Challenges for first-principles methods in theoretical and computational physics: multiple excitations in many-electrons systems and the Aharonov-Bohm effect in carbon nanotubes
The objective of this research is to understand the temperature variation in dielectric materials of different geometry. The work is divided into three major segments. The Thermal Wave model has been taken into consideration as the classical Fourier law of heat conduction breaks down when a dielectric material of sub-micron geometry is heated rapidly. The first part of the work discusses primarily about the temperature distribution in a semi-infinite dielectric material, followed by the temperature profile in a finite body (plate) and finally mathematical formulation is presented for a two-layered body. The thermal wave equation is used because in dielectric materials the lag time due to temperature (taut) is much less than the lag time due to heat flux (tauq), ( taut <<tauq) and hence all the terms describing the effects of taut in the governing equation used for expressing the phenomena of Hyperbolic Heat Conduction in a material can be neglected. Boundary conditions of first and second kind are applied to the thermal wave equation for all three cases that are discussed later in the study. The classical Laplace Transform method has been used as a tool to analyze the mathematical models for all the illustrations presented in the study. Analytical solutions are obtained for semi-infinite and finite bodies for different boundary conditions and a mathematical formulation has been presented to calculate the heat flux at the interface for a two-layered dielectric body. Due to large complexity of the problem and intense use of algebra several Mathematica subroutines are developed to compute and examine the thermal behavior of dielectric materials during rapid heating.
- Pub Date:
- Engineering, Mechanical;Physics, High Temperature;
- Condensed Matter - Strongly Correlated Electrons;
- Condensed Matter - Mesoscale and Nanoscale Physics
- PhD thesis. http://phd.fisica.unimi.it