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Th. doct.-ing.--Génie électrique--Grenoble--I.N.P., 1983. N°: DI 336.

Th. 3e cycle--Génie électronique--Toulouse--I.N.P., 1982. N°: 147.

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Anomalous electrical behaviour may appear in the d.c. and a.c. characteristics of metals or semiconductors in which the current is determined by both voltage and temperature. Theoretical investigations have been carried out by assuming different models of heat flow and the conditions for the appearance of thermal breakdown and Negative Resistance (NR) have been obtained for both metals and semi-conductors. For purely longitudinal heat flow, NR is predicted for metals while for semi-conductors, the d.c. characteristic is of the "breakdown" type without NR. On the other hand, the radial heat flow model predicts NR for semi-conductors and the conductivity modulation due to the radial temperature distribution causes a concentration of current-density along the axis, giving rise to the "thermal pinch" effect. For metals, this model does not predict NR and the resistivity modulation confines the current-density within a small depth from the surface giving rise to the "thermal skin effect". NR is also predicted for the model considering longitudinal heat flow with surface heat loss, the d.c. λ-K thermal theory, in semi-conductors whereas for metals, the theory does not predict NR. For the applicability of the λ-K thermal theory, the specimen must be thin enough to ensure an isothermal cross-section. The a.c. impedance of the specimen with a small a.c. voltage superimposed on the d.c. bias has been obtained for the λ-K thermal theory. Theoretical analysis shows that a non-zero surface loss parameter λ is essential for attaining NR in semiconductors. Experiments were performed with metals and semiconductors in an attempt to check the d.c. and a.c. λ-K thermal theories. Comparison of the experiments with the theory shows that for semi-conductors, the λ-K thermal theory is valid for current-density J ≤20 amps.cm-² while for metals, it is valid for J ≤5 x 10⁴ amps.cm-². The measured a.c. characteristics at both low and high frequencies are interpreted on the basis of the a.c. λ-K thermal theory but over the intermediate frequency region, the theory offers no explanation for the "circular arc" locus of impedances observed experimentally for both metals and semi-conductors. The present investigation enables one to determine the character of heat flow from measurements of the electrical characteristics of the specimen and also to distinguish the thermal effects which may be present in other experiments (e.g. on the "magnetic pinch"). / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A critical survey of the present state of the quantum statistical theory of thermal conductivity is given. Recently several attempts have been made to extend Kubo's treatment of electrical conduction to other irreversible transport processes in -which the interaction between the driving system and the system of interest is not precisely known. No completely satisfactory solution of the problems involved is contained in the literature. In this thesis, a detailed derivation of a Kubo-type formula for thermal conductivity is given, using essentially the concepts and methods of Nakajima and Mori, with no pretense that it settles the problem completely. Some general remarks are made on the evaluation of a Kubo-type expression, in particular, the use of Van Hove's master equations and the reduction of the usual N-particle formula to a single particle formula. An explicit calculation of thermal conductivity is made for the simple model of elastic electron scattering by randomly distributed, spherically symmetric impurities. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this study, topology optimisation for heat-conducting paths in a three-dimensional domain was investigated. The governing equations for the temperature distribution were solved using the finite volume method, the sensitivities of the objective function (average temperature) were solved using the adjoint method, and finally, the optimal architecture was found with the method of moving asymptotes (MMA) using a self programmed code. A two-dimensional domain was evaluated first as a validation for the code and to compare with other papers before considering a three-dimensional cubic domain. For a partial Dirichlet boundary, it was found that the converged architecture in three dimensions closely resembled the converged architectures from two dimensions, with the main branches extending to the outer corners of the domain. However, the partial Dirichlet boundary condition was not realistic, and to represent a more realistic case, a full Dirichlet boundary was also considered. In order to investigate a full Dirichlet boundary condition, the domain had to be supplied with an initial base for the architecture to allow variation in the sensitivities. It was found that the width and height of this base had a significant effect on the maximum temperature. A height of 0.04 with a base width of 0.24 proved to be the most effective, since this small base gave the MMA enough freedom to generate a tree structure. It was first assumed that this base should be in the centre of the bottom boundary and this was later proved. The results showed again that the maximum temperature decreased with an increase in the conductivity ratio or volume constraint. The architectures were similar to the partial Dirichlet boundary, again with the main branches extending to the outer corners of the domain. The main branches were thinner compared with the partial Dirichlet boundary and fewer secondary branches were observed. It was concluded that a full Dirichlet boundary could be solved using topology optimisation, if the boundary was supplied with an initial base. With the successful implementation of the full Dirichlet boundary with one initial base, multiple bases were investigated. First, two bases were used and it was assumed that the optimal placement for these bases was in the centre of each respective half of the bottom boundary, which was later confirmed. The optimal width and height of 0.24 and 0.04 respectively were again optimal for each specific base. The same procedure was followed for four bases and it was assumed that the optimal placement was in the centre of each respective quadrant of the bottom boundary, which was also later confirmed. The optimal width and height of 0.12 and 0.04 respectively were found for this case. With this established, optimisation runs for different conductivity ratios and volume constraints were completed for two and four bases. It was found that two bases offered increased performance in terms of the maximum temperature compared with one base. An increase in performance was also observed when using four bases compared with two bases. A maximum of 20.4% decrease in the maximum temperature was observed when comparing four bases with one. Keywords: topology, optimisation, conduction, three-dimensional / Dissertation (MSc)--University of Pretoria, 2014. / gm2014 / Mechanical and Aeronautical Engineering / Unrestricted

One of the basic goals in engineering is to formulate models which will provide a means for analytically predicting observed phenomenon. For some time, the partial differential equations describing the steady state and transient conduction of heat within a solid have been available. However, the straight forward use of these equations is often restricted due to the surface geometry of the solid. If the surface geometry is at all irregular, exact solutions will in general not exist. In that case, a solution is sought by some approximate numerical technique. The two techniques most often used are the finite difference method and the finite element method. The finite difference method is fairly simple to understand, but is difficult to apply to a problem with irregular boundaries. On the other hand, it is not a trivial matter to completely understand the finite element method, although it can handle irregular boundaries with greater ease than the finite difference method. To bridge the gap between these two methods, a third method is developed in this work which has the simplicity of the finite difference method, and can handle irregular boundaries with the ease of the finite element method.

Thermocouples are generally used as devices to determine the internal temperature of any material. The purpose of the temperature measuring device is to measure the temperature which would exist at some known location if the device were not present. The thermocouples are embedded in the material in order to study the temperature-time history of the point of location. The presence of the thermocouple induces error in the temperature measured. This error becomes significant if heat is conducted into or away from the point of measurement by the sensor itself, or if the sensor insulates the point. This would result from much larger thermal conductivity of the thermocouple assembly than the surrounding material. This error in the temperature measurement will be called "conduction error."