Thermal modeling of multi-shape heating sources on n-layer electronic board

Abstract

The present work completes the toolbox of analytical solutions that deal with resolving steady-state temperatures of a multi-layered structure heated by one or many heat sources. The problematic of heating sources having non-rectangular shapes is addressed to enlarge the capability of analytical approaches. Moreover, various heating sources could be located on the external surfaces of the sandwiched layers as well as embedded at interface of its constitutive layers. To demonstrate its relevance, the updated analytical solution has been compared with numerical simulations on the case of a multi-layered electronic board submitted to a set of heating source configurations. The comparison shows a high agreement between analytical and numerical calculations to predict the centroid and average temperatures. The promoted analytical approach establishes a kit of practical expressions, easy to implement, which would be cumulated, using superposition principle, to help electronic designers to early detect component or board temperatures beyond manufacturer limit. The ability to eliminate bad concept candidates with a minimum of set-up, relevant assumptions and low computation time can be easily achieved.