Resistance network-based thermal conductivity model for metal foams

A network model for the estimation of effective thermal conductivity of open-celled metal foams is pre-sented. A nodal network representation of three aluminum foam samples from DUOCEL – 10 ppi, 20 ppi and 40 ppi – is constructed out of X-ray microtomography data obtained by computed tomography (CT) scanning of the samples using a commercial CT scanner. Image processing and 3D skeletonization are performed with commercially available image processing software. The effective thermal conductivity is estimated through a 1D conduction model, representing individual ligaments as an effective thermal resistance using the topological information from the scan data. The effective thermal conductivity data thus obtained are compared with the Lemlich theory and other pore-based models. Further, microstruc-tural characterization of foam features – pore size, ligament thickness, ligament length and pore shapes – is performed. All the three foam samples are observed to have similar pore shapes and volumetric poros-ity, while the other features scale with the pore size. For a given porosity the computed permeability is found to scale as the square of the pore diameter, as also noted by previous researchers

Simulated Microstructural Evolution and Design of Porous Sintered Wicks

Porous structures formed by sintering of powders, which involves material-bonding under the application of heat, are commonly employed as capillary wicks in two-phase heat transport devices such as heat pipes. These sintered wicks are often fabricated in an ad hoc manner, and their microstructure is not optimized for fluid and thermal performance. Understanding the role of sintering kinetics-and the resulting microstructural evolution-on wick transport properties is important for fabrication of structures with optimal performance. A cellular automaton model is developed in this work for predicting microstructural evolution during sintering. The model, which determines mass transport during sintering based on curvature gradients in digital images, is first verified against benchmark cases, such as the evolution of a square shape into an areapreserving circle. The model is then employed to predict the sintering dynamics of a sideby-side, two-particle configuration conventionally used for the study of sintering. Results from previously published studies on sintering of cylindrical wires are used for validation. Randomly packed multiparticle configurations are then considered in two and three dimensions. Sintering kinetics are described by the relative change in overall surface area of the compact compared to the initial random packing. The effect of sintering parameters, particle size, and porosity on fundamental transport properties, viz., effective thermal conductivity and permeability, is analyzed. The effective thermal conductivity increases monotonically as either the sintering time or temperature is increased. Permeability is observed to increase with particle size and porosity. As sintering progresses, the slight increase observed in the permeability of the microstructure is attributed to a reduction in the surface area

Microtomography-Based Simulation of Transport Through Open-Cell Metal Foams

Important heat transfer parameters of aluminum foams of varying pore sizes are investigated through CT-scanning at 20 micron resolution. Small sub-samples from the resulting images are processed to generate feature-preserving, finite-volume meshes of high quality. All three foam samples exhibit similar volumetric porosity (in the range ~91–93%), and thereby a similar thermal conductivity. Effective tortuosity for conduction along the coordinate directions is also calculated. Permeability simulations in the Darcy flow regime with air and water show that the foam permeability is isotropic and is of the order of 10^-7m^2. The convective heat transfer results computed for this range of Reynolds numbers exhibit a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered

Advances in Fluid and Thermal Transport Property Analysis and Design of Sintered Porous Wick Microstructures

Sintered porous structures are ubiquitous as heat transport media for thermal management and other applications. In particular, low-porosity sintered packed beds are used as capillary-wicking and evaporation-enhancement structures in heat pipes. Accurate prediction and analysis of their transport characteristics for different microstructure geometries is important for improved design. Owing to the random nature and geometric complexity of these materials, development of predictive methods has been the subject of extensive prior research. The present work summarizes and builds upon past studies and recent advances in pore-scale modeling of fluid and thermal transport within such heterogeneous media. A brief review of various analytical and numerical models for simplified prediction of transport characteristics such as effective thermal conductivity, permeability, and interfacial heat transfer is presented. More recently, there has been a growing interest in direct numerical simulation of transport in realistic representations of the porous medium geometry; for example, by employing nondestructive 3D imaging techniques such as X-ray microtomography. Future research directions are identified, looking beyond techniques intended for material characterization alone, and focusing on those targeting the reverse engineering of wick structures via modeling of the physical sintering fabrication processes. This approach may eventually be employed to design intricate sintered porous structures with desired properties tailored to specific applications

