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

3D Reconstruction and Design of Porous Media from Thin Sections

Characterization and design of fluid-thermal transport through random porous sintered beds is critical for improving the performance of two-phase heat transport devices such as heat pipes. Two-dimensional imaging techniques are quite well developed and commonly employed for microstructure and material characterization. In this study, we employ 2D image data (thin sections) for measuring critical microstructural features of commercial wicks for use in correlation-based prediction of transport properties. We employ a stochastic characterization methodology based on the two-point autocorrelation function, and compare the predicted properties such as particle and pore diameters and permeability with those from our previously published studies, in which 3D x-ray microtomography data was employed for reconstruction. Further, we implement a reconstruction technique for reconstructing a three-dimensional stochastic equivalent structure from the thin sections. These reconstructed domains are employed for predicting effective thermal conductivity, permeability and interfacial heat transfer coefficient in single-phase flow. The current computations are found to compare well with models and correlations from the literature, as well as our previous numerical studies. Finally, we propose a new parametrized model for the design of porous materials based on the nature of the two-point autocorrelation functions. Using this model, we reconstruct sample three-dimensional microstructures, and analyze the influence of various parameters on fluid-thermal properties of interest. With advances in additive manufacturing techniques, such an approach may eventually be employed to design intricate porous structures with properties tailored to specific applications

Optimization Under Uncertainty Applied to Heat Sink Design

Optimization under uncertainty (OUU) 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

Effective Anisotropic Properties-Based Representation of Vapor Chambers

An easy-to-use representation of vapor chambers is developed in terms of effective anisotropic properties. This approach enables accurate simulation of the vapor chamber represented as a solid conduction block by assigning appropriate values to its effective density, specific heat, in-plane thermal conductivity, and through-plane thermal conductance. These effective properties are formulated such that the vapor chamber operation in terms of steady-state and transient thermal responses matches a full, physical simulation of phase change and energy transport in the vapor core; they are intrinsic properties that can be applied independently of the boundary conditions and heat input

Simultaneous measurement of temperature and strain in electronic packages using multi-frame super-resolution infrared thermography and digital image correlation

For microelectronic components and systems, reliability under thermomechanical stress is of critical importance. Experimental characterization of hotspots and temperature gradients, which can lead to deformation in the component, relies on accurate mapping of the surface temperature. One method of non-invasively acquiring this data is through infrared (IR) thermography. However, IR thermography is often limited by the typically low resolution of such cameras. Additionally, the unique surface finish preparations required to infer physical deformation using digital image correlation (DIC) generally interferes with the ability to measure the temperature with IR thermography, which prefers a uniform high emissivity. This work introduces a one-shot technique for the simultaneous measurement of surface temperature and deformation using multiframe super-resolution-enhanced IR imaging combined with digital image correlation (DIC) analysis. Multiframe super-resolution processing uses several sub-pixel shifted images, interpolating the image set to extract additional information and create a single higher-resolution image. Measurement of physical deformation is incorporated using a test sample with a black background and low-emissivity speckle features, heated in a manner that induces a non-uniform temperature field and stretched to induce physical deformation. Through processing and filtering, data from the black surface regions used for surface temperature mapping are separated from the speckle features used to track deformation with DIC. This method allows DIC to be performed on the IR images, yielding a deformation field consistent with the applied tensioning. While both the low- and super-resolution data sets can be successfully processed with DIC, super-resolution helps reduce noise in the extracted deformation fields. As for temperature measurement, using super-resolution is shown to allow for better removal of the speckle features and reduce noise, as quantified by a lower mean deviation from the spatial moving average

Numerical Investigation of Pressure Drop and Heat Transfer through Reconstructed Metal Foams and Comparison against Experiments

Direct numerical simulation of transport in foam materials can benefit from realistic representations of the porous-medium geometry generated by employing non-destructive 3D imaging techniques. X-ray microtomography employs computer-processed X-rays to produce tomographic images or slices of specific regions of the object under investigation, and is ideally suited for imaging opaque and intricate porous media. In this work, we employ micro-CT for numerical analysis of air flow and convection through four different high-porosity copper foams. All four foam samples exhibit approximately the same relative density (6.4% - 6.6% solid volume fraction), but have different pore densities (5, 10, 20, and 40 pores per inch, PPI). A commercial micro-computed tomography scanner is employed for scanning the 3D microstructure of the foams at a resolution of 20 μm, yielding stacks of two-dimensional images. These images are processed in order to reconstruct and mesh the real, random structure of the foams, upon which simulations are conducted of forced convection through the pore spaces of the foam samples. The pressure drop values from this μCT based CFD analysis are compared against prior experimental results; the computational interfacial heat transfer results are compared against the values predicted by an empirical correlation previously reported, revealing excellent agreement between the numerical and experimental/empirical hydraulic and thermal results, thus highlighting the efficacy of this novel approach

