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Equations governing the incident heat flux distribution beneath a lamp-reflector system were developed. Analysis of a particular radiant heating facility showed good agreement between theory and experiment when a lamp power loss correction was used. In addition, the theory was employed to estimate thermal disruption in the radiation field caused by a protruding probe.
This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.
"Knowledge about the dynamics of the D double prime region is a key to unlock some fundamental mysteries of the Earth heat engine which governs a wide range of global geophysical processes from tectonics to geodynamo." This benign sentence makes complete sense to many geophysicists. But for many others, it makes sense all except the odd nomenclature "D double prime". One knows about the crust, upper and lower mantle, outer and inner core, but where is the D double prime region? What meaning does it try to convey? Where is D prime region, or D, or A, B, C regions for that matter, and are there higher-order primes? How does such an odd name come about anyway? D double prime, or more "simply" D", is a generic designation given to the thin shell, about 200 km thick, of the lowermost mantle just above the core-mantle boundary inside the Earth. Incidentally, whether D" is "simpler" than "D double prime" depends on whether you are pronouncing it or writing/typing it; and D" can be confusing to readers in distinguishing quotation marks (such as in the above sentences) and second derivatives, and to word processors in spelling check and indexing.
Laminar film condensation under the simultaneous influence of gas-liquid interface shear and body force (g force) is analyzed over a flat plate. Important parameters governing condensation and heat transfer of pure vapor are determined. Mixtures of condensable vapor and noncondensable gas are also analyzed. The conditions under which the body force has a significant influence on condensation are determined.
Considerable uncertainty remains as to the importance of mechanisms governing decadal and longer variability of the Walker Circulation, its connection to the tropical climate system, and prospects for tropical climate change in the face of anthropogenic forcing. Most contemporary climate models suggest that in response to elevated CO2 and a warmer but more stratified atmosphere, the required upward mass flux in tropical convection will diminish along with the Walker component of the tropical mean circulation as well. Alternatively, there is also evidence to suggest that the shoaling and increased vertical stratification of the thermocline in the eastern Pacific will enable a muted SST increase there-- preserving or even enhancing some of the dynamical forcing for the Walker cell flow. Over the past decade there have been observational indications of an acceleration in near-surface easterlies, a strengthened Pacific zonal SST gradient, and globally-teleconnected dislocations in precipitation. But is this evidence in support of an ocean dynamical thermostat process posited to accompany anthropogenic forcing, or just residual decadal fluctuations associated with variations in warm and cold ENSO events and other stochastic forcing? From a modeling perspective we try to make headway on this question by examining zonal variations in surface energy fluxes and dynamics governing tropical upper ocean heat content evolution in the WCRP CMIP5 model projections. There is some diversity among model simulations; for example, the CCSM4 indicates net ocean warming over the IndoPacific region while the CSIRO model concentrates separate warming responses over the central Pacific and Indian Ocean regions. The models, as with observations, demonstrate strong local coupling between variations in column water vapor, downward surface longwave radiation and SST; but the spatial patterns of changes in the sign of this relationship differ among models and, for models as a whole, with observations. Our analysis focuses initially on probing the inter-model differences in energy fluxes / transports and Walker Circulation response to forcing. We then attempt to identify statistically the El Nino- / La Nina-related ocean heat content variability unique to each model and regress out the associated energy flux, ocean heat transport and Walker response on these shorter time scales for comparison to that of the anthropogenic signals.
Reduced gravity does not significantly affect the thermal histories in the M551 specimen, even if molten metal flow pattern is different from that in terrestrial conditions. Thermal histories corresponding to terrestrial experimental conditions were calculated by use of the computer programs. Heat conduction through brazing alloy (M552 experiment) is improved in the Skylab conditions, because of the increased extent, rate and uniformity of braze spreading in space. Effects of reduced gravity on heat flow in the M553 specimen are insignificant, because convection effects appear instantaneously and conduction is a governing factor on the heat flow.
The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.
The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.
