D. de Cogan

Sub-surface feature location and identification using inverse TLM techniques

This paper describes several techniques involving transmission line matrix modelling which can be used to locate and characterize inhomogeneous features within a circuit package where the thermal response to heating of the underside is inspected at the top surface. These are used to confirm a semi-empirical thermal non-destructive testing approach to the determination of the lateral dimensions of a feature. The time to maximum contrast is an important parameter which can be used to estimate the depth of the same feature. This paper then describes our approach to the determination of feature thermal parameters and the influence of measurement noise on overall accuracy of the estimate.

The relationship between parabolic and hyperbolic transmission line matrix models for heat-flow

Abstract Transmission line matrix (TLM) algorithms for lossy electrical network provide a solution for the telegraphers equation. In spite of the fact that these constitute a lossy wave equation analogue, they have been successfully used to model thermal problems. This paper discusses the relationship between the hyperbolic and parabolic formulations and shows how TLM can be successfully applied in both regimes.

INVERSE THERMAL MODELING USING TLM

Transmission line matrix (TLM) is a discrete numerical time-domain modeling technique that can frequently be reduced to a closed-form solution of the diffusion equation. In many cases the inverse operation of the TLM method is hampered by the imbalance between the number of available equations and the number of unknowns. This article outlines the nature of the problem for Gaussian temperature profiles and shows how simple optimization can be used to obtain initial or early-time thermal information.

TLM modelling of thermal processes in magneto-optic multi-layered media

This paper introduces the application of the transmission line matrix (TLM) method for simulating thermal effects in magneto-optic multi-layers irradiated with a Gaussian laser beam. A model using linear heating compares favourably with an accepted semi-analytical treatment. Comparison with available experimental data suggests that thin film media of this type display a temperature-dependent, thermal conductivity. Simulations involving nonlinear heat flow have also been performed. Because there are no equivalent experimental data available for comparison, a series of tests with hypothetical data was undertaken. The results underline the urgent need for experimental measurements of the temperature-dependence of thermal conductivity in these materials.

DISCRETE MODELS OF HEAT FLOW IN LAYERED MATERIALS USING SIMPLE AND CORRELATED RANDOM WALKS

The paper reviews some discrete probabilistic numerical techniques with particular emphasis on heat flow in inhomogeneous materials. The effects of different nodal configurations on the development of suitable algorithms are outlined and we suggest a new and consistent description for the discrete apparent effusivity. Our approach is then discussed in the context of TLM, and analogues are presented for flux relaxation time and effusivity.

IMPEDANCE TRANSFORMATIONS AND MESH COARSENING IN TLM HEAT FLOW MODELING

Numerical models of multimaterial systems are often constrained by stiffness factors, which impede numerical efficiency. Thus, heat flow simulations in problems involving widely different thermal time constants can require excessively fine meshes, extremely small iteration time steps, or both. The transmission line matrix method is an unconditionally stable technique that uses a network of impedances and resistances to model thermal diffusion, This paper outlines a method by which these parameters can be transformed as a means of improving computational efficiency while maintaining compatibility with microscopic models.

An equivalent circuit for the analysis of transmission line matrix (TLM) scattering algorithms

The transmission line matrix (TLM) method is a technique which is widely used for modelling physical phenomena. This paper outlines an equivalent-circuit model based on the superposition of current and voltage source contributions.