Predicting Thermal Stresses Induced by Conjugate Heat Transfer

Thermal stresses developed in electronic systems mainly depend, not only on average temperature values, but rather on wall temperature profiles. These profiles are difficult to predict unless one uses detailed finite element or finite difference modeling and simulation techniques. This type of analysis is only suitable at final design phases were geometrical details are available or being finalized. It is not suitable at early design phases to get a rapid estimate of wall thermal gradients to orient design appropriately. Standard approaches involving correlations for the heat transfer coefficient fail to predict temperature profiles for many reasons. In fact, these correlations depend on temperature profile as an input. In most engineering applications, walls are neither infinitely conducting nor of negligible conductivity to justify the usage of either uniform temperature or uniform heat flux assumptions. Correlations addressing conjugate heat transfer would not be able to solve the problem, unless a large number of them were available covering all possible combinations of fluid and wall conditions. Besides, the case of multiple heat sources, quite common in modern systems, can never be correctly handled by such an approach. The flexible profile technology was proposed earlier to model heat transfer in either solids (conduction) or fluids (forced convection. The model depends on domain (fluid or solid) geometry and physical properties, regardless of the particular set of applied boundary conditions, including that of multiple heat sources. Combining a fluid flexible profile model with a solid one, will allow predicting wall temperature profiles, with an adjustable level of precision, depending on the number of degrees of freedom retained. It will be applied in this paper to predict thermally induced stresses in some simple test cases as a demonstrator of the potentials behind this approach.