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The United Downs Deep Geothermal Project (UDDGP) is situated near Redruth in Cornwall and is the first deep (5 km) geothermal power project to commence in the UK. Two deviated geothermal wells, one of which is the deepest UK onshore borehole, have been completed to measured depths of 2393 m and 5275 m (2214 m and 5054 m true vertical depth). These intersect the NNW-SSE-trending Porthtowan Fault Zone (PTFZ), within the Early Permian Cornubian Batholith. High heat flow values in SW England, double the UK background, make the region a favourable geothermal target, with elevated geothermal gradients of 36 °C/km compared to the UK average of 26 °C/km. The high surface heat flow is principally caused by the elevated U, Th and K within the crust. The Cornubian Batholith is composite and can be divided, near surface, into five different granite types (G1-G5) that were formed through variable degrees of source rock partial melting at different temperatures, and fractional crystallisation processes. As a consequence, the granites have heterogeneous U, Th and K contents that control heat generation and heat flow. Previous high-resolution airborne gamma-ray data has demonstrated the spatial variation in near-surface granite heat production, and the Rosemanowes Hot Dry Rock (HDR) Project has provided U, Th and K distributions to depths of 2652 m in the Carnmenellis Granite. However, challenges remain for modelling the high surface heat flow due to uncertainties relating to the radioelement concentrations at greater depths, the volume and distribution of the granites and petrogenetic controls on the U and Th distribution. To address these issues, the research had three aims: 1) to evaluate potential biases involved in the sampling and analysis of drill cuttings and to develop a robust analytical procedure; 2) to reassess genetic models for the Cornubian Batholith, specifically the Carnmenellis granite, from U and Th data; 3) determine the heat flow at United Downs and place the heat production profile and petrogenesis of the granites within the context of the 1D heat budget model for SW England lithosphere. Drill cutting biases occur due to wellbore processes (e.g. cutting depth constraints, contamination), surface sampling (e.g. loss of fines) and laboratory analysis (e.g. measurement volumes in a given size fraction). The effects of these issues on the representivity of the cuttings are evaluated from modelling cutting depth constraints during well transport, quantifying compositional variations between the coarse (> 2 mm) and bulk (> 63 um) cutting fractions, and statistical analysis on the measurement volumes. The evaluation of the UDDGP cuttings illustrated that they have a depth resolution of c. 10 m. Soft, friable and liberated accessory minerals concentrate within the fines and are preferentially lost within the bulk cutting fraction (> 63 μm) compared to the coarse fraction (>2 mm). Despite these biases, reliable interpretation of the geochemical and mineralogical data is still possible as the natural granite variability is greater than the biases produced during drilling. A multi-proxy approach, using mineralogy, whole rock geochemistry, mineral chemistry and U-Pb zircon geochronology was used to understand the granite petrogenesis and emplacement mechanisms. The proxies identified four granite facies, derived from discrete batch melting events over a period of c. 4.3 Ma. Two granite sub-groups exhibit internal fractionation trends. The dominant compositional control are heterogeneities in the source rock and melt temperature, contrary to previous petrogenetic interpretations that invoked fractional crystallisation (Chappell & Hine, 2006; Simons et al., 2016). Spectral gamma (U, Th) forms a reliable proxy for separating non-cogenetic and cogenetic melts, and thus can be used for future petrogenetic studies, well correlation and understanding the origins of the U and Th distributions with depth. The United Downs temperature field was evaluated using the equilibrium temperature log, high temperature (170 °C) thermal conductivity measurements, spectral gamma (U, Th, K) wireline log and a 1D heat balance model. The heat flow of United Downs was determined to be 114 mWm-2 (± 10%), similar to previous estimates from the Rosemanowes Hot Dry Rock Project. There is a substantial increase in Th below 3000 m that indicates the deeper parts of the batholith contribute substantially to overall heat production. Despite the high heat production at depth, it is still not enough to reconcile surface high heat flows with the current granite thickness models, therefore deeper heat sources must be invoked. Overall this thesis has characterised the geology and temperature field to a depth of 5,054 m from the United Downs Deep Geothermal Project (UD-1). The research has contributed to the understanding of the temperature gradients and anomalously high heat flows that are characteristic of SW England. Granite heat production has been linked in a petrogenetic context for the first time within SW England.

