Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, Italyany specific hierarchical heterostructure with the aim tooptimize its performance. Development of VAT for thedescription of transport phenomena in heterogeneous mediawill be applied to optimization of heat dissipation from aheterogeneous media. The media is an unspecified porous(heterogeneous) layer and the optimization process isaccomplished with rigor using the idea of scaled energytransport. The enhancement of heat transport is statedmathematically in a way that the lower scale conventionalmicro channel transport enhancement and the performance ofthe total device are incorporated for optimization.In earlier work by Travkin and Catton (1998, 2001) andGratton et al. (1996) a procedure to optimize a semiconductorheat sink design was developed. Optimal control variables forheat sink design are generated from VAT equations andcontrolled by VAT equations. The variable design parametersare constrained between upper and lower bounds due tophysical limitations. Computer aided numerical simulation cannot yet replace experimental work, but with the aid ofcomputer calculations micro channel design can be focused onachieving recommended optimum properties. Modelcalculations can be used to examine the sensitivity of porousmedia performance to key performance parameters.Global optimization over continuous spaces is oftenneeded in scientific research and systems optimization. Thereare a number of possibilities for the investigation ofoptimization strategies (DE, DOE, Gur, etc). Typically, thetask is to optimize certain properties of a system by choosingand addressing appropriate system parameters. When the costfunction is nonlinear and non-differentiable, the methods ofchoice are often direct search approaches. The general strategyin direct search methods is to generate variations in theparameter vector and a decision is made to accept or deny thenewly derived parameters. Most standard direct searchmethods use the greedy criterion to make decisions such that anew parameter vector is accepted if it has an improved costfunction. The basic approach to a stochastic search is the hillclimbingprocedure in which a random location is picked tobegin and the location is moved to its neighboring positionwith a better evaluation value. Although this providesconvergence fairly quickly, these algorithms run the risk ofbeing trapped in a local maximum. On the other hand, parallelsearch techniques have built-in safeguards againstmisconvergence by running several vectors simultaneously.We will use Design of Experiments (DoE), a methodologyon how to conduct and plan experiments in order to extract themaximum amount of information in the fewest number ofruns. It is a time tested approach with a known outcome. DoEis a structured, organized method for determining therelationship between factors affecting a process and the outputof that process. After screening, the goal of the investigation isusually to create a valid map of the experimental domain(local space) given by the significant factors and their ranges.This is done with a quadratic polynomial model. The higherorder models have an increased complexity and therefore alsorequire more experiments than screening designs. After theplanning stage, when the set of experiments are laid outaccording to a statistical design, the planned experiments aremade, either in parallel, or one after another. Each experimentgives results, i.e. values of the response variables. Thereafter,these data are analysed by means of multiple regression, orgeneralizations thereof such as PLS and O-PLS. This gives amodel relating the factors to the results, showing which factorsare important, and how they combine in influencing theresults. The model is then used to make predictions, e.g. howto set the factors to achieve desired (optimal) results.Information about the DoE commercial code that we used canbe found at the URL: http://www.smatrix.com/fusion-pro.htmlVAT Based Conservation EquationsAn important feature of VAT is being able to considerspecific medium types and morphologies, lower-scalefluctuations of variables (temperature, velocity and pressure),cross-effects of different variable, and interface variablefluctuations effects. Another important feature of VAT ispassing thermal physical information through different scalesin hierarchical manner, starting form the lowest scale andending with the macro scale. It is not possible to include all ofthese characteristics in current models using conventionaltheoretical approaches. The VAT approach has the followingdesirable features:1. Effects of interfaces and boundaries can be includedin the modeling.2. The effect of morphology of the different phases(solid, liquid and vapor) are incorporated. Themorphology description is directly incorporated intothe integro-differential field equations.3. Separate and combined fields and their interactionsare described described exactly through the integralterms appearing in the field equations. Noassumptions about effective transport coefficents arerequired.4. Effective coefficients correct mathematicaldescription - those "theories" used right now for thatpurpose, are only approximate descriptions - oftensimply wrong.5. Deliberate design and optimization of materials usinghierarchical physical descriptions based on the VATgoverning equations can be used to connectproperties and morphological characteristics to heatexchanger features.The governing equations used in the analysis are thevolume averaged momentum and energy equations describingtransport phenomena within and between the fluid and solidphase (Travkin and Catton, 2001). The averaged turbulentmomentum equation is©EDA Publishing/THERMINIC 2008 178ISBN: 978-2-35500-008-9