Thermally enhanced greases made of dispersions of small conductive particles suspended in fluidic polymers can offer significant advantages when used as a thermal interface material (TIM) in microelectronics cooling applications. A fundamental problem which remains to be addressed is how to predict the effective thermal conductivity of these materials, an important parameter in establishing the bulk resistance to heat flow through the TIM. <br /><br /> The following study presents the application of two simple theorems for establishing bounds on the effective thermal conductivity of such inhomogeneous media. These theorems are applied to the development of models which are the geometric means of the upper and lower bounds for effective thermal conductivity of base fluids into which are suspended particles of various geometries. <br /><br /> Numerical work indicates that the models show generally good agreement for the various geometric dispersions, in particular for particles with low to moderate aspect ratios. The numerical results approach the lower bound as the conductivity ratio is increased. An important observation is that orienting the particles in the direction of heat flow leads to substantial enhancment in the thermal conductivity of the base fluid. Clustering leads to a small enhancement in effective thermal conductivity beyond that which is predicted for systems composed of regular arrays of particles. Although significant enhancement is possible if the clusters are large, in reality, clustering to the extent that solid agglomerates span large distances is unlikely since such clusters would settle out of the fluid. <br /><br /> In addition, experimental work available in the literature indicates that the agreement between the selected experimental data and the geometric mean of the upper and lower bounds for a sphere in a unit cell are in excellent agreement, even for particles which are irregular in shape.

Thermally enhanced greases made of dispersions of small conductive particles suspended in fluidic polymers can offer significant advantages when used as a thermal interface material (TIM) in microelectronics cooling applications. A fundamental problem which remains to be addressed is how to predict the effective thermal conductivity of these materials, an important parameter in establishing the bulk resistance to heat flow through the TIM. <br /><br /> The following study presents the application of two simple theorems for establishing bounds on the effective thermal conductivity of such inhomogeneous media. These theorems are applied to the development of models which are the geometric means of the upper and lower bounds for effective thermal conductivity of base fluids into which are suspended particles of various geometries. <br /><br /> Numerical work indicates that the models show generally good agreement for the various geometric dispersions, in particular for particles with low to moderate aspect ratios. The numerical results approach the lower bound as the conductivity ratio is increased. An important observation is that orienting the particles in the direction of heat flow leads to substantial enhancment in the thermal conductivity of the base fluid. Clustering leads to a small enhancement in effective thermal conductivity beyond that which is predicted for systems composed of regular arrays of particles. Although significant enhancement is possible if the clusters are large, in reality, clustering to the extent that solid agglomerates span large distances is unlikely since such clusters would settle out of the fluid. <br /><br /> In addition, experimental work available in the literature indicates that the agreement between the selected experimental data and the geometric mean of the upper and lower bounds for a sphere in a unit cell are in excellent agreement, even for particles which are irregular in shape.

Inherent safety is claimed for gas-cooled pebble bed reactors, such as the South African Pebble Bed Modular Reactor (PBMR), as a result of its design characteristics, materials used, fuel type and physics involved. Therefore, a proper understanding of the mechanisms of heat transfer, fluid flow and pressure drop through a packed bed of spheres is of utmost importance in the design of a high temperature Pebble Bed Reactor (PBR). In this study, correlations describing the effective thermal conductivity through packed pebble beds are examined. The effective thermal conductivity is a term defined as representative of the overall radial heat transfer through such a packed bed of spheres, and is a summation of various components of the overall heat transfer. This phenomenon is of importance because it forms an intricate part of the self-acting decay heat removal chain, which is directly related to the PBR safety case. In this study standard correlations generally employed by the thermal fluid design community for PBRs are investigated, giving particular attention to the applicability of the correlations when simulating the effective thermal conductivity in the near-wall region. Seven distinct components of heat transfer are examined namely: conduction through the solid, conduction through the contact area between spheres, conduction through the gas phase, radiation between solid surfaces, conduction between pebble and wall, conduction through the gas phase in the wall region, and radiation between the pebble and wall surface. The effective thermal conductivity models are typically a function of porosity in order to account for the pebble bed packing structure. However, it is demonstrated in this study that porosity alone is insufficient to quantify the porous structure in a randomly packed bed. A new Multi-sphere Unit Cell Model is therefore developed, which accounts more accurately for the porous structure, especially in the near-wall region. Conclusions on the applicability of the model are derived by comparing the simulation results with measurements obtained from various experimental test facilities. This includes the PBMRs High Temperature Test Unit (HTTU) situated on the campus of the North-West University in Potchefstroom in South Africa. The Multi-sphere Unit Cell Model proves to encapsulate the impact of the packing structure in a more fundamental way and can therefore serve as the basis for further refinement of models to simulate the effective thermal conductivity. / Thesis (PhD (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2010

