Prediction of Device Temperatures with Depth-Averaged Models of the Flow Field over Printed Circuit Boards

Introduction Prediction of Device Temperatures with Depth-Averaged Models of the Flow Field over Printed Circuit Boards Convective heat transfer from electronic devices mounted on a printed circuit board is simulated with an efficient Computational Fluid Dynamics (CFD) model. The computer time necessary to calculate a solution to the flow field is greatly reduced by solving the depthaveraged (DA) flow equations for the fluid flowing above the devices. The DA flow field is then coupled to the full, three-dimensional energy equation in the fluid and in the solid materials comprising the circuit board and the electronic devices. Because the temperature is determined by solving the conjugate problem, no heat transfer coefficient needs to be specified on the outer surface of the devices. This paper provides an overview of the theory behind the depth-averaged and three-dimensional energy equation models. Incorporation of the essentially two-dimensional depth-averaged flow fields in the three-dimensional energy equation is described. The combination of the DA flow field and the three-dimensional energy equation does not yield the same level of detail as a conventional threedimensional CFD code. The advantage of this approach, however, is that it makes significantly lower demands on the computational hardware and it obtains useful solutions in much less time than conventional CFD codes. Technological advances in semiconductor electronics have produced computer components with increasing sophistication and increasing numbers of transistors per component. An unwanted consequence of higher circuit density is an increase in the power dissipation rate per unit volume for the individual components and for the computer cabinet in which they are housed. As a result thermal management of electronic components and electronic enclosures has become an integral part of electronic equipment design. The topological complexity of electronic equipment makes it difficult to apply the results of classic theoretical and experimental studies to the details of thermal problems in electronic packaging. A single board is placed in a cabinet that forms complex flow passages, which can be changed as optional cards are added or removed. Circuit boards are assembled from small devices having varying sizes and shapes. Though there is a trend toward fewer, larger packages, circuit boards still have a geometric complexity far beyond that found in the classical problems of convective heat transfer. To address this gap in information many studies have been performed for the geometry and flow regimes found in electronic equipment. Moffat and Ortega (1988) survey a broad range of experimental data applicable to circuit board analysis. Given an adiabatic heat transfer coefficient and the thermal wake function one can estimate the average temperature of an electronic device with relatively simple calculations. The utility of this approach has been demonstrated by comparison with detailed computer modeling (Anderson, 1994). The intense competition and short product design cycles in the computer industry require that packaging engineers find design solutions quickly. This pressure has resulted in the development and use of computer-based design tools. Thermal network methods have been used to create models of varying detail and complexity. This technique can be used to simulate the internal details of a single component, or an entire computer cabinet. Ellison (1989) describes net-