The continuous power increase and miniaturization of modern electronics requires increasingly effective thermal management systems. The thermo-hydraulic performance is investigated by a conjugate heat transfer and computational fluid dynamics model to investigate the optimum geometry and coolant composition in various microchannel heat sinks to enhance cooling. Firstly, a single-phase laminar nanofluid flow in microchannel heat sinks with a straight or twisted tape has been investigated. Swirl flow with the highest nanoparticle volume fraction was found to provide the lowest thermal resistance and contact temperature. Secondly, hydro-thermal performance-enhancing tape inserts were numerically tested featuring (i) radial gaps between the tape and the tube, (ii) tape twist with axial pitch distances of 0, L/2, or L/4, (iii) zero, one, or two 90-degree angular steps between consecutive tape segments, (iv) alternating clockwise and anti-clockwise consecutive twisted tape segments, and combinations of these features. The radial gaps produced both a hydraulic and thermal performance loss. All tape twist, angular steps, four L/4 alternating pitch consecutive helical tape and twist direction reversal combinations produced better thermal performance gains to hydraulic loss trade-offs than the baseline microchannel configuration with no tape. Thirdly, rectangular, twisted and zig-zag fins were inserted into a plain rectangular duct to enhance the cooling. The combinations of zig-zag fins and 3% Al₂O₃ nanofluid provided the best thermal performance. Finally, further research addressed and solved the inconsistent implementation of the two-phase mixture model for nanofluids in a minichannel heat sink to improve the heat prediction performance with respect to a single-phase approach, using appropriate physical modelling assumptions. By varying the volume fraction α_nf of the second phase between 2% and 50%, the two-phase mixture model predicted heat transfer coefficient, pressure drop, and second law efficiency values converging to the single-phase model ones at increasing α_nf.

An understanding of the subsurface thermal regime is beneficial to many disciplines, including petroleum and geothermal exploration, carbon capture and storage (CCS) and nuclear waste sequestration. This project developed and tested a new methodology for determining subsurface temperature using a non-invasive approach based on the velocity information derived from seismic reflection data. By solving a one-dimensional steady state approximation of Fourier's Law, it is possible to determine a bulk thermal gradient as a function of depth, enabling the determination of temperatures across an entire volume using this methodology, termed reflection seismic thermometry. There are two principal components to this methodology, requiring 1) a bulk thermal conductivity structure and 2) heat flow and/or temperature data to condition the model. The first component uses an empirical velocity to thermal conductivity transform whilst the second uses sparse temperature data from boreholes or a bottom simulating reflector (BSR) to derive the shallow thermal regime and heat flow. The thermometry workflow has been applied to three case studies; in the Lüderitz Basin, offshore Namibia; the Blake Ridge, offshore USA; and the North Viking Graben (NVG) in the North Sea. In the frontier Lüderitz Basin, a BSR was identified and used to derive heat flow of 60-70 mW m⁻². The Aptian source rock interval here was shown to presently be in the gas generative window. On Blake Ridge borehole velocities and a BSR were used to determine heat flow (43-56 mW m⁻²) and subsurface temperatures. Finally, methodology validation was conducted in the North Sea Basin using a high-resolution 3D full waveform inversion (FWI) velocity dataset calibrated with 141 wells. Forward models of subsurface temperatures were calibrated against the borehole temperatures, with inverse modelling used to derive heat flow at km scale lateral resolution. The availability of a fast track velocity volume for this area allowed comparison with the FWI derived thermal model results. It was found that stacking velocities were lower than well and FWI velocities, leading to overprediction of subsurface temperature. Modelling the temperature profile for CCS well 31/5-7 showed bottom hole temperature (BHT) within 6 °C of recorded BHT. With application and verification of the method in different basins, the versatility of the work conducted is demonstrated. It is envisioned that this technique opens avenues for the seismic characterisation of thermal regime in disparate settings and varied disciplines.