The operating temperature of a loop heat pipe (LHP) is governed by the saturation temperature of its compensation chamber (CC); the latter is in turn determined by the balance among the heat leak from the evaporator to the CC, the amount of subcooling carried by the liquid returning to the CC, and the amount of heat exchanged between the CC and ambient. The LHP operating temperature can be controlled at a desired set point by actively controlling the CC temperature. The most common method is to cold bias the CC and use electric heater power to maintain the CC set point temperature. The required electric heater power can be large when the condenser sink is very cold. Several methods have been developed to reduce the control heater power, including coupling block, heat exchanger and separate subcooler, variable conductance heat pipe, by-pass valve with pressure regulator, secondary evaporator, and thermoelectric converter. The paper discusses the operating principles, advantages and disadvantages of each method.
Layering two-dimensional van der Waals materials provides a high degree of control over atomic placement, which could enable tailoring of vibrational spectra and heat flow at the sub-nanometer scale. In this work, using spatially resolved ultrafast thermoreflectance and spectroscopy, we uncover the design rules governing cross-plane heat transport in superlattices assembled from monolayers of graphene (G) and MoS 2 (M). Using a combinatorial experimental approach, we probe nine different stacking sequences, G, GG, MG, GGG, GMG, GGMG, GMGG, GMMG, and GMGMG, and identify the effects of vibrational mismatch, interlayer adhesion, and junction asymmetry on thermal transport. Pure G sequences display evidence of quasi-ballistic transport, whereas adding even a single M layer strongly disrupts heat conduction. The experimental data are described well by molecular dynamics simulations, which include thermal expansion, accounting for the effect of finite temperature on the interlayer spacing. The simulations show that an increase of ~2.4% in the layer separation of GMGMG, relative to its value at 300 K, can lead to a doubling of the thermal resistance. Using these design rules, we experimentally demonstrate a five-layer GMGMG superlattice “thermal metamaterial” with an ultralow effective cross-plane thermal conductivity comparable to that of air.
In this paper, the budget terms in the transport equations of the Reynolds stresses, the turbulent kinetic energy (TKE), the internal energy, and the turbulent heat flux are computed using a direct numerical simulation (DNS) database of hypersonic turbulent boundary layers (TBLs) subject to favorable pressure gradients (FPG). Study of the Reynolds stress and TKE budgets shows that FPG has a damping effect on turbulence production, transport, and destruction. The semilocal scaling fails to collapse the Reynolds stress and TKE budget terms between the zero pressure gradient (ZPG) and the strong FPG cases, suggesting that the mechanical nonequilibrium due to FPG leads to changes in Reynolds-stress and TKE transport that cannot be captured by Morkovin’s hypothesis. Minimal change is seen in the internal energy budget in the presence of FPG, indicating a minimal impact due to FPG on the mean thermal field. While the near-wall transport of wall-normal turbulent heat flux is largely governed by the balance between the turbulent viscous-thermal transport term and the turbulent viscous-thermal dissipation term, the transport of the streamwise turbulent heat flux is influenced by contributions from almost all of the budget terms. For the strong FPG case in particular, production due to both the mean and the fluctuating strain rates begins to play a significant role in the near-wall transport of the streamwise turbulent heat flux, and their inclusion or modeling may be required to accurately predict turbulent heat fluxes for a strong FPG.
In this paper the results of an experimental investigation of thermoacoustic convection (TAC) heat transfer phenomenon in both zero-gravity and gravity environment are presented and compared with pure conduction heat transfer. The numerical solutions of the governing equations obtained by others for TAC heat transfer phenomenon are also discussed. The experimental results show that for rapid heating rate at a boundary, the contribution of TAC heat transfer to a gas could be significantly (one order of magnitude) higher than heat transfer rate from pure conduction. The results also show significantly reduced transient time in heat transfer processes involving thermoacoustic convective heat transfer mode in both space and gravity environment.
Numerical calculations governing the efficiency of coronal loop heating by the resonant absorption of shear Alfven waves are reported. The loop structure is modeled by a class of axisymmetric force-free equilibria of a long straight cylinder, approximating a large aspect ratio loop. For a range of parameters characterizing the evolution of solar coronal loops, the absorption bandwidth falls in the frequency range of the photospheric motions due to granulation and p-modes. Resonant Alfven wave absorption is thus a viable mechanism for coronal loop heating.