Simultaneous Wick and Fluid Selection for the Design of Minimized-Thermal-Resistance Vapor Chambers under Different Operating Conditions

The thermal resistance of a vapor chamber is primarily governed by conduction across the evaporator wick and the saturation temperature gradient in the vapor core. The relative contributions of these two predominant resistances can vary dramatically with vapor chamber operating conditions and geometry. In the limit of very thin form factors, the contribution from the vapor core thermal resistance dominates the overall thermal resistance of the vapor chamber; recent work has focused on working fluid selection to minimize overall thermal resistance in this limit. However, the wick thermal resistance becomes increasingly significant as its thickness increases to support higher heat inputs while avoiding the capillary limit. It therefore becomes critical to simultaneously consider the contributions of the wick and vapor core thermal resistances in the development of a generalized methodology for vapor chamber working fluid selection. The current work uses a simplified thermal-resistance-network-based vapor chamber model to explore selection of working fluids and wick structures that offer the minimum overall thermal resistance as a function of the vapor chamber thickness and heat input. An illustrative example of working fluid selection, for cases with and without the contribution of wick thermal resistance, is first used to demonstrate the potential significance of the wick thermal resistance on fluid choice. This influence of the wick on working fluid selection is further explained based on the wick properties (effective pore radius, permeability, and effective thermal conductivity). The ratio of effective pore radius to wick permeability is found to be the most critical wick parameter governing the overall vapor chamber resistance at thin form factors where minimizing the wick thickness is paramount; the wick conductivity becomes an equally important parameter only at thicker form factors. Based on this insight, a new approach for vapor chamber design is demonstrated, which allows simultaneous selection of the working fluid and wick that provides minimum overall thermal resistance for a given geometry and operating condition

Heat Pipe Dryout and Temperature Hysteresis in Response to Transient Heat Pulses Exceeding the Capillary Limit

The balance between the capillary pressure provided by the wick in a heat pipe or vapor chamber and the flow resistance to liquid resupply at the evaporator determines the maximum heat load that can be sustained at steady state. This maximum heat load is termed as the capillary limit; operation at steady heat loads above the capillary limit will result in dryout at the evaporator wick. However, different user needs and device workloads can lead to highly transient heat loads in applications ranging from con- sumer electronic devices to server processors. In these instances, the operation of heat pipes must be assessed in response to brief transient heat loads which could be higher than the notional capillary limit that governs dryout at steady state. In the current study, experiments are performed to characterize the transient thermal response of a heat pipe subjected to heat input pulses of varying duration that ex- ceed the capillary limit. Transient dryout events due to a wick pressure drop exceeding the maximum available capillary pressure can be detected from an analysis of the measured temperature signatures. It is demonstrated that under such transient heating conditions, a heat pipe can sustain heat loads higher than the steady-state capillary limit for brief periods of time without experiencing dryout. If the heating pulse is sufficiently long as to induce transient dryout, the heat pipe may experience an elevated steady- state temperature even after the heat load is reduced back to a level lower than the capillary limit. The steady-state heat load must then be reduced to a level much below the capillary limit to fully recover the original thermal resistance of the heat pipe. This characteristic temperature hysteresis following tran- sient dryout has significant implications for the use of heat pipes for pulsed power dissipation. Further experiments are performed to bound the range of heat loads over which the temperature hysteresis is present following a transient dryout event

Two-phase Flow Morphology and Local Wall Temperatures in High-Aspect-Ratio Manifold Microchannels

Manifold microchannel heat sinks can dissipate high heat fluxes at moderate pressure drops, especially during two-phase operation. High-aspect-ratio microchannels afford a large enhancement in heat transfer area; however, the flow morphology in manifold microchannels during two-phase operation, as well as the resulting thermal performance, are not well understood. In this work, a single manifold microchan- nel representing a repeating unit in a heat sink is fabricated in silicon with a bonded glass viewing window. Samples of different channel lengths (750 μm and 1500 μm) and depths (125 μm, 250 μm, and 10 0 0 μm) are considered; channel and fin widths are both maintained at 60 μm. Subcooled fluid (HFE-7100) is delivered to the channel at a constant flow rate such that the fluid velocity at the inlet is ~1.05 m/s in all cases. A high-speed camera is used to visualize the two-phase flow in the channel through the glass sidewall; an infrared camera measures the temperature distribution on the opposite channel sidewall. The flow visualizations reveal that vapor nucleation occurs at stagnation regions below the manifold near the inlet plenum and at both corners adjacent to the channel base. For deep chan- nels (10 0 0 μm), at sufficiently high heat fluxes, vapor completely covers the base of the channels and liquid does not re-wet the surface in this region. This newly identified vapor blanketing phenomenon causes a significant decrease in performance and an increase in the measured channel wall temperatures. This study reveals the critical role of the two-phase flow morphology in manifold microchannel heat sink design