Technological advances in integrated circuits have resulted in sizeable increases in density of electronic components. As a result, much greater amounts of memory are available for product developers. One major problem which is a by-product of the advances in computing power, is a very large increase in heat load. For example, the heat flux at the chip level on IBM mainframes has increased by over an order of magnitude compared to the early IBM 303X mainframes. The performance of the electronic components is very much related to temperature values in the components. If the maximum temperature exceeds some value (typically 85° C), a severe degradation in performance will result. Consequently, heat transfer is playing an ever increasing role in packaging technology.

The presentation will begin with a brief background of cooling challenges in IBM high end systems. This is followed by a presentation on an integrated approach for modeling of thermal problems related to electronic cooling. In particular, the use of an interface program that enables the extraction of mechanical related information (geometry, material property, ..) from a 2D circuit board design resulting in an automatic creation of 3D CATIA(1) solid models is presented. The required CFD model is then constructed in CATIA using a special function key developed jointly with Vimba (1991). The rest of the presentation will focus on applications of CFD to electronic packages, and will conclude by highlighting some of the CFD challenges that are of special interest to applied mathematicians.

The first problem is the solution to a system-level benchmark problem in electronics cooling consisting of a box with covers, floppy drive, hard file, power supply, planar, fans, feature cards and Single In-line Memory Modules (SIMM's) is described. The benchmark problem, proposed in an earlier paper (joint work with Linton), is solved using an integrated solid model based pre-processor coupled with a commercially available Computational Fluid Dynamics (CFD) package.

The second problem is the computation of the internal resistance of a TCM. A numerical model of an entire TCM module (without resorting to symmetry conditions) is presented. The model includes a 10 x 10 array of pistons, and a h All the chips (10 x 10) are included in the model by u thermocoupling technique to introduce the interface resistance between the chip and the piston. This is joint work with Free.

The third problem is a conjugate model of a 9 x 9 pinned fin heat sink for both parallel and impinging flow. The conduction problem is solved using a network model, and the convection problem is solved using a Finite Control Volume (FCV) technique. This is also joint work with Free.

The last problem is a turbulent modeling challenge in electronic cooling applications. Most of the flow regimes in electronic cooling lie in the transitional regime. A number of investigators have used the k- model; unfortunately, the model is best suited for much higher Reynolds numbers. The low-Reynolds number version of the k- model, employing damping functions on the k and equations, has been widely used for resolving the low-velocity near-wall region but requires a high computational time which makes it impractical. In this last section, the use of LVEL (a scheme that requires a knowledge only of the wall distances and the local velocities) is described. The model performs as well as the older Lam-Bremhorst-Yap and 2-layer-k- models, but is considerably less computationally expensive. This is joint work with Gan-Li and Spalding.

The talk will conclude by summarizing some of the challenges in CFD applications in electronic systems which could be of interest to applied mathematicians.

1996-1997 Mathematics in High Performance Computing