Inverse Model for Predicting Thermal Abnormality of the Transient Process Triggered by Defective Electronics Element - A. Dantsker; W. Pryor; J. Brito (International Journal of Energy and Thermal Applications, 2025)
The paper presents a model for predicting thermal abnormalities in Printed Circuit Boards (PCBs) by approximating the thermal process of electric elements with heating from point sources. Circuit board heat sources are defined as point and non-point. The point heat source is a small electronic heating element that can be approximated as having originated from one point on the circuit board. A non-point source is one with heat distributed over a large area of the electronic board. The non-point heat source is approximated with a set of point sources with distances that guarantee the accuracy with such replacement. This approximation allows the tshermal process to be defined from the set of arbitrary heat elements. The mathematical expression for heat exchange from such a set of point heat sources is provided. The downside of the proposed algorithm is an increase the complexity of the algorithm by raising the number of point sources. Future research directions for algorithm optimization, such as analytical methods for defining the level of discretization of continuous heat sources, are covered. Another promising direction reveals using the theory of hypernumber for solving heat exchange partial differential equation with a small amount of non-point sources approximation for sequential hypernumber solution. The adaptive event approach is used to compute the intensity of internal heat from the electronic element in the inverse engineering of the thermal process. The adaptive approach includes the minimization of the sum of the squared differences between the theoretical direct model and the temperatures identified from the infrared image for the corresponding points. The direct model for calculating the transient thermal process from multiple heating elements uses the Green function theory. The intensities of the heat sources are computed using linear matrix equations. Before simulation, the hot spots are identified by calculating the temperature gradient over time. The gradient that would exceed the defined threshold is the condition for defining the heat source parameters with an inverse model and simulating the prediction of the temperatures. The proposed mathematical approach can be used for electronics circuit board design to minimize the size of the board by solving the optimization problem of not exceeding the defined maximum temperature.
Keywords: Point heat source; green function; hypernumber; inverse model; least square