Inherent safety is claimed for gas-cooled pebble bed reactors, such as the South African Pebble Bed Modular Reactor (PBMR), as a result of its design characteristics, materials used, fuel type and physics involved. Therefore, a proper understanding of the mechanisms of heat transfer, fluid flow and pressure drop through a packed bed of spheres is of utmost importance in the design of a high temperature Pebble Bed Reactor (PBR). In this study, correlations describing the effective thermal conductivity through packed pebble beds are examined. The effective thermal conductivity is a term defined as representative of the overall radial heat transfer through such a packed bed of spheres, and is a summation of various components of the overall heat transfer. This phenomenon is of importance because it forms an intricate part of the self-acting decay heat removal chain, which is directly related to the PBR safety case. In this study standard correlations generally employed by the thermal fluid design community for PBRs are investigated, giving particular attention to the applicability of the correlations when simulating the effective thermal conductivity in the near-wall region. Seven distinct components of heat transfer are examined namely: conduction through the solid, conduction through the contact area between spheres, conduction through the gas phase, radiation between solid surfaces, conduction between pebble and wall, conduction through the gas phase in the wall region, and radiation between the pebble and wall surface. The effective thermal conductivity models are typically a function of porosity in order to account for the pebble bed packing structure. However, it is demonstrated in this study that porosity alone is insufficient to quantify the porous structure in a randomly packed bed. A new Multi-sphere Unit Cell Model is therefore developed, which accounts more accurately for the porous structure, especially in the near-wall region. Conclusions on the applicability of the model are derived by comparing the simulation results with measurements obtained from various experimental test facilities. This includes the PBMRs High Temperature Test Unit (HTTU) situated on the campus of the North-West University in Potchefstroom in South Africa. The Multi-sphere Unit Cell Model proves to encapsulate the impact of the packing structure in a more fundamental way and can therefore serve as the basis for further refinement of models to simulate the effective thermal conductivity. / Thesis (PhD (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2010

Nanofluids consist of nanometer-sized particles or fibers in colloidal suspension within a host fluid. They have been studied extensively since their creation due to their often times anomalous and unique thermal transport characteristics. They have also proven to be quite valuable in terms of the scientific knowledge gained from their study and their nearly unlimited industrial and commercial applications. This research has expanded the science of nanofluids into a previously unexplored field, that of cryogenic nanofluids. Cryogenic nanofluids are similar to traditional nanofluids in that they utilize nanometer-sized inclusion particles; however, they use cryogenic fluids as their host liquids. Cryogenic nanofluids are of great interest due to the fact that they combine the extreme temperatures inherent to cryogenics with the customizable thermal transport properties of nanofluids, thus creating the potential for next generation cryogenic fluids with enhanced thermophysical properties. This research demonstrates that by combining liquid oxygen (LOX) with Multi-Walled Carbon Nanotube (MWCNT) inclusion particles, effective thermal conductivity enhancements of greater than 30% are possible with nanoparticle volume fractions below 0.1%. Three distinct cryogenic nanofluids were created for the purposes of this research, each of which varied by inclusion particle type. The MWCNT's used in this research varied in a number of physical characteristics, the most obvious of which are length and diameter. Lengths vary from 0.5 to 90 microns and diameters from 8 to 40 nanometers. The effective thermal conductivity of the various cryogenic nanofluids created for this research were experimentally determined by a custom made Transient Hot Wire (THW) system, and compared to each other and to more traditional nanofluids as they vary by type and particle volume fraction. This work also details the extensive theoretical, experimental, and numerical aspects of this research, including a rather detailed literature review of many of the salient sciences involved in the study of cryogenic nanofluids. Finally, a selection of the leading theories, models, and predictive equations is presented along with a review of some of the potential future work in the newly budding field of cryogenic nanofluids.

