Series solution of an eddy-current problem for a sphere withvarying conductivity and permeability profiles

Two-parameter families of analytical solutions are found for a single-turn coil symmetrically located above a two-layer sphere. Several cases are considered where the conductivity and relative magnetic permeability of the outer spherical layer are functions of the distance ρ from the sphere's center. The change in impedance of the coil is obtained in terms of a series containing Bessel functions. Computational impedance results are presented for different values of the parameters of the problem and the exact conductivity and permeability profiles are given diagrammatically for comparison with the impedance results     

Gas Coil Collapse due to Iron Carbonyl

A coil for preheating natural gas, placed in the flue of a primary reformer, collapsed due to the formation of a thick deposit on the inside which prevented heat transfer. It was found that the deposit consisted of ferrous oxide transported from a colder portion of the gas line by formation of iron carbonyl. Carbon monoxide was generated by the cleaning cycle of a thio compound removal unit.     

Impedance of a single-turn coil due to a double-layered sphere withvarying properties

This paper presents an analytical solution for the change in impedance in a coil due to the presence of a conducting double-layered sphere symmetrically situated with respect to the coil. In the case where the relative magnetic permeability, μ(r)=r^α, of the outer sphere is a function of the distance r from the center of the sphere, where a is an arbitrary real number, the solution is expressed in the form of a series containing Bessel functions and can be used to compute the change of impedance. Numerical results for the case α=-2 are presented     

Temperature fields due to thermomechanical coupling in a compressible viscoelastic sphere

Summary Internal cyclic loading of a viscoelastic hollow sphere is considered. The influence of the material properties in dilatation and shear on the heat generation and temperature distribution is analysed.For common polymeric materials the elastic and viscoelastic dilatational properties are found to be of less improtance than the temperature dependence in shear.

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Durch thermomechanische Kopplung hervorgerufene Temperaturfelder in einer kompressiblen viskoelastischen Kugel

Zusammenfassung Betrachtet wird eine viskoelastische Hohlkugel unter zyklischem Innendruck. Der Einfluß der Materialeigenschaften in Dilatation und Schub auf Wärmeentwicklung und Temperaturverteilung wird untersucht. Es zeigt sich, daß für gewöhnliche Polymere die elastischen und viskoelastischen Materialeigenschaften bei Dilatation von geringerer Bedeutung als die Temperaturabhängigkeit der Materialeigenschaften bei Schub sind.

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With 5 Figures     

Electromagnetic scattering from a multilayered sphere located in an arbitrary beam

A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.     

Thermal conductivity of a material containing cracks of arbitrary shape

The problem of thermal conductivity of a material containing microcracks of arbitrary shape (including non-flat ones) is considered. The resistivity contribution tensor of a crack – the quantity that determines the decrease in the overall conductive properties of a solid due to introduction of such cracks – is derived on the basis of the solution for the strength of a singularity of the heat flux near a crack tip (heat flux intensity factor). The approach is illustrated with several examples. It is also shown how the resistivity contribution tensor can be used to calculate effective conductive properties in the framework of various self-consistent schemes – effective media, effective field and differential scheme.     

Stresses in a fuselage model due to concentrated radial loads

Experimental values of shear and direct stresses on cross–sections of a fuselage model, due to concentrated radial loads applied to a frame, are compared with values predicted by a matrix force analysis. The results include the effect of cut–outs in the surface of the shell. Comparisons are also made of the direct stress on the inner flange of the directly–loaded frame and of the frames bounding the cut–outs. Results indicate that the degree of accuracy of the theoretical stresses is adequate for the purpose of design.     

Simulation of microelectrode impedance changes due to cell growth

Observation of impedance changes caused by cell growth on microelectrodes provides information about cell coverage and other important quantities, such as the cell-electrode gap. In this paper, we use finite-element simulations to calculate the impedance changes caused by cell growth on electrodes comparable in size to the cell. Parameters describing the impedance of the electrode without cells are derived from measurement. The results show that the impedance magnitude is expected to increase by at least 100% for partial cell coverage. We also report the frequency dependence of the magnitude and phase of the impedance and compare the simulation results with a lumped-element model. The simulation results are important for the design and modeling of arrays of cell-sized electrodes and also for the interpretation of experiments.     

Magnetostatic image theory for an arbitrary current loop in frontof a permeable sphere

Magnetostatic image theory recently introduced for the problem of a circular current loop in front of a permeable sphere centered on the axis of the loop is generalized to the case of an arbitrary current loop outside the sphere. The theory is derived by finding the image for a current element outside the sphere. As an application, the image for a straight line current is seen to result in a surface current in the form of a circular disk. The present theory is also seen to reproduce that for the circular loop as a special case. The analytic form of the image current is simple enough to be applicable in small-scale computation for problems involving a permeable sphere and stationary current     

Change in impedance of a single-turn coil due to a flaw in a conducting half space

