Date of Award

Spring 2004

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Weizhong Dai


Heat transport at the microscale is the subject of intense investigation due to the growing need to fabricate microstructures for applications in nanotechnology. The need to control the spread of the thermal process zone has led to the development of high power short-pulse lasers. During thermal processing, impurities may form in the material. An amplification of the thermal energy around the impurities may result in severe damage occurring or in the failure of the thermal process. A thorough analysis of the way the impurities dissipates the thermal energy is therefore necessary to minimize the potential damage and optimize the thermal processing.

The classical theory of heat diffusion, which is averaged over many grains, is inadequate in describing the transport phenomenon. Single energy equations developed to describe the transport phenomenon include a third-order mixed derivative with respect to space which makes them numerically inefficient. In this study, we will consider a microsphere subjected to an ultrafast laser pulse. The transport phenomenon is modeled by the two-step parabolic heat transport equations in three dimensional spherical coordinates. We will develop an energy estimate to establish the well-posedness of the problem, a three-level finite difference scheme to solve the transport equations, and prove that the finite difference scheme is unconditionally stable. The scheme will be applied to investigate the temperature rise in a gold sphere subjected to a short-pulse laser.