Heat from electrical devices, car engines, industrial processes and even our own body heat are an abundant, albeit difficult to harvest, energy source in today's society. As the extent of the climate crisis becomes clearer, recovering such waste heat can be an important step to design improved devices and reduce greenhouse gas emissions as well as the use of fossil fuels. Thermoelectric materials and devices are uniquely positioned to recover this waste heat and transform it to electricity due to their conversion characteristics and potentially small size. In addition, ever-increasing demands on computing power as well as further downscaling in chip sizes necessitates on-chip spot cooling and temperature sensing, which can be provided by thermoelectric devices. So far, whenever research in thermoelectrics seemed to be at a dead end, a new approach, such as for example most recently nanostructuring and reduced dimensionality, have reinvigorated the field. While this has lead to unprecedented advances in the figure of merit, now regularly reported above unity, thermoelectric devices are still lacking the required conversion efficiency to compete with conventional heat engines, leaving them an option mostly for niche applications. Particularly in low-dimensional devices and structures, theoretically predicted high and competitive efficiency values are hard to obtain due to environmental factors and inherent limits in device design. In this dissertation, influences on the thermoelectric properties of carbon nanostructures due to coupling configurations, defects, geometrical considerations and other local effects are studied. A first experiment investigates the power factor in C₆₀ molecules, contacted via electroburned graphene nanoconstrictions. The results suggest a threefold way to increase the achievable power factor in zero-dimensional structures: positioning the molecular energy levels close to the Fermi energy levels of the leads, ensuring the tunnel coupling is optimized for the desired operating temperature and, in order to achieve a maximum power factor, the tunnel couplings to the source and drain need to be equal. Building on these conclusions, a temperature dependent study of the power factor in graphene quantum dots was performed, suggesting that a quantum dot can work as a quantum heat valve especially when contacted by non-ideal heat conducting leads. Apart from highlighting the importance of leads that conduct heat well to achieve a high performance, the findings also again emphasize the potentially detrimental effect tunnel coupling has on the power factor. In order to analyse more localised effects, a Scanning Thermal Microscopy (SThM) approach was used to record thermoelectric maps (of both the Seebeck and Peltier effect) of graphene bow ties, revealing a geometrically dependent change in the Seebeck coefficient due to the impact of electron scattering at the graphene edges. This effect is exploited later to fabricate single-material graphene thermocouples that achieve an order of magnitude higher sensitivity than previously reported single-material metal thin film thermocouples. Lastly, Scanning Thermal Gate Microscopy (STGM) is developed, improving on the previously used SThM technique to achieve high resolution in thermovoltage maps at a fast scanning rate. STGM is then applied to graphene single-layer/bilayer junctions, demonstrating the influence of metallic contacts, layer thickness changes and local strain on the spatially distributed Seebeck coefficient in graphene. The effects studied in this dissertation are aimed at helping to further the understanding of local thermoelectric properties and opening the path to improve on current device design and performances as well as facilitating the elimination of parasitic noise caused by undesirable thermoelectric effects.

Pecos County, located in the Permian Basin of west Texas, is a deep sedimentary basin within which the Delaware Basin and Central Basin Platform are located. Significant oil and gas activity has occurred here over nearly 100 years. This activity has yielded substantial available well data for temperature and heat flow analyses. While several national-scale heat flow and temperature-at-depth data sets exist, very few county-level studies within Texas are available. Well data from the National Geothermal Data System (NGDS) are used to construct a Pecos County heat flow model and four temperature-at-depth models (3.5, 5.0, 6.5, and 10.0 km depths), using 947 data points available in Pecos County. Wells are distributed throughout the county, with higher well densities occurring in the north, northeast, and south-central portions. A radiogenic heat production model was incorporated to account for radioactive decay within the basement and sedimentary sections. Results show below-average heat flow (< 65 mW/m²) across the Central Basin Platform and average to above-average heat flow in the Delaware Basin in comparison to previous national heat flow models. High heat flows (>90 mW/m²) were calculated in portions of south and south-central Pecos County. Temperature-at-depth models indicate the lowest temperatures occurring across the Central Basin Platform and eastern Delaware Basin. Temperatures are elevated near the center of the county, with the highest temperatures located in south and south-central Pecos County. Temperature-at-depth model values are comparable with recorded well datapoints around the depth intervals of interest. Maximum temperatures for developed models at 3.5, 5.0, 6.5, and 10.0 km depths are 195°C, 213°C, 232°C, and 273°C, respectively. Findings show that calculated heat flow and temperature-at-depth in southern Pecos County is higher than those calculated for the region in existing national-scale models. Higher than average heat flow and temperature-at-depth anomalies can be attributed in part to higher radiogenic heat production (15.26 mW/m²) than previously estimated and increased model resolution compared to earlier national-scale heat flow and temperature models. Other possible explanations include shallow plutonic complexes, advective groundwater flow, and the Sierra Madera impact and crater. Pecos County has suitable temperatures for geothermal electricity production (> 150°C) at as shallow as 3.5 km depth, and most of the county reaches this temperature by 6.5 km depth. Opportunity exists for co-production of oil and gas and geothermal energy from existing wells at depths where this temperature is met or exceeded

