# 3D Inverse Heat Transfer Methodologies for Microelectronic and Gas Turbine Applications

The objective of this doctoral research was to develop a versatile inverse heat transfer approach, that would enable the solution of small scale problems present in microelectronics, as well as the analysis of the complex heat flux in turbines. An inverse method is a mathematical approach which allows the resolution of problems starting from the solution. In a direct problem, the boundary conditions are given, and using the governing physics principles and equations you can calculate the solution or physical effect. In an inverse method, the solution is provided and through the physical equations, the boundary conditions can be determined. Therefore, the inverse method applied to heat transfer means that we know the variation of temperature (effect) over time and space. With the temperature input, the geometry, thermal properties of the test article and the heat diffusion equation, we can compute the spatially- and temporally-varying heat flux that generated the temperature map.

This doctoral dissertation develops two inverse methodologies: (1) an optimization methodology based on the conjugate gradient method and (2) a function specification method combined with a regularization technique, which is less robust but much faster. We implement these methodologies with commercial codes for solving conductive heat transfer with COMSOL and for conjugate heat transfer with ANSYS Fluent.

The goal is not only the development of the methods but also the validation of the techniques in two different fields with a common purpose: quantifying heat dissipation. The inverse methods were applied in the micro-scale to the dissipation of heat in microelectronics and in the macro-scale to the gas turbine engines.

In microelectronics, we performed numerical and experimental studies of the two developed inverse methodologies. The intent was to predict where heat is being dissipated and localized hot spots inside of the chip from limited measurements of the temperature outside of the chip. Here, infrared thermography of the chip surface is the input to the inverse methods leveraging thermal model of the chip. Furthermore, we combined the inverse methodology with a Kriging interpolation technique with genetic algorithm optimization to optimize the location and number of the temperature sensors inside of the chip required to accurately predict the thermal behavior of the microchip at each moment of time and everywhere.

In the application for gas turbine engines, the inverse method can be useful to detect or predict the conditions inside of the turbine by taking measurements in the outer casing. Therefore, the objective is the experimental validation of the technique in a wind tunnel especially designed with optical access for non-contact measurement techniques. We measured the temperature of the outer casing of the turbine rotor with an infrared camera and surface temperature sensors and this information is the input of the two methodologies developed in order to predict which the heat flux through the turbine casing. A new facility, specifically, an annular turbine cascade, was designed to be able to measure the relative frame of the rotor from the absolute frame. In order to get valuable data of the heat flux in a real engine, we need to replicate the Mach, Reynolds, and temperature ratios between fluid and solid. Therefore, the facility can reproduce a large range of pressures and flow temperatures. Because some regions of interest are not accessible, this researchprovides a significant benefit for understanding the system performance from limited data. With inverse methods, we can measure the outside of objects and provide an accurate prediction of the behavior of the complete system. This information is relevant not only for new designs of gas turbines or microchips, but also for old designs where due to lack of prevision there are not enough sensors to monitor the thermal behavior of the studied system.