An inverse heat conduction-convection conjugated problem in estimating the unknown volumetric heat generation of an encapsulated chip

Abstract

A three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP) is investigated in this work. The goal is to estimate the unknown spatially dependent volumetric heat generation of an encapsulated chip. The functional form of the volumetric heat generation is considered to be unknown prior to the estimation. Therefore, it is known as the category of function estimation in inverse problems. Optimization is performed using the conjugate gradient method (CGM) because this method does not require a priori information regarding the functional form of the unknown functions. Using this method, a large number of unknowns can be corrected and estimated in each iteration, and good estimations can always be obtained. This efficient algorithm has never been applied to the IHCCCP. The results of the inverse estimations are verified using numerical simulations with various inlet air velocities and measurement errors. They reveal that using exact measurements always produces accurate volumetric heat generation and that the regular air velocity does not affect the estimates. The measurement errors and their influence on the estimated heat generation are analyzed. Finally, it is concluded that because the inverse problem is ill-posed, the estimated heat generation becomes less accurate as the measurement error increases.