The problem of detection and characterization of a flaw in a conducting half-space using an eddy-current coil oriented parallel to the interface is examined. An expression is derived for a first order approximation for the change in complex impedance due to a flaw located within the conducting medium. The overall impedance is a function of the radius and lift-off distance of the test coil and the conductivity of the material. An analytical expression is derived for the change in impedance as a function of the electric fields at the position of the flaw. It is found to be an integral over the volume of the flaw of the electric fields found with and without the flaw being present. The limiting case of a degenerate point flaw may be examined in greater detail by allowing the field in the presence of the flaw to be approximated by the unperturbed field. For flaws small enough that the field does not vary much over its volume, the field may be even further approximated by using just the value of the field at the position of the centroid of the flaw. Plots are shown to illustrate the behavior of the change in impedance as a function of the radial range of the flaw and the depth of the flaw centroid, using previously derived expressions for the fields for the unflawed case.     

Matching radio frequency identification tag compact dipole antennas to an arbitrary chip impedance

A method for matching dipole antennas to capacitive or inductive arbitrary complex impedances is proposed for ultra high frequency radio frequency identification (RFID) tag antenna designs. It can be applied to straight, capacitive-loaded, meander or any small high-Q dipole topology. For this purpose, design stages are provided with the corresponding formulas. The reflection coefficient simulations and measurements of four implemented prototypes show the expected output when the RFID frequency band, bandwidth, chip impedance and maximum tag size are required as inputs for the method. The eventual S11 < 10 dB bandwidth depends on the chip impedance Q factor and the antenna size. How this bandwidth is manifested in terms of the read range is also discussed. A length ratio of up to 31.1% regarding the standard Λ/2 dipole at resonance is obtained.     

Failure due to semielliptical surface cracks under arbitrary stress distributions

A procedure is described that is based on the two-dimensional weight function equation of Rice. This enables one to determine the equilibrium semiellipses characterized by a constant stress intensity factor along the crack-tip line for any stress distribution. The applicability is explained for the special case of thermal stresses caused by a thermal shock. Local stress intensity factors are estimated for the same stresses by using solutions for exponential stress distributions. A comparison of the two methods showed good agreement.     

Eddy current probe impedance due to a flaw: The influence of phase-shifted fields

An approximate formula for the change in impedance of an eddy current two-coil probe situated above a conducting medium with a volumetric flaw is derived in this paper. The primary field is generated by the superposition of two phase-shifted alternating currents of the same frequency. The Lorentz reciprocity theorem and a layer approximation are used to obtain the change in impedance. Numerical results for different values of the phase difference are presented. These results can be used for developing more selective eddy current testing methods.     

Evaluation of thermal conductivity from temperature profiles

A new dynamic technique for the measurement of thermal conductivity is being developed at IMGC. The experiment consists in bringing the specimen to high temperatures with a current pulse and in measuring the temperature profiles during the free cooling period. Different techniques can be used to extract the information on thermal conductivity from the profiles. The numerical computation of thermal conductivity from the experimental temperature profiles in absolute space is possible, but it is difficult and cumbersome because one must know and take into the account the exact position of the infinitesimal elements of the specimen in different profiles. Computations in tube-space (a fictitious space where no thermal expansion occurs) are simpler and lead to less complex numerical computations. Complementary techniques to evaluate thermal conductivity as a function of temperature or at constant temperature are presented with a discussion of advantages and disadvantages of each method. Computer simulations have tested the precision of the complex software. Numerically generated temperature profiles from known thermophysical properties have been obtained and thermal conductivity has been recomputed from the profiles. The relative difference using different computational approaches and different fitting functions is always less than 0.1%.Paper presented at the Third Workshop on Subsecond Thermophysics, September 17–18, 1992, Graz, Austria.     

Numerical analyses of the thermal conductivity of random hollow sphere structures

This paper presents Lattice Monte Carlo (LMC) and Finite Element (FE) analyses on the effective thermal conductivity of sintered Metallic Hollow Spheres Structures (MHSS). A novel analysis technique applying LMC permits the utilisation of large high resolution models and can be based on Computed Tomography (CT) images. As a consequence, simulations are performed using the real geometry and no simplifications, such as the use of model structures, need to be introduced. In the first part, the influence of the micro-porosity on the effective thermal conductivity of the cell wall material is determined. Using these results, the second part of the analyses directly addresses the thermal properties of sintered MHSS. The findings of the LMC analyses are compared with FE results.     

Excess electrical conductivity due to fluctuations of quench-condensed superconducting Nb films

The resistive transition of superconducting Nb films evaporated onto a liquid-He-cooled substrate has been investigated, and shows a rounding characteristic of the thermal fluctuations. Transition curves have been measured above and below the superconducting transition temperatureT _c in the absence of a magnetic field. The excess electrical conductivity due to fluctuations aboveT _c of quench-condensed Nb films is well described in terms of the sum of the contributions from the Aslamazov-Larkin term and from the Maki-Thompson term, in contradistinction to the case of quench-condensed Bi, Ga, and Pb films. This suggests that thermal phonons play an important role in the contribution of the Maki term.