The evolution of oceanic crust plays an integral role in global heat flow, geochemical cycles, and in shaping the environmental conditions harboring the crustal biosphere. Because oceanic crust is normally buried beneath several kilometers of water and encompasses a vast area of the Earth’s rigid surface, spatially extensive and coherent geophysical data are difficult to acquire in the oceanic domain. Consequently, our current understanding of the evolution of oceanic crust is based on partially conflicting compilations of data that are acquired at different scales and using different methods. Here I present geophysical constraints from an extensive seismic dataset that continuously covers 0-70 Ma crust in the western South Atlantic. Analysis of regional seismic velocity trends in the upper crust shows a continuous increase in basement velocity to crustal ages of at least 58 Ma. This trend indicates an evolution of upper crustal velocities that lasts significantly longer than measured or predicted by previous studies. The results provide evidence for ongoing hydrothermal circulation in relatively old upper crust, which is consistent with heat flow studies. To further test this concept, I used high-resolution seismic velocity models to estimate detailed porosity and permeability distributions that constrain models of hydrothermal fluid flow at five different crustal ages. The resulting advective and conductive surface heat fluxes are consistent with both predictions of heat flux by lithospheric cooling models and measured conductive heat flux at the seafloor. Additionally, computed hydrothermal volume fluxes largely agree with global estimates for the modeled crustal ages. The models are therefore consistent with a “sealing age” of ~65 Ma, which is also inferred from a compilation of global heat flow measurements at the seafloor. Close to the Rio Grande Rise, an oceanic plateau west of the study area, a fine-scale seismic velocity model reveals multiple large fault zones penetrating at least ~1.5 km into the crust. These faults likely accommodate differential subsidence between thickened, warm oceanic plateau crust and cold oceanic crust. Modeled fluid fluxes are elevated along the interpreted fault zones and across the seafloor. Crust adjacent to oceanic plateaus may exhibit elevated levels of tectonic activity and fluid flow globally. The estimated global volume of fluid entering the ocean in this type of setting amounts to 43 km³, which is ~2% of the hydrothermal flux in the axial region. This potentially has implications for global chemical cycles, the hydration of mature oceanic crust, and the oceanic crustal biosphere.

Two-thirds of submarine volcanism in the Earth's ocean basins is manifested along mid-ocean ridges and the remaining one-third is revealed along intraoceanic arcs and seamounts. Hydrothermal systems and the circulation patterns associated with these volcanic settings remove heat from the solid Earth into the deep ocean. Hydrothermal circulation continues to remove and redistribute heat in the crust as it ages. The heat and mass fluxes added to the deep ocean influence mixing in the abyssal ocean thereby affecting global thermohaline circulation. In addition to removing heat, hydrothermal processes extract chemical components from the oceanic and carry it to the surface of the ocean floor, while also removing certain elements from seawater. The resulting geochemical cycling has ramifications on the localized mineral deposits and also the biota that utilize these chemical fluxes as nutrients. In this dissertation, I analyze observed conductive heat flow measurements in the Panama Basin and borehole thermal measurements in Brothers Volcano and use mathematical models to estimate advective heat and mass fluxes, and crustal permeability. In the first manuscript, I use a well-mixed aquifer model to explain the heat transport in a sediment pond in the inactive part of the Ecuador Fracture Zone. This model yields mass fluxes and permeabilities similar to estimates at young upper oceanic crust suggesting vigorous convection beneath the sediment layer. In the second manuscript, I analyze the conductive heat flow measurements made in oceanic between 1.5 and 5.7 Ma on the southern flank of the Costa Rica Rift. These data show a mean conductive heat deficit of 70%, and this deficit is explained by various hydrothermal advective transport mechanisms, including outcrop to outcrop circulation, transport through faults, and redistribution of heat by flow of hydrothermal fluids in the basement. In the third manuscript, I analyze the borehole temperature logs for two sites representative of recharge and discharge areas of hydrothermal systems in the Brothers Volcano. I develop upflow and downflow models for fluids in the borehole and formation resulting in estimated of flow rates and permeabilities. All three independent research works are connected by the common thread of utilizing relatively simple mathematical concepts to get new insights into hydrothermal processes in oceanic crust.