Abstract This research paper focuses on the thermo-hydro-mechanical (THM) modeling of brine migration in a heated borehole test conducted as part of the ongoing Brine Availability Test in Salt (BATS) at the Waste Isolation Pilot Plant (WIPP) in New Mexico. It is a component of the international collaboration project DECOVALEX-2023 (DEvelopment of COupled models and their VALidation against EXperiments), which aims to understand the THM processes governing brine flow in heated rock salt repositories through collaborative analysis by multiple research teams. Using the TOUGH–FLAC simulator, THM simulations were performed and compared with data from the BATS phase 1a. This experiment involved two identical horizontal-borehole arrays, one heated and one serving as a control, both equipped with sensor arrays. Analysis of measurements revealed water flow rate surges during heater power transitions, with the highest jump observed during cooling. Acoustic emission activity exhibited distinct patterns in response to heater power changes, suggesting that damage to rock salt is particularly pronounced during the cooling phase. The THM simulations successfully captured these phenomena, highlighting the significance of thermal effects, brine migration, and mechanical behavior in predicting brine availability in heated and damaged rock salt. Our modeling also revealed the critical interplay between heating and cooling-induced damage and its influence on flow properties, particularly affecting brine inflow estimation. Notably, we found that cooling-induced brine inflow spikes result from increased permeability due to tensile dilatancy. These findings have important implications for the development of robust containment strategies and enhance our understanding of the complex processes involved in repository performance.
The considered region comprises 81% of the surface of Mars. Thermal inertia I is a composite surface property, which is equal to the square root of the product of three factors, including the thermal conductivity, the density, and the specific heat. I is the sole thermal parameter which governs the temperature variation of a periodically heated homogeneous surface, and, as such, is the prime intermediary between remote temperature observations and their geologic interpretation. The values for the thermal inertia found imply particulate surface materials. The variation in Martian surface thermal conductivity is about two orders of magnitude. Three large regions of low-inertia material are defined. Low-inertia material always possesses high albedo. There is a general tendency for higher-thermal-inertia surfaces to be darker but exceptions occur which may be related to a thin mantling of light dust or bonding of light material.
Summary Distributed temperature sensing (DTS) is a valuable tool to diagnose multistage hydraulic fracture treatments. When a stage interval is shut in, the clusters that take more fluid during pumping warm up more slowly. Therefore, the fluid volume injected into each cluster can be quantitatively interpreted by numerical inversion of the warm-back temperature behavior. This general concept assumes that the different warm-back behavior is controlled by only the injected fluid volume; however, recent observations of DTS data indicate that completion configurations significantly influence the warm-back behavior. This paper investigates the completion effects on the DTS interpretation. In ideal conditions, when a stage is fractured, the upstream stage intervals should show an almost uniform temperature that is close to the injected fluid temperature. This is due to the high fluid velocity of injected fluid in the wellbore, and the upstream intervals have not been perforated (noncommunicating intervals), so the only heat transfer is heat conduction between the wellbore fluid and the surrounding reservoir. But the field DTS data show considerably irregular variations in temperature along the upstream stage intervals. These variations are caused by the completion effects. The nonuniform temperature profile is caused by different heat transfer behavior induced by completion hardware along the production casing string, such as joints, clamps, and blast protectors, and by the sensing cable location in the cement, as well as the cement quality. Because the varying heat transfer behavior impacts the warm-back behavior as well as the temperature profile, the completion effects need to be considered in DTS interpretation. A method of DTS interpretation considering the completion effects to diagnose multistage fracture treatments was developed. Because the heat transfer between a wellbore and a reservoir depends on the overall heat transfer coefficient describing heat conduction through the completion in a forward model, this parameter needs to be tuned all along the wellbore. To calibrate the completion effect, the temperature inversion is conducted using the temperature measured at a stage interval that is upstream of a stage interval currently being treated. Because the interpreted stage interval is not perforated at that time, the thermal behavior at the noncommunicating interval is governed by only the heat conduction through the completion environment. Once the effective values of the overall heat transfer coefficient are estimated along the interpreted stage interval, they can be assumed to be constant physical parameters. Then, the fluid volume distribution is interpreted by using the effective overall heat transfer coefficient profile along each interval. This study provides a field application of the developed interpretation method. The new interpretation method provides more accurate diagnosis of fracture treatments by DTS interpretation.
