Heat Transfer From a Finned Surface in Ducted Air Jet Suction and Impingement

Comparing the assumptions of Models #1 and #3, we can see that the level of accounting for the three-dimensional nature of PTH is identical. The material properties in both models are assumed to be temperature-dependent and dependent on the stress levels. There are some insignificant differences. For example, the Model #3 accounts for a variable barrel thickness, whereas the Model #1 assumes that the barrel thickness is constant for the entire PTH barrel. Without any complications, both models can be developed in an identical manner. This is true as far as both models are axisymmetric. Of course, the FE method has the advantage to consider the general 3D elements what in the closed-form solution would be very cumbersome. This fact, however, does not relate to the comparison of Models #1 and #3. Comparing Figs. 1‐3 with cross-sections of actual PTH’s ~Fig. 4!, we can see that application of FE method does not bring the model geometry closer to the real structure. The material properties used in FE model are those typically used in the microelectronic industry. For example, the barrel-copper properties are taken from the tests of board layer plating—though there exists evidence that these coppers may have significantly different properties, as well as the properties of plated copper may vary in the range of 650 percent ~Safranek @5#!. In addition to this indefiniteness in the geometry and material properties, it is known for such FE multimaterial models that there is a high mesh sensitivity of the numerical results. Therefore, we cannot consider the FE model’s quantitative results to be highly accurate. High dependence of the failure indicators ~maximum equivalent plastic strains! on many geometrical and material parameters of the structure makes it impossible to generalize conclusions derived from one pilot set of results to all PTH structures. These limitations of the FE method must be taken into consideration when a tool for the stress analysis of a microelectronic structure is chosen. Exchange of opinions on these issues would be very useful for our engineering community. References @1# Orringer, O. and Tong, P., 1984, ‘‘Uses and abuses of the finite element method,’’ Proceedings of SPIE, the International Society for Optical Engineering, Vol. 450, Bellingham, Washington, DC, pp. 2‐33. @2# Subbarayan, G., Ramakrishna, K., and Sammakia, B. G., 1997, ‘‘The Impact of Interfacial Adhesion on PTH and Via Stress State,’’ ASME J. Electron. Packag., 119, pp. 260‐267. @3# Engelmaier, W., 1988, ‘‘Plated Through Hole Failures in Thermal Cycling: Analytical Considerations,’’ Technical Report IPC-TR-579, Lincolnwood, IL. @4# Mirman, B., 1988, ‘‘Mathematical Model of a Plated-Through Hole under a