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7-9 October 2009, Leuven, Belgium Temperature as a First-Class Citizen in Chip Design Sachin S. Sapatnekar University of Minnesota, USA Abstract- With new technology trends, arising through a confluence of factors such as Moore's law scaling and 3D integration, the role of thermal design is inexorably shifting from package-centric issues towards on-chip optimizations. This talk overviews the roots of this change, the circuit effects of elevated temperatures, and on-chip optimizations for effective thermal management. Text unavailable at the time of printing. ©EDA Publishing/THERMINIC 2009 1 ISBN: 978-2-35500-010-2
7-9 October 2009, Leuven, Belgium Toward a Rational Modeling of Convection M. N. Sabry French University in Egypt, Shourouk, EGYPT Present address: Mansoura University, Mansoura, EGYPT, Abstract - The thermal design of huge systems, huge in terms of number of components not their size, enforces the usage of dedicated SW packages in which each component needs to be modeled adequately. Detailed 3D modeling is not possible at early design phases. An adequate compact thermal model (i.e. one with very few degrees of freedom) of each component should be used instead. It must be cast in a form that makes it usable in SW packages, to model the behavior of each component regardless of surrounding objects. This fact has long been recognized for thermal conduction problems, which was solved using the socalled Boundary Condition Independent (BCI) models. For convection, the model universally admitted is that of the Heat Transfer Coefficient (HTC), which is obviously not BCI. It can always be used for small systems using a spread sheet that will have to be manually readapted for each new system topology. For large systems, automated BCI model generation is mandatory, which is the objective of this work. In this work, a new approach is proposed that generalizes achievements in building BCI compact models for thermal conduction to thermal convection. It offers many advantages over classical HTC models, including in particular its ability to handle conjugate heat transfer problems in a much more accurate, although a bit more involved, way. The level of complexity remains orders of magnitude less than full 3D analysis, which makes the proposed approach adapted for preliminary design phases. I. INTRODUCTION Heat Transfer Coefficient (HTC) by convection has been used since more than a century with success by engineers worldwide to address practical problems and get rapidly an estimate allowing them to take adequate engineering decisions. The alternative would have been either to do costly experiments or time consuming detailed calculations which are either unavailable or undesirable at early design phases. They can be unavailable if for instance the supplier does not wish to reveal details under intellectual property rights. They are undesirable because of the large amount of data and CPU time that have to be supplied, while design main features are not yet set. The success of HTC modeling approach is in part due to the backing of a rigorous similarity theorem extending the validity of a relatively small set of experimental results to a significantly wider range of applications. When designing systems containing a huge number of components, dedicated SW packages should be used. This will require a model describing overall component behavior in a simple way, i.e. with very few degrees of freedom, which will be called here a compact model. A mandatory property of such models is to describe component physical behavior, i.e. its intrinsic flux-potential relation, regardless of neighboring objects nature. This property has long been recognized for thermal conduction, under the name of Boundary Conditions Independence (BCI). Models not satisfying this condition are useless in large system simulation unless we provide a whole set of models, one for each possible combination, which is obviously not adequate. In hand, or spread sheet assisted, calculations of rather small systems, thermal engineers have sufficient experience to build adequate models for each topology. These models will have to be revised for different topologies (see below) which is obviously not adequate for automated calculations of large systems. In the next section it will be shown why the concept of HTC fails to satisfy the BCI condition and what are the consequences. In fact, the apparent simplicity of HTC is both one of the main reasons of its success as well as its weaknesses. Discrepancies of the order of a factor of 4 or more were reported between different experimental results by different research teams for the same geometry and under seemingly the same conditions. Discrepancies are so frequent and so important that they cannot be simply explained by noncareful experimental measurements of all teams other than my own team! What if there was a fundamental reason behind them What if the concept of HTC was too simplistic to be an adequate model even for rough calculations of a precision of say 50-100% In this work, a suggested generalization of the BCI approach used earlier for thermal conduction to thermal convection problems will also be presented, starting from basic principles through a careful analysis of assumptions needed to reach the well known equation named ‘Newton’s law of cooling’ (although Newton can claim innocence because he never postulated it!): Q = h A (T w – T f ) (1.1) where Q is the heat transfer rate, T w and T f are respectively ‘representative’ wall and fluid temperatures, A is the area across which heat flows and finally h is our HTC. II. GENERAL FEATURES IMPLIED BY PHYSICS The starting point would be the governing partial differential equations. Only forced convection with uniform physical properties will be considered in order to keep the problem linear. Since the objective is fundamental, to understand why a given modeling approach is better than the other, and since convection is a sufficiently complicated physical phenomenon, ©EDA Publishing/THERMINIC 2009 2 ISBN: 978-2-35500-010-2
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