The combined radiation/conduction heat transfer in high-porosity, high-temperature fibrous insulations was investigated experimentally and numerically. The effective thermal conductivity of fibrous insulation samples was measured over the temperature range of 300-1300 K and environmental pressure range of 1.33 x 10(exp -5)-101.32 kPa. The fibrous insulation samples tested had nominal densities of 24, 48, and 72 kilograms per cubic meter and thicknesses of 13.3, 26.6 and 39.9 millimeters. Seven samples were tested such that the applied heat flux vector was aligned with local gravity vector to eliminate natural convection as a mode of heat transfer. Two samples were tested with reverse orientation to investigate natural convection effects. It was determined that for the fibrous insulation densities and thicknesses investigated no heat transfer takes place through natural convection. A finite volume numerical model was developed to solve the governing combined radiation and conduction heat transfer equations. Various methods of modeling the gas/solid conduction interaction in fibrous insulations were investigated. The radiation heat transfer was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. A genetic-algorithm based parameter estimation technique was utilized with this model to determine the relevant radiative properties of the fibrous insulation over the temperature range of 300-1300 K. The parameter estimation was performed by least square minimization of the difference between measured and predicted values of effective thermal conductivity at a density of 24 kilograms per cubic meters and at nominal pressures of 1.33 x 10(exp -4) and 99.98 kPa. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements at other densities and pressures. The numerical model was also validated by comparison with a transient thermal test simulating reentry aerodynamic heating conditions.
Internal combustion engine driven combined heat and power (CHP) systems produce power while the waste heat is recovered and used for another purpose. For µCHP systems (less than 50kWe output) overall efficiencies can reach over 90% for products currently on the market throughout the world. On a fuel basis this offers an advantage over using grid-based power and another fuel for heat. Additionally, the cost of natural gas on an energy unit basis is significantly less expensive than electric power. This difference can lead to substantial savings for the end user of a CHP system. In some parts of the world, particularly Germany and Japan, µCHP has become a common part of the heat and distributed generation equipment mix. Market analysis conducted in 2012 showed that in North America there is potential of a 5,300 units per year market for µCHP, resulting in an annual energy savings of approximately 13.5 TBtu and more than $84 million in annual customer savings. However, µCHP still has not seen much market penetration in North America. This study helps to identify some of the reasons why, address roadblocks that still need to be overcome and provide experience to established best practices. Nine commercial sites were initially identified (fitness club, surgical center, senior community, resort and spa, commercial laundry, two multi-family housing, restaurant and manufacturing facility). Systems from two different manufacturers were installed at five sites total, but due to unforeseen circumstances, only three of those sites were finally commissioned: test data were collected by Oak Ridge National Laboratory. While not all systems were installed as intended, the project resulted in the following key findings: Micro combined heat and power is an unfamiliar technology for building owners and plumbing and electrical contractors that serve the buildings most suited for µCHP. Manufacturers will need to be aggressive in providing training and providing broad support to successfully bring the technology to market.; The proper integration of µCHP into other building systems is the most critical part of a successful installation. Manufacturers will need to be able to provide the expertise to train, advise and support the mechanical contractors during the design and installation of the heat integration system.; Regulations governing µCHP varies across the country. There are a few UL standards (UL 2200 and UL 1741) that apply nationally. Emissions are governed by EPA except in California where the California Air Resources Board (CARB) has established their own standard. Requirements that dictate installation and interconnection are dependent on local building codes and local utility processes and requirements. Some out of date building codes do not offer clear guidance for these requirements, leading to confusion. This makes developing training and determining broadly applicable best practices difficult.; Installation costs of µCHP are a key factor in making an installation successful. It is critical that these costs and all national, state and local regulations be understood and accounted for by all parties involved in the installation before a project is undertaken.; A robust customer service organization is important to meet the needs of the customers. These systems require annual maintenance and service and local capability is needed to keep costs inline.