Heat Flow Experiments Research Articles

The surface temperatures of flat areas on the Moon

Lunar surface temperature (LST) is a quantity of special interest for interpreting the thermal character of the regolith. It is affected by the solar irradiance, earthshine, and heat flow for the flat areas on the Moon. We present an improved transient temperature model to calculate temperatures of lunar flat surfaces. The model consists of one-dimensional thermal diffusion equation and two boundary conditions. The improved lunar surface boundary condition allows one to precisely determine the effective solar irradiance (ESI) and earthshine. The simulated surface temperatures suggest consistency with the measured temperatures from the thermocouples of Apollo 15 and 17 heat flow experiments. From the LST simulated with the improved model, it is found the annual-seasonal variations present obvious latitude characters, with the highest surface temperature occurring in late October, November, and December separately at high (>∼72°) latitudes, middle latitudes, and low (<∼20°) latitudes, respectively; the lowest surface temperatures occur in late July. Furthermore, the discrepancies between the maximum and minimum temperatures decrease as latitude increases, as do the maximum and minimum lunar surface temperatures. The surface daytime temperature would change by 179.4 K with a 1322.5 W/m2 change in the ESI. A 0.12 W/m2 and 0.02 W/m2 change of the earthshine and heat flow would lead to 0.5 and 0.09 K in surface nighttime temperature, respectively.

Retrieval of lunar polar heat flow from Chang’E-2 microwave radiometer and Diviner observations

The internal heat flow related to the Moon’s composition, interior structure, and evolution history is not well-constrained and understood on a global scale. Up to now, only two in situ heat flow experiments, Apollo 15 and 17 were deployed nearly 50 years ago. The measured high values of heat flow might be influenced by lateral heat at highland/mare boundaries and enhanced by heat production from radioactive elements enriched unit, and may also be disturbed by astronauts’ activities. In this study, we proposed a new method to retrieve heat flows at two permanently shadowed craters, Haworth and Shoemaker of the Moon’s south pole, from Chang’E-2 microwave radiometer data and Diviner observations. Our results show that the average heat flow is 4.9 ± 0.2 mW/m2. This provides a constraint for the bulk concentration of Thorium within the lunar south polar crust 656 ± 54 ppb, which helps us understand the Moon’s thermal evolution and differentiation.

THE HEAT BALANCE FOR EXTERNAL COMPOSITE WALLS

<jats:p>One of the first steps in reducing energy consumption for heating and cooling buildings is developing of thermal insulation envelope of building. Nowadays contemporary walls have constructions composed from different layers – which make composite structures. We have developed model of the heat balance and based on that model simulation that could analyze and determine the heat balance and temperature distribution inside the buildings in dependence from external conditions and temperature distribution inside the walls and on their boundaries between different layers. All cases represents passive isolation, where the heat balance depend only on materials characteristics, on their heat transfer coefficients, thermal conductance properties and thickness of used materials. For various combinations of today available construction and insulating materials, we have calculated the overall coefficients of heat transmission. Our calculations confirm advantage of usage hollow bricks instead solid bricks, and placing insulation layers on the outer side of walls. Furthermore, those simulations will serve as test for the wider project of the dynamic heat flow experiments in general structures and among them in nanostructures as well.</jats:p>

Potential effects of atmospheric collapse on Martian heat flow and application to the InSight measurements

Heat flow is an important constraint on planetary formation and evolution. It has been suggested that Martian obliquity cycles might cause periodic collapses in atmospheric pressure, leading to corresponding decreases in regolith thermal conductivity (which is controlled by gas in the pore spaces). Geothermal heat would then build up in the subsurface, potentially affecting present–day heat flow — and thus the measurements made by a heat–flow probe such as the InSight HP3 instrument. To gauge the order of magnitude of this effect, we model the diffusion of a putative heat pulse caused by thermal conductivity changes with a simple numerical scheme and compare it to the heat–flow perturbations caused by other effects. We find that an atmospheric collapse to 300 Pa in the last 40 kyr would lead to a present–day heat flow that is up to 2−8% larger than the average geothermal background. Considering the InSight mission with expected 5−15% error bars on the HP3 measurement, this perturbation would only be significant in the best-case scenario of full instrument deployment, completed measurement campaign, and a well–modelled surface configuration. The prospects for detecting long-term climate perturbations via spacecraft heat–flow experiments remain challenging.