The heat transfer phenomena in the near-wall region of a randomly packed pebble bed are important in the design of a Pebble Bed Reactor (PBR), especially when considering the safety case during accident conditions. At higher temperatures the contribution of the radiation heat transfer component to the overall heat transfer in a PBR increases significantly. The wall effect present in the near-wall region of a packed pebble bed affects the heat transfer in this region. Various correlations exist to predict the effective thermal conductivity through a packed pebble bed, but not all of the correlations consider the contribution of radiation and some are only applicable to the bulk region. Experimental research has been done on the heat transfer through a packed pebble bed. However, most of the results are case specific and cannot necessarily be used to validate models or simulations to predict the effective thermal conductivity of a pebble bed. The objective of this study is to develop a methodology that uses experimental work together with Computational Fluid Dynamics (CFD) simulations to predict the effective thermal conductivity in the near-wall region of a randomly packed pebble bed, and to separate the conduction and radiation components of the effective thermal conductivity. The proposed methodology inter alia includes experimental tests and the calibration of a CFD model to obtain numerical results that correlate well with the experimental results. To illustrate the proposed methodology the newly constructed Near-wall Effect Thermal Conductivity Test Facility (NWETCTF) was used to gather experimental results for the temperature and heat transfer distribution through a randomly packed pebble bed. Two identical but separate experimental tests were performed and the results of the two tests were in good agreement. From the experimental results the effective thermal conductivity was derived. The effect of the near-wall region on the heat transfer and the significance of radiation at higher temperatures are evident from the results. Recommendations were made for future experimental work with the NWETCTF from the findings of the investigation. A numerically packed pebble bed that is representative of the experimental pebble bed was generated using the Discrete Element Method (DEM) and a CFD model was set up for the heat transfer through the pebble bed using STAR-CCM+.. The CFD results showed trends similar to that of the experimental results. However, some discrepancies were identified that must be addressed in future studies by calibrating the CFD model. The effective thermal conductivity for the numerical simulation was determined using the CFD results and the conduction and radiation components were separated. / MSc (Mechanical Engineering), North-West University, Potchefstroom Campus, 2015

The heat transfer phenomena in the near-wall region of a randomly packed pebble bed are important in the design of a Pebble Bed Reactor (PBR), especially when considering the safety case during accident conditions. At higher temperatures the contribution of the radiation heat transfer component to the overall heat transfer in a PBR increases significantly. The wall effect present in the near-wall region of a packed pebble bed affects the heat transfer in this region. Various correlations exist to predict the effective thermal conductivity through a packed pebble bed, but not all of the correlations consider the contribution of radiation and some are only applicable to the bulk region. Experimental research has been done on the heat transfer through a packed pebble bed. However, most of the results are case specific and cannot necessarily be used to validate models or simulations to predict the effective thermal conductivity of a pebble bed. The objective of this study is to develop a methodology that uses experimental work together with Computational Fluid Dynamics (CFD) simulations to predict the effective thermal conductivity in the near-wall region of a randomly packed pebble bed, and to separate the conduction and radiation components of the effective thermal conductivity. The proposed methodology inter alia includes experimental tests and the calibration of a CFD model to obtain numerical results that correlate well with the experimental results. To illustrate the proposed methodology the newly constructed Near-wall Effect Thermal Conductivity Test Facility (NWETCTF) was used to gather experimental results for the temperature and heat transfer distribution through a randomly packed pebble bed. Two identical but separate experimental tests were performed and the results of the two tests were in good agreement. From the experimental results the effective thermal conductivity was derived. The effect of the near-wall region on the heat transfer and the significance of radiation at higher temperatures are evident from the results. Recommendations were made for future experimental work with the NWETCTF from the findings of the investigation. A numerically packed pebble bed that is representative of the experimental pebble bed was generated using the Discrete Element Method (DEM) and a CFD model was set up for the heat transfer through the pebble bed using STAR-CCM+.. The CFD results showed trends similar to that of the experimental results. However, some discrepancies were identified that must be addressed in future studies by calibrating the CFD model. The effective thermal conductivity for the numerical simulation was determined using the CFD results and the conduction and radiation components were separated. / MSc (Mechanical Engineering), North-West University, Potchefstroom Campus, 2015

