Nicolaos J. Siakavellas

Two simple models for analytical calculation of eddy currents in thin conducting plates

Two simple models are proposed for the analytical calculation of eddy currents induced by a time-varying magnetic field in thin conducting plates of various shapes. In the first model, it is assumed that the current paths are determined exclusively by the shape of the plate. This assumption makes evident a shape factor that characterizes the shape of the plate under investigation and is independent of the dimensions of the plate. Thus, several important parameters, such as the equivalent resistance of the plate, the total circulating current, etc., are expressed analytically as a function of this shape factor. The application of the model makes possible the estimation of the total eddy current, circulating in plates of any shape, but the accuracy of this estimate is strongly affected by the shape of the plate. This model is then improved for plates having symmetrical shapes by taking into consideration the principle of minimum energy dissipation. The results, obtained by the improved model for the total circulating current, are in good agreement with the results obtained numerically as well as with analytical results obtained by the use of variational methods.

Influence of Some Parameters on the Effectiveness of Induction Heating

We have investigated the effectiveness of heating conductive plates by induction in low frequencies analytically and numerically, in relation to the shape of the plate, the area of the region exposed to the magnetic flux, and the position of the exposed region with respect to the center of the plate. We considered both uniform and nonuniform magnetic fields. For plates with equivalent area exposed to the same uniform magnetic flux, the one with the most symmetrical shape is heated most effectively. If a coil is employed for the excitation, the results depend on the shape of the plate, the shape of the coil section, and the coil lift-off. When only the central region of a plate is exposed to a variable magnetic flux, there is a specific value of the exposed area for which the power dissipated in the plate material reaches a maximum. The most effective heating of a plate partially exposed occurs when the axis of the exciting coil is at the plate center.

Smart patterned surfaces with programmable thermal emissivity and their design through combinatorial strategies

The emissivity of common materials remains constant with temperature variations, and cannot drastically change. However, it is possible to design its entire behaviour as a function of temperature, and to significantly alter the thermal emissivity of a surface through the combination of different patterns and materials. We show that smart patterned surfaces consisting of smaller structures (motifs) may be designed to respond uniquely through combinatorial strategies by transforming themselves. The smart surfaces can passively manipulate thermal radiation—without the use of electronics—because their modus operandi has already been programmed into their intrinsic characteristics; the environment provides the energy required for their activation. Each motif emits thermal radiation in a certain manner, as it changes its geometry; however, the spatial distribution of these motifs causes them to interact with each other. Therefore, their combination and interaction determine the global behaviour of the surfaces, thus enabling their a priori design. The emissivity behaviour is not random; it is determined by two fundamental parameters, namely the combination of orientations in which the motifs open (n-fold rotational symmetry) and the combination of materials (colours) on the motifs; these generate functions which fully determine the dependency of the emissivity on the temperature.

The Importance of Analytic Solutions for Verification: Application to the Secondary Magnetic Flux of a Conductive Disk

The method and value of analytical methods and the importance of analytic solutions for verification must be emphasised to both under- and post-graduate students. So, they must be able to: (i) derive by their own expressions for the quantities of interest, and (ii) test their numerical results by an independent method. Hence, they must be motivated to try to solve any problem analytically, before proceeding to a numerical solution. Towards this aim, a sample problem is proposed and an analytic expression is derived for the secondary magnetic flux induced in a conductive disk by a time-varying magnetic field. This expression, involving elliptic and improper integrals, is finally reduced into a single integral, depending on the current distribution on the disk. Next, an analytical solution for a simplified version of the problem is obtained, which may be used for verification of the numerical solution of the more complex and general problem.

Bioinspired Temperature-Responsive Multilayer Films and Their Performance under Thermal Fatigue

The structure of certain nonliving tissues determines their self-shaping and self-folding capabilities in response to a stimulus. Predetermined movements are realized according to changes in the environmental conditions due to the generated stresses of the multilayer anisotropic structure. In this study, we present bioinspired responsive anisotropic multilayer films and their fabrication process which comprises low-cost techniques. The anisotropic multilayer materials are capable of deforming their geometry caused by small temperature changes (<40 °C). The mismatch in the thermo-mechanical properties between three or more anisotropic thin layers creates responsive materials that alter their shape owing to the developed internal stresses. The movements of the material can be controlled by forming anisotropic homogenous metallic strips over an anisotropic thermoplastic layer. As a result, responsive multilayer films made of common materials can be developed to passively react to a temperature stimulus. We demonstrate the ability of the anisotropic materials to transform their geometry and we present a promising fabrication process and the thermal fatigue resistance of the developed materials. The thermal fatigue performance is strongly related to the fabrication method and the thickness of the strips. We studied the thermal fatigue performance of the materials and how the thermal cycling affects their sensitivity, as well as their failure modes and crack formation.

Eddy current modelling in a coupled electromagnetic‐mechanical problem

Solves a coupled electromagnetic‐mechanical problem ‐ that of a cantilevered conductive plate in crossed steady and time‐varying magnetic fields ‐ by using a semi‐analytical method and an eddy current model. Assumes that the magnetic flux variation induces two electromotive forces to the plate; one due to the time‐varying magnetic field and the other to the plate movement in the steady magnetic field. Considers two equivalent LR circuits and notes that the superposition of their currents yields the total circulating current in the plate. Couples this electromagnetic model to the one‐dimensional beam bending model, adopted for the structural analysis of the problem and derives the system of the coupled electromagnetic‐mechanical equations. Calculates analytically some of the parameters involved in these equations so that the numerical computation of the remaining unknowns is very rapid. Concludes that the results are in agreement with the experiment and with results obtained by numerical methods treating, in three dimensions, the electromagnetic aspects of the problem. Notes that the fully numerical methods are very much CPU time consuming.