Application of Finite Difference Method for determining lunar regolith diurnal temperature distribution

This study was performed in order to verify viability of using finite difference method and proposed simple astrometrical model for modelling heat transfer in lunar regolith. The concept was examined by developing FD model of heat flow for upper 0,9 m of lunar regolith, and comparing obtained results with in situ measurements provided by Apollo 15 and 17 heat flow experiments. The model was based on FDM approximation of Fourier’s law for one dimensional transient heat flow. Both constant and temperature-dependent thermophysical properties of lunar regolith were obtained from in situ measurements. Thermal boundary conditions were assumed on in situ measurements and on remote sensing based analytical model. In order to approximate Sun's position at lunar sky, simple analytical astrometric model of lunar rotation was developed. Matlab 2012a was used to conduct the calculations. Stable solutions were obtained for latitudes between 0 and 80°. Satisfactory agreement between Apollo 15 and 17 in situ measurements and FDM modelling was observed. A conclusion was reached, that both FDM and proposed astrometrical model are to be successfully applied for modelling heat transfer in lunar regolith.

Reaction kinetic studies of metal-doped magnesium silicides

Metal-doped magnesium silicides are promising thermoelectric materials for waste heat recovery application at 500–800 K because of their low density, large natural availability, non-toxicity, good thermal stability, and transport properties. Reaction kinetics of metal-doped magnesium silicides, Mg2SiXm (X = Ti, Nb, Mn, and Co; m = 0.02, 0.04, and 0.08 mol) were investigated in this study. A simple and rapid synthesis of Mg2SiXm samples was carried out using pelletizing, and sintering method at 773–823 K for 300 s. The effect of metal doping on the lattice constants of Mg2SiXm samples was examined using X-ray diffraction technique. Differential thermal analysis heat flow experiments were conducted on (2Mg + Si + mX) sample mixtures to study the solid-state reaction kinetics of Mg2SiXm alloys formation at different scan rates of 0.08, 0.16, 0.25, 0.33 Ks−1. Activation energies for the formation reaction of Mg2Si were determined using Ozawa, and Kissinger–Akahira–Sunrose equations. A 3-D diffusion-controlled reaction mechanism was proposed based on Coats–Redfern (CR) model. The effect of concentration of the metal-dopants on the formation activation energies of Mg2SiXm was investigated using the CR equation plots.

Compressional stress effect on thermal conductivity of powdered materials: Measurements and their implication to lunar regolith

Thermal conductivity of powdered materials under vacuum conditions is a valuable physical parameter in the context of planetary sciences. We report results of thermal conductivity measurements of 90–106μm and 710–1000μm glass beads, and lunar regolith simulant using two different experimental setups for varying the compressional stress and the temperature, respectively. We found the thermal conductivity increase with the compressional stress, for example, from 0.003 to 0.008Wm−1K−1 for the glass beads of 90–106μm in diameter at the compressional stress less than 20kPa. This increase of the thermal conductivity is attributed the areal enlargement of the contacts between particles due to their elastic deformation. The thermal conductivity increased also with temperature, which primarily represented enhancement of the radiative heat conduction between particles. Reduction of the estimated radiative conductivity from the effective thermal conductivity obtained in the first experiment yields the relation between the solid conductivity (conductive contribution through inter-particle contacts) and the compressional stress. We found that the solid conductivity is proportional to approximately 1/3 power of the compressional stress for the glass beads samples, while the regolith simulant showed a weaker exponent than that of the glass beads. We developed a semi-empirical expression of the thermal conductivity of the lunar regolith using our data on the lunar regolith simulant. This model enabled us to estimate a vertical distribution of the lunar subsurface thermal conductivity. Our model provides an examination