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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. May 27, 2016. / Heat transfer in a wall with temperature dependent thermal conductivity and internal heat generation is considered. We rst focus on the steady state models followed by the transient heat transfer models. It turns out that the models considered are non-linear. We deliberately omit the group-classi cation of the arbitrary functions appearing in the models, but rather select forms of physical importance. In one case, thermal conductivity and internal heat generation are both given by the exponential function and in the other case they are given by the power law. We employ the classical Lie point symmetry analysis to determine the exact solutions, while also determining the optimal system for each case. The exact solutions for the transient models are di cult to construct. However, we rst use the obtained exact solution for the steady state case as a benchmark for the 1D Di erential Transform Method (DTM). Since con dence in DTM is established, we construct steady state approximate series solutions. We apply the 2D DTM to the transient problem. Lastly we determine the conservation laws using the direct method and the associated Lie point symmetries for the transient problem / MT2016

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering, 2017. / In traditional two-dimensional shock wave theory the reflection of a shock wave off a surface is treated as an adiabatic process and that the reflection surface is perfectly rigid and smooth with an inviscid flow of the fluid. In reality it has been found that these assumptions are not entirely accurate, and that although they are a good indication in the regular and irregular reflection domains of shock waves over the surface, viscous and thermal effects are present within the flow field. It has been experimentally shown that the transition of regular reflection to irregular reflection exceeds the theoretical limit, which is known as the von Neumann paradox. This paradox has largely been accounted for in the formation of a viscous boundary layer behind the reflected shock wave, based on numerous experimental and computational studies. However, the thermal effects in the reflection process have largely been neglected as the assumption of heat transfer between the post-shock wave gas and the reflection surfaces is assumed to be invalid. These thermal effects were investigated by testing materials with a varying range of thermal conductivities (1.13 to 401 W/mK) and similar surface roughness’s below the suggested limit for hydraulic smoothness. Each experiment placed two test pieces at the same incidence angle, symmetrically in the shock tube. This allowed flow properties to be exactly the same for the two materials being tested with a single plane shock wave. Test Mach numbers ranged from 1.2790 to 1.3986, with tests conducted at shock wave incidence angles of 36◦, 40◦, 60◦ and 70◦. This allowed both the regular and irregular reflection domains to be tested. Shadowgraph images were created using a z-configuration optical set up. These shadowgraph images were analysed quantitatively based on the angles measured as well as qualitatively based on flow features and symmetry. Both the quantitative and qualitative tests indicated that there was a difference in the angles between the reflected shock waves and surfaces based on the material thermal conductivity. In the quantitative tests the value of this angle was larger for materials with a lower thermal conductivity, and smaller for ones with a higher thermal conductivity for the regular reflection cases. In the irregular reflection cases the angle between the reflected and incident shock waves was larger for materials with a higher thermal conductivity. The materials with midrange thermal conductivities had reflection angles that lay within the bounds of the glass and copper angle values. The qualitative images supported these findings showing asymmetry in materials with different thermal conductivities with the intersection of reflected shock waves lying closer to the material with a higher thermal conductivity. Control experiments using test pieces made from an identical material showed no bias due to the location of the test piece in the shock tube / XL2018

Thesis advisor: Zhifeng Ren / Silicon germanium alloys (SiGe) have long been used in thermoelectric modules for deep-space missions to convert radio-isotope heat into electricity. They also hold promise in terrestrial applications such as waste heat recovery. The performance of these materials depends on the dimensionless figure-of-merit ZT (= S2σ T/ κ), where S is the Seebeck coefficient, σ the electrical conductivity, κ the thermal conductivity, and T is the absolute temperature. Since 1960 efforts have been made to improve the ZT of SiGe alloys, with the peak ZT of n-type SiGe reaching 1 at 900 - 950 C. However, the ZT of p-type SiGe has remained low. Current space-flights run on p-type materials with a peak ZT ~ 0.5 and the best reported p-type material has a peak ZT of about 0.65. In recent years, many studies have shown a significant enhancement of ZT in other material systems by utilizing a nanostructuring approach to reduce the thermal conductivity by scattering phonons more effectively than electrons. Here we show, using a low-cost and mass-production ball milling and direct-current induced hot press compaction nanocomposite process, that a 50% improvement in the peak ZT, from 0.65 to 0.95 at 800 - 900C is achieved in p-type nanostructured SiGe bulk alloys. The ZT enhancement mainly comes from a large reduction in the thermal conductivity due to the increased phonon scattering at the grain boundaries and crystal defects formed by lattice distortion, with some contribution from the increased electron power factor at high temperatures. Moreover, nanocomposite approaches have been used to study the thermoelectric properties of other material systems such as bismuth telluride (Bi-Te), bismuth antimony (Bi-Sb), and half-Heusler phases. We observed a significant improvement in peak ZT of nanostructured p- and n-type half-Heusler compounds from 0.5 to 0.8 and 0.8 to 1.0 respectively. The ZT improvement is mainly due to the reduction of thermal conductivity. This nanostructure approach is applicable to many other thermoelectric materials that are useful for automotive, industrial waste heat recovery, space power generation, or solar power conversion applications. / Thesis (PhD) — Boston College, 2010. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: David A. Broido / Using density functional perturbation theory and a full solution of the linearized phonon Boltzmann transport equation (BTE), a parameter-free theory of semiconductor thermal properties is developed. The approximations and shortcomings of previous approaches to thermal conductivity calculations are investigated. The use of empirical interatomic potentials in the BTE approach is shown to give poor agreement with measured values of thermal conductivity. By using the adiabatic bond charge model, the importance of accurate descriptions of phonon dispersions is highlighted. The extremely limited capacity of previous theoretical techniques in the realm of thermal conductivity prediction is highlighted; this is due to a dependence on adjustable parameters. Density functional perturbation theory is coupled with an iterative solution to the full Boltzmann transport equation creating a theoretical construct where thermal conductivity prediction becomes possible. Validation of the approach is demonstrated through the calculation of a range of thermal properties for a set of polar and non-polar semiconductors which are compared with measured values. The agreement between theory and measurement is very good, confirming the promise of the theoretical approach. Due to the significant computational effort required by the parameter-free calculations, new forms for room temperature relaxation time approximations are derived. The resulting forms produce thermal conductivity values in very good agreement with the ab initio data across a wide temperature range. It is therefore shown that accurate relaxation time approximations can be developed, fixing the adjustable parameters to the ab initio theory avoiding any comparison with measured data. This approach improves the accuracy of phonon relaxation times compared with previous models. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The thesis has the objective of design a methodological model for evaluate and compare the behaviour of external walls exposed to moisture phenomena. The comparison is related to different variables us for example: thermal conductivity, thermal transmitance, moisture content in the element along the time, P.O. Fanger theory of comfort, risk grouwth of mould among the others parameters. The model is developed in function of two softwares that permit sensibilyze the performance of building elements in relation of the presence of different quantities of moisture inside of them along the year. In this case, the model is probe with the use of TRNSYS 15 and WUFI 3.2 Pro softwares. The results show that there are many differences in the analysis of the different parameters in the cases with the materials in dry and wet state. Also, is possible to realize that the improve of any constructive solutions they are amortized in periods of time that no exceed more than three years in relation to the save of energy for the improvement in the themal conductivity of the materials.