The thermal conductivity of minerals in Earth's lowermost mantle is important for the thermal and chemical evolution of Earth. In the thermal boundary layer separating the core and mantle, the bulk thermal conductivity helps determine the heat flux out of the core. The core heat flux is an important unknown, which has implications for the energy available to power the core geodynamo, the age of the solid inner core, and the style of mantle convection. Measurements of thermal conductivity at high pressure and temperature conditions do not agree on the value at CMB conditions, and estimates range from about 5 W/mK to 15 W/mK. Recent experiments have helped constrain the pressure dependence of thermal conductivity at constant temperature. However, phase transitions in mantle minerals, such as the spin transition in ferropericlase, could complicate the extrapolation of lower pressure and temperature measurements to the conditions at the core-mantle boundary (CMB).In this dissertation, I build on a new method to measure thermal conductivity at high pressures and temperatures using continuous wave laser heating in the diamond anvil cell and apply it to pressure induced phase transitions. I test the method using the face-centered-cubic (B1) to body-centered-cubic (B2) phase transition in NaCl. This study produced thefirst measurement of NaCl thermal conductivity across the B1-B2 phase transition.I use the method developed for ionic salts and apply it to the mantle mineral, ferroper- iclase, (Mg,Fe)O, over the pressure range of 22 GPa to 61 GPa. This range of pressure includes the reported spin transition of octahedrally coordinated iron, from the high spin state to the mixed spin state. Material properties such as the bulk modulus and sound velocity decrease sharply with pressure in the mixed spin state. I measure a correlative reduction of thermal conductivity with pressure. This measurement is consistent with independent thermo-reflectance measurements of ferropericlase thermal diffusivity.Combining new ferropericlase thermal conductivity measurements with those of bridgmanite, and accounting for the spin transition, an updated thermal conductivity profile for the mantle can be calculated. The spin transition reduction has only a minor effect on the depth dependence of mantle thermal conductivity. This is due to the dominant modal percentage of bridgmanite, which is about 80% of the mantle by volume. Including the spin transition effect, I find an increase in thermal conductivity of the mantle by a factor of about 2 from the top of the lower mantle to the core-mantle boundary. These results are consistent with other recent studies, which use different measurement techniques.The thermal conductivity depth dependence of ferropericlase and bridgmanite using the methods in this dissertation result in a CMB bulk thermal conductivity of 5.2 W/mK. Ac- counting for uncertainty in the thickness and temperature change across the CMB, this thermal conductivity maps to a total heat flux of 5.1 to 9.3 TW. This range is consistent with an old inner core, the crystallization of which has has been integral to powering the geodynamo for a significant portion of Earth's history. Future work to bring existing measurements of thermal conductivity at CMB pressures into agreement will need to resolve questions about the temperature dependence at the extreme conditions of the lowermost mantle.In a separate study, I use an analogous application of the heat equation to model the mass transport of sediment on hillslopes. Hillslope processes are important for understand- ing how surface landforms evolve over time. The application of linear diffusion to describe the transport of grains down slope is used to date geomorphic surfaces. However, several lines of evidence, from theoretical considerations, to laboratory experiments and field observations suggest that the linear diffusion equation has limited predictive power for modelling of scarp degradation. Here we use high resolution elevation data and optically stimulated luminescence dates of sediment from a set of terrace risers in New Zealand and show that those degraded terrace risers are better explained by nonlinear diffusion.

