demonstrating the deterioration of the cross-polarization performance due to the antenna's finite wall thickness. The theoretical and experimental results have shown very good agreement except for the cross-polarization values below -32 dB predicted by theory. >

Domain walls of finite thickness in general relativity.

The case of a domain wall of finite thickness is examined by use of two different expressions for the energy-stress tensor of domain walls but no symmetry condition. It is found that the equations of general relativity show that such walls cannot be in static equilibrium, and further even nonequilibrium walls can be consistent with Einstein's equations only under very special circumstances.

Leidenfrost boiling of methanol droplets on hot porous/ceramic surfaces

An experimental and analytical study of film boiling methanol droplets on a porous/ceramic surface is reported. Droplet evaporation times in the wetting and film boiling regimes were measured on a polished stainless-steel surface and three ceramic/alumina surfaces of 10%, 25% and 40% porosity. It was found that the Leidenfrost temperatures increased as surface porosity increased. The Leidenfrost point of the 10% and 25% porous surfaces were nearly 100 K higher and 200 K higher, respectively, than that of the polished stainless-steel surface; methanol droplets could not be levitated on the 40% porous surface at surface temperatures as high as 620 K, which was the maximum surface temperature which could be imposed on this particular material with our apparatus. The evaporation time of liquid deposited on this surface was thus almost two orders of magnitude lower than for levitated droplets on the three other surfaces tested at the same temperature. In the Leidenfrost regime droplets evaporated faster on the porous surfaces than on the stainless-steel surface, and the evaporation time decreased with increasing surface porosity at the same surface temperature. The reduced evaporation times were thought to have their origin in a decrease of the vapor film thickness separating the droplet from the ceramic surface due to vapor absorption and flow within the ceramic material. An analysis of flow in a horizontal channel bounded by an impermeable ẇall above and a permeable wall of finite thickness below was used to model the film boiling process. The results provided a basis for correlating our evaporation time measurements.

The acoustic sealing of holes and slits in walls

The sound transmission through circular holes and through long slits in a wall of finite thickness is computed for oblique plane waves. These openings may be filled by porous absorber materials and/or they may be sealed at their end planes by plastic sealing layers. The absorber materials are modelled by their acoustic characteristic data (propagation constant and wave impedance) and the sealing layers are represented by masses. The analysis is treated as a boundary problem. The final quantities are the transmission coefficient or the transmission loss. Numerical results show the influence of the design parameters. It is found that the performance of openings with a porous and/or plastic sealing cannot be approximated by the results for empty and open holes or slits. As a result of these studies it is recommended to use a transmission loss of the hole reduced by its cross-sectional area and to use a transmission loss of the slit reduced by its width as the final quantities, once the sound transmission through such openings should be standardized. These reduced transmission losses are nearly independent of the area under most conditions of parameters and frequency.

Wave loads on a stationary floating bottomless cylindrical body with finite wall thickness

This paper aims at presenting a method for solving the linearised diffraction problem of the interaction between regular sinusoidal, small amplitude incident waves and a bottomless cylindrical floating body with a vertical symmetry axis and finite wall thickness, through the idealisation of the flow field around the structure using ring elements. The horizontal and vertical excitation forces, the rolling moment, the resulting wave motion inside the cylinder, as well as the pressure distribution on the wetted surface of the structure are obtained by solving the diffraction boundary-value problem through the implementation of the Galerkin method. The analytical predictions are compared with other analytical results and pertinent experimental data. Finally, the influence of the wall thickness on the wave loads and the fluid motion inside the pond is examined.

Magnetohydrodynamic stability of a resistive fluid limited by a nonideal boundary

A new set of boundary conditions for a resistive plasma that takes into account the effect of a nonideal rigid wall of finite conductivity and thickness, is derived. These conditions, in cylindrical geometry, take the form of a system of integrodifferential equations involving the perturbed plasma variables v1, B1, T1, at the inner surface of the rigid wall. This system of integrodifferential equations is numerically solved, using a numerically stable scheme, and is implemented in an existing linear one-dimensional resistive initial value code, the Ripple IVA, developed by Dibiase and Killeen [Comput. Phys. 24, 158 (1977)]. An approximate solution of the problem, valid in a neighborhood of the time origin, is also derived. Attention is then focused on the linear behavior of resistive tearing and interchange modes as a function of the ratio of plasma and wall conductivity as well as the magnetic Lundquist number S, especially for high-beta equilibria of the reversed field pinch (RFP) type.

Effect of contact resistance on steady MHD flows through circular pipes having constant conductivity and finite wall thickness

The steady flow of viscous, electrically conducting liquids through circular pipes having finite wall thickness and conductivity under an applied uniform transverse magnetic field is considered. A uniform contact resistance at the solid/liquid interface is taken into account. An exact solution and its numerical calculations are presented.

Coaxial waveguide to circular cylindrical waveguide junction

The abrupt junction between a coaxial waveguide with hollow inner and a cylindrical waveguide has previously been analysed using a moment method for the case where the hollow inner has an infinitesimally thin wall. The paper describes modifications which permit a wall of finite thickness to be accommodated.