electronics cooling magazine recently posted an article by richard sampson that references previous work on the topic by the by the author for the american society of mechanical engineers (asme) in 2005, which argues against the use of volume-weighted, effective thermal conductivity in thermal modeling of a pcb because of the errors in pcb temperature that could result.

this article argues against using effective thermal conductivity in thermal modeling
of pcb. (wikimedia commons)

sampson explained, “a common feature of the thermal analysis of electronic equipment is the complexity of the heat flow paths in the hardware. nowhere is this more evident than the printed circuit board, where the multiple layers of complex trace patterns present a daunting thermal modeling task.”

he added, “since the traces are important heat transfer paths, which cannot be ignored in the thermal design, analysts have resorted to a procedure in which volume weighting of the trace and board thermal conductivities is used to define a volume weighted, effective thermal conductivity, k_vw.”

this process is called “smearing” and sampson argues that there is an “inherent inaccuracy” in this process and with assumptions about thermal conductivity values.

“modeling errors can also occur wherever there are regions of a pcb that are predominantly board material,” he continued. “the use of an effective conductivity such as the above value of 40 w/m-c, instead of a typical board conductivity of 0.59 w/m-c, in the calculation of heat flow across these regions is unrealistic.”

rather than using effective thermal conductivity, sampson outlines new methods that can be more useful for thermal engineers.

he concluded, “a related procedure is proposed that allows the analyst to employ an fdm (finite difference model) to compute an effective thermal conductivity, k_eff, that is more accurate than the volume weighted, effective  conductivity, k_vw. this effective conductivity can then be used in an fem (finite element model) to compute board temperatures and perform parametric studies. this approach takes advantage of the strong points of both fdm and fem.”

read sampon’s full article for electronics cooling at https://www.electronics-cooling.com/2017/04/problem-effective-thermal-conductivity.

also, read his paper for the asme from 2005 at http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1576709.