Evaporation analysis in sintered wick microstructures

Heat pipes offer passive transport of heat over long distances without incurring a significant drop in temperature. Topological and microstructural details of the wick material embedded in a heat pipe help determine its thermal performance. A good understanding of pore-scale transport phenomena is crucial to enhancing heat pipe performance. In this study, pore-scale analysis of thin-film evaporation through sintered copper wicks is performed. X-ray microtomography is employed to generate geometrically faithful, feature-preserving meshes. Commercial sintered wicks with particle sizes in the range of 45-60 mu m, 106-150 mu m and 250-355 mu m and with approximately 61% porosity are considered. The capillary pressure, characteristic pore radius, percentage thin film area and evaporative mass and heat fluxes are computed using a volume of fluid (VOF) approach. Two different solution strategies are employed to stabilize the numerical solution and to improve convergence. After verifying that these strategies yield the correct solution, the VOF model is used to obtain static meniscus shapes in the pore space of the sintered wick samples. The meniscus shape is then held fixed and steady-state, thin-film evaporation analysis is performed. Liquid-vapor phase change heat transfer is modeled using a modified Schrage equation. Based on the present analysis, the best performing sample (particle size range) is identified along with the optimum contact angle. (C) 2013 Elsevier Ltd. All rights reserved

Optimization Under Uncertainty for Electronics Cooling Design Applications

Optimization under uncertainty is a powerful methodology used in design and optimization to produce robust, reliable designs. Such an optimization methodology, employed when the input quantities of interest are uncertain, yields output uncertainties that help the designer choose appropriate values for input parameters to produce safe designs. Apart from providing basic statistical information such as mean and standard deviation in the output quantities, uncertainty-based optimization produces auxiliary information such as local and global sensitivities. The designer may thus decide the input parameter(s) to which the output quantity of interest is most sensitive, and thereby design better experiments based on just the most sensitive input parameter(s). Another critical output of such a methodology is the solution to the inverse problem, i.e, finding the allowable uncertainty (range) in the input parameter(s), given an acceptable uncertainty (range) in the output quantities of interest. We apply optimization under uncertainty to the problem of heat transfer in fin heat sinks with uncertainties in geometry and operating conditions. The analysis methodology is implemented using DAKOTA, an open source design and analysis kit. A response surface is first generated which captures the dependence of the quantity of interest on inputs. This response surface is then used to perform both deterministic and probabilistic optimization of the heat sink, and the results of the two approaches are compared

XMT-Based Direct Simulation of Flow and Heat Transfer through Open-cell Aluminum Foams

Three aluminum foam samples of varying pore sizes -10 ppi, 20 ppi and 40 ppi - are CT-scanned using a commercial X-ray scanner at 20 micron resolution for measuring and comparing important heat transfer parameters such as effective thermal conductivity and Nusselt number. Small sub-samples from the resulting stack of images are processed to generate feature-preserving high-quality finite-volume meshes. It is observed that all three foam samples exhibit similar volumetric porosity (in the range ~91-93%), and thereby a similar thermal conductivity. For the domain sizes considered, the samples exhibit anisotropic conduction along the three coordinate directions of the mesh, which is attributed to the randomness of the structure and the small domain sizes considered. The values of average effective thermal conductivity are compared with a number of previous experimental and simulation results. Effective tortuosity for conduction along the coordinate directions is also calculated. Permeability simulations in the Darcy flow regime with air and water show that foam permeability is isotropic and is of the order of 10-7 m2. The resulting friction factor variation with Reynolds number is validated against published results. Nusselt numbers are also computed for this range of Reynolds numbers. The heat transfer results exhibit a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered