Transient coupled thermal/electrical analysis of a printed wiring board

The impact of coupling of the thermal and electrical solutions for a given circuit board is demonstrated to be important for the accurate prediction of temperature profiles. The significance of this has been demonstrated in numerous real life cases and the coupled solution has been shown to be a much better representation of the actual observed numbers in every instance. This paper presents a numerical investigation of transient and steady-state heat transfer in a multilayered printed wiring board (PWB) where heat is dissipated as a result of flow of electrical current in various areas in the board. The numerical model consists of a six-layer PWB with eight capacitors on each side of the board. Electrical current enters the board through "load" terminal blocks and leaves the board through "return" terminal blocks. The load layers and the return layers are electrically and thermally connected using "vias". The transient solution is performed for two minutes in order to examine a "worst case" condition for the given configuration. In these types of applications, the heat dissipation distribution is not known prior to the solution and must be evaluated by simultaneously solving the electrical field. This is accomplished through a "coupled electrical/thermal solution" scheme, where the voltage field is solved throughout the region knowing electrical loads and boundary conditions (in addition to thermal and flow fields) during each iteration. The most recent temperature field is used to update the electrical resistivity of the conductors in the model. The power dissipation is then calculated for all elements. For an element in a Cartesian coordinate system the power dissipation as a result of Joulian heating is given by: P_Element=(Δo_x)²/R_x+(Δo_y)²/R_y+(Δo_z)²/R _z where Rx, R_y and R_z are resistance x, y and z directions.