Thermal properties of one dimensional nanostructures are of interest for thermoelectric energy conversion. Thermoelectric efficiency is related to non dimensional thermoelectric figure of merit, ZT=S^2 o T/k, where S ,o , k and T are Seebeck coefficient, electrical conductivity, thermal conductivity and the absolute temperature respectively. These physical properties are interdependent. Therefore, making materials with high ZT is a very challenging task. However, nanoscale materials can overcome some of these limitations. When the size of nanomaterials is comparable to wavelength and mean free path of energy carriers, especially phonons, size effect contributes to the thermal conductivity reduction without bringing about major changes in the electrical conductivity and the Seebeck coefficient. Therefore, the figure of merit ZT can be manipulated. For example, the thermal conductivities of several silicon nanowires were more than two orders of magnitude lower than that of bulk silicon values due to the enhanced boundary scattering. Among the nanoscale semiconductor materials, Silicon-Germanium(SiGe) alloy nanowire is a promising candidate for thermoelectric materials The thermal conductivities of SiGe core-shell nanowires with core diameters of 96nm, 129nm and 177nm were measured using a batch fabricated micro device in a temperature range of 40K-450K. SiGe nanowires used in the experiment were synthesized via the Vapour-Liquid-Solid (VLS) growth method. The thermal conductivity data was compared with thermal conductivity of Si and Ge nanowires. The data was compared with SiGe alloy thin film, bulk SiGe, Si/SixGe1-x superlattice nanowire, Si/Si0.7Ge0.3 superlattice thin film and also with the thermal conductivity of Si0.5Ge0.5 calculated using the Einstein model. The thermal conductivities of these SiGe alloy nanowires observed in this work are ~20 times lower than Si nanowires, ~10 times lower than Ge nanowires, ~3-4 times lower than Si/SixGe1-x superlattice thin film, Si/SixGe1-x superlattice nanowire and about 3 time lower than bulk SiGe alloy. The low values of thermal conductivity are majorly due to the effect of alloy scattering, due to increased boundary scattering as a result of nanoscale diameters, and the interface diffuse scattering by core-shell effect. The influence of core-shell effect, alloy scattering and boundary scattering effect in reducing the thermal conductivity of these nanowires opens up opportunities for tuning thermoelectric properties which can pave way to thermoelectric materials with high figures of merit in the future.

The thermal conductivity, thermopower, and electrical resistivity of (R1.5Ce0.5)RuSr2Cu2O10-delta (R=Gd, Eu) polycrystalline samples with different oxygen doping level are investigated in temperature range 1.8-300 K. Much attention is focused on the dependence of the effect of the annealing in high oxygen pressures as well as the effect of aging on transport coefficients in normal and superconducting states. It was found that the process of deoxydation goes faster for Ru-1222(Eu) samples than for Ru- 1222(Gd) samples, which results in more pronounced granular effects in Ru-1222(Eu) samples. The relative contribution to the thermal conductivity due to electrons and phonons was estimated by using the Wiedemann-Franz relation and the resistivity data. The calculation showed that the maximum electron contribution for Ru-1222(Eu) is about 0.75% and that for Ru-1222(Gd) samples is around 4 %.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1930. / Typescript. Title from PDF title page (viewed Nov. 6, 2008). Includes bibliographical references (p. [37]). Online version of the print original.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Includes bibliographical references (leaf 59). Also available on the Internet.