Measurements of in situ planetary thermal conductivity are typically made using long needle-like probes inserted in a planet's surface, which measure effective thermal conductivity (ETC) in radial direction (parallel to surface). The desired vertical (perpendicular to surface) ETC is assumed to be the same as the horizontal. However, ETC of particle beds in vertical and horizontal directions is known to be an anisotropic property under low compressive pressures. This study further examines the anisotropy of bed ETC under low and high compressive pressures in both vacuum and air environments. The ratio of vertical to horizontal stress, K0, is measured for the particles used in these experiments. A resistance network heat transfer model has been developed in predicting the vertical and the horizontal ETC as a function of applied compressive pressure. The model predicts vertical ETC by using only macro-contact thermal resistances for both high and low applied compressive pressure regimes. It is proposed that the vertical and horizontal ETC of particle beds under uniaxial compression is related by compressive pressures in each direction. The horizontal compressive pressure, which is perpendicular to the applied compressive pressure, can be calculated with the use of at-rest pressure coefficient and subsequently used in macro-contact thermal resistance to predict the horizontal ETC. The vertical ETC is obtained using the same model by substituting vertical compressive pressure into macro-contact thermal resistance. A two-dimensional axisymmetric finite element model in the COMSOL Multiphysics software package has been developed to simulate heat transfer coupled with structural deformation of spheres under compressive pressures in a simple cubic (SC) packing arrangement. The numerical model is used as a tool to predict the lower limit of bed ETC as well as validating thermal contact resistance used in the theoretical model. The predictions from the numerical model can be extended to particle beds with different packing arrangements.

Thermal conductivity is an important thermophysical property needed for effectively predicting nuclear fuel performance. As part of the Next Generation Nuclear Plant (NGNP) program, the thermal conductivity of tri-isotropic (TRISO) fuel needs to be measured over a temperature range characteristic of its usage. The composite nature of TRISO fuel requires that measurement be performed over the entire length of the compact in a non-destructive manner. No existing measurement system is capable of performing such a measurement. A measurement system has been designed based on the steady-state, guarded comparative-longitudinal heat flow technique. The system is capable of measuring cylindrical samples with diameters ∼12.3 mm (∼0.5 in.) with lengths ∼25 mm (∼1 in.). The system is currently operable in a temperature range of 100-700°C for materials with thermal conductivities on the order of 10-70 W*m-1*K-1. The system has been designed, built, and tested. An uncertainty analysis for the determinate errors of the system has been performed finding a result of 6%. Measurements have been performed on three calibration/validation materials: a certified glass ceramic reference material, 99.95% pure iron, and Inconel 625. The deviation of the validation samples is < 6-8% from the literature values. In addition, surrogate NGNP compacts and NGNP graphite matrix-only compacts have been measured. The results give an estimation of the thermal conductivity values that can be expected. All the results are presented and discussed. A Finite Element Analysis was done to compare the accuracy of multiple effective conductivity models. The study investigated the effects of packing structure, packing fraction, matrix thermal conductivity, and particle heat generation. The results show that the Maxwell and the Chiew & Glandt models provide the most accurate prediction of the effective thermal conductivity of the TRISO fuel compacts. Finally, a discussion of ongoing work is included as well as the possibility of correlating effective thermal properties of fuel compacts to their constituents with measurements of well-defined samples.

Recent trend of minimization in microprocessors has introduced increasing self-heating effects in FinFET and MOSFET transistors. To study these self-heating effects, we developed self-consistent 3D models of FinFET and MOSFET basic logic gates, and simulated steady-state thermal transport for the worst heating case scenario. Incorporating size-dependent effective thermal conductivity of thin films instead of bulk values, these simulations provide a more accurate prediction of temperature rise in the logic gates. Results of our simulations predict higher temperature rise in FinFETs, compared to MOSFETs. Existence of buried oxide layer and confined geometry of FinFET structure are determined to be the most contributing to this higher temperature rise. To connect the results of our simulations to higher scale simulations, we proposed an equivalent thermal conductivity for each basic logic gate. These values were tested and found to be independent of the magnitude of chosen boundary conditions, as well as heat generation rate.