Natural gas hydrates are crystalline inclusion compounds that form within the pore space of marine sediments along continental margins worldwide. These hydrate deposits host highly compressed gas molecules, most commonly methane, and are proposed to be the largest dynamic reservoir of organic carbon on this planet. As such, it is tremendously important for both climate scientists and countries in need of energy security to understand the controls on hydrate formation, stability, and decomposition in response to natural and manmade environmental stresses. This study utilizes industry quality 3-dimensional (3D) seismic reflection data combined with Integrated Ocean Drilling Program (IODP) drilling data collected during the NanTroSEIZE project in the Kumano Forearc Basin, offshore Japan. Our aim is to investigate natural gas hydrate occurrence, the 3D distribution and behavior of the base of gas hydrate stability (BGHS) in response to surface and underlying deformation processes, fluid flow patterns, zones of concentrated hydrate deposits, and a gas in place resource estimate for hydrate concentration zones near the BSR. Three types of BSRs including upper, lower, and a primary gas hydrate related BSRs were identified and mapped a across a region of 27 km by 11 km. The primary BSR, inferred to be the BGHS, is a widespread, continuous feature, and the depths of the primary BSR clearly show the complex controls that underlying basement deformation from compressional tectonics, and surface sedimentation and mass wasting events exert on the BGHS. Upper BSRs mark paleo-BGHS in the seaward regions, as well as the top of hydrate concentration zones above the BSR in two regions of the basin. Mixed gas, BGHS modeling provides compelling evidence that the lower BSRs could mark a Structure-II methane-ethane gas hydrate BGHS below a Structure-I methane hydrate BGHS. While 3D BSR-derived heat flow values were found to range from 42 -54 mWm-2 , which indicates that focused fluid advection is not presently active, drilling and seismic data provide evidence for thermogenic gas migration from depth up into basin sediments. Gas charged fluids are identified in the seismic data as high amplitude reflections (HARS) and low velocity zones beneath the BGHS, and migration appears to proceed as diffuse flow up landward dipping permeable strata, through short-range hydrate recycling in response to BGHS repositioning and up/laterally outward from deep cutting normal faults. Deep fluids potentially charge the four zones of concentrated gas hydrate deposits identified above the BSR. The hydrate concentration zones (HCZs) presented in this study are analogous to the confirmed methane HCZs in the eastern Nankai Trough, and should be considered highly prospective reservoirs.

Abstract: New data and revised processing methods yielded a revised understanding of the geothermics of the Phanerozoic strata in Saskatchewan. Temperatures increase with depth from 5 °C at 100 m to 120 °C at 3200 m. Average integral geothermal gradients range between 25 and 30 °C•km-1. Geothermal gradients are higher than average between the Cypress Hills and Swift Current; in the Weyburn-Estevan area; and at Yorkton. Anomalously cold areas are present near the Alberta border and at Saskatoon. Hot anomalies are present due to excess basement heat generation, the insulating effect of low thermal conductivity shale packages, and topographic effects. Colder than average areas coincide with areas of low heat flow. No extremely high geothermal gradients (>50 °C•km-1) or significant vertical heat flow differences (>10 mW•m-2) exist along the outcrop edge, therefore heat conduction is considered the main heat transfer method in the basin.

3D seismic reflection data were acquired by the R/V Langseth and used to extract heat flow information using bottom-simulating reflector (BSR) depths across the southern Costa Rica convergent margin. These data are part of the CRISP Project, which will seismically image the Middle America subduction zone in 3D. The survey was conducted in an area approximately 55x11 km, northwest of the Osa Peninsula, Costa Rica. For the analysis presented here, seismic data were processed using a post-stack time migration. The BSR—a reverse polarity seismic reflection indicating the base of the gas hydrate phase boundary—is imaged clearly within the slope-cover sediments of the margin wedge. If pressure is taken into account, in deep water environments the BSR acts as a temperature gauge revealing subsurface temperatures across the margin. Two heat flow models were used in this analysis. In the Hornbach model BSR depth is predicted using a true 3D diffusive heat flow model combined with Integrated Ocean Drilling Program (IODP) thermal conductivity data and results are compared with actual BSR depth observations to constrain where heat flow anomalies exist. In the second model heat flow values are estimated using the heat flow equation. Uniform heat flow in the region should result in a deeper BSR downslope toward the trench due to higher pressure; however results indicate the BSR is deepest at over 325 meters below the seafloor (mbsf) further landward and shoals near the trench to less than 100 mbsf, suggesting elevated heat flow towards the toe of the accretionary prism. Heat flow values also reflect this relation. In addition to this survey-wide trend, local heat flow anomalies appear in the form of both circular patterns and linear trends extending across the survey, which can be related to mounds, thrust faults, folds, double BSRs, and seafloor erosion imaged in the seismic data. I suggest that these areas of higher local heat flow represent sites where advection of heat from deep, upward-migrating, thermogenically-sourced fluids and/or gases may be taking place. These heat flow trends have implications for not only earthquake nucleation, but also methane hydrate reserve stability.

