Predictions of shape and temperature for heating elements in an electronic package by inverse heat transfer method

The aim of this study is to present a novel inverse heat transfer method, which incorporates an automatic-filter scheme with the conjugate gradient method, for identifying shapes and temperature of heating elements embedded in a rectangular package. In this report, shapes of the heating elements are visualized by using node-matrix images. A group of unknown heating elements with different shapes, positions, and temperatures are nondestructively identified simply based on the data of the upper surface temperature of the rectangular package. Effects of temperature measurement uncertainty, grid size, and number of measurement points on the top surface on the identification accuracy are evaluated. Results show that the geometric and thermal conditions of the heating elements embedded can be predicted precisely by using the present approach. The approach is found to be stable and insensitive to the temperature measurement uncertainty, and without overwhelming mathematical manipulation, the form of objective function becomes flexible.