Optimal package design of stacks of convection-cooled printed circuit boards using entropy generation minimization method

Thermal optimization of a stack of printed circuit boards using entropy generation minimization (EGM) method is presented. The study consists of two parts. One is focused on the entropy generation of a module in periodically fully-developed channel flow (PDF), while the other is the optimization applied to electronic packages composed of a stack of printed circuit boards. In the process of optimizing electronics packaging, consideration is given to two constraints which are the maximum junction temperature specified by a chip manufacturer and the allowable pressure difference across the channel maintained by cooling fans. Governing thermal-fluid flow equations in the laminar-flow regime are numerically integrated subject to the appropriate boundary conditions. After the flow and temperature fields are solved, the volumetric rate of local entropy generation in the PDF is integrated to determine the total entropy generation rate in the system which consists of two components, one by heat transfer and the other by viscous friction. The Reynolds number, block geometry and bypass flow area ratio are varied to search for an optimal channel spacing using the EGM method whose validity is borne out by comparing with those obtained by the conventional thermal optimization (or overall thermal conductance) method. A dimensionless optimal board spacing parameter C is derived which involves the relative migration speed (or time) of heat transfer and viscous friction over the PDF channel length. A correlation equation is derived which expresses C in terms of the Reynolds number and block geometry. This equation can be employed in the optimal design of electronic packages.