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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

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."