Ever since the discovery of seafloor hydrothermal systems at mid ocean ridges, scientists have been trying to understand the complex dynamic processes by which thermal energy is transported advectively by chemically reactive aqueous fluids from Earth's interior to the surface. Hydrothermal systems are generally assumed to consist of a heat source and a fluid circulation system. Understanding the interconnected physical, chemical, biological, and geological processes at oceanic spreading centers is important because these processes affect the global energy and biogeochemical budgets of the Earth system. Despite two decades of focused study of hydrothermal systems, several key questions remain concerning the behavior and evolution of hydrothermal vent systems. Among these are: (a) the partitioning of heat transport between focused and diffuse flow, and (b) the spatial extent and distribution of hydrothermal recharge. These are the main topics of investigation in this thesis. To address these issues, I first use a single-pass modeling approach using a variety of observational data in a simple parametric scale analysis of a hydrothermal vent field to determine fundamental parameters associated with the circulation and magmatic heat transfer for a number of seafloor hydrothermal systems for which the constraining data are available. To investigate the partitioning of heat flux between focused high temperature and diffuse flow I extend the one-limb single pass model to incorporate two single-pass limbs to represent deep and shallow circulation pathways. As a result, I find that 90% of the heat output is from high temperature fluid circulating in the deep limb even though much of the heat loss appears at the seafloor as low-temperature diffuse flow. Next, I use the parametric description of hydrothermal circulation to investigate hydrothermal recharge at the East Pacific Rise 9°50′ N hydrothermal site. Using a 1-D model of recharge through an area of 10⁵ m² elucidated by microseismicity in the oceanic crust I find that anhydrite precipitation is likely to result in rapid sealing of pore space in the recharge zone. This would lead to rapid decay of hydrothermal venting, which is contrary to observations. Then I consider two-dimensional numerical models of hydrothermal circulation in a porous box heated from below. The preliminary results of these models suggests that the anhydrite precipitation zone will be more diffuse, but additional work is needed to test whether anhydrite precipitation will seal the pore space.

Many astrophysical plasmas and some laboratory plasmas are relativistic: either the thermal speed or the local bulk flow in some frame approaches the speed of light. Often, such plasmas are magnetized in the sense that the Larmor radius is smaller than any gradient scale length of interest. Conventionally, relativistic MHD is employed to treat relativistic, magnetized plasmas; however, MHD requires the collision time to be shorter than any other time scale in the system. Thus, MHD employs the thermodynamic equilibrium form of the stress tensor, neglecting pressure anisotropy and heat flow parallel to the magnetic field. We re-examine the closure question and find a more complete theory, which yields a more physical and self-consistent closure. Beginning with exact moments of the kinetic equation, we derive a closed set of Lorentz-covariant fluid equations for a magnetized plasma allowing for pressure and heat flow anisotropy. Basic predictions of the model, including its thermodynamics and the dispersion relation's dependence upon relativistic temperature, are examined. Further, the model is applied to two extant astrophysical problems.

Throughout this paper, we study heat flow in random versus homogeneous media. The main goal is to study in what sense the temperature uepsilon(x, o) in a medium with random d by d conductivity matrix a converges to the temperature u(x) of a medium with a constant (effective) d by d conductivity matrix q (where o represents randomness and x represents position in d-dimensional space). Assume a has uniformly elliptic symmetric part; this guarantees that heat always flows from warmer to cooler regions and never vice versa. In the one dimensional case (d = 1), explicit solutions of random and deterministic ODE's are derived. From these explicit solutions and two ergodic theorems, some convergence and nonconvergence results follow. It turns out that q11, is not the expectation of a11, but rather 1E1/a11 . In the case d ≥ 3, variational solutions are constructed for the constant conductivity PDE, the random conductivity PDE, and the effective conductivity matrix q. Then using Green's functions, the Von Neumann ergodic theorem, and the construction of the Fourier transforms of uepsilon and u (in x), we prove a uniform convergence and a fractional-derivative-convergence result. In doing so, we extend Koslov's convergence-in-variance result. The nonconvergence result in the one dimensional case and the correction term in the Papanicolaou-Varadhan strong convergence theorem both suggest that our fractional-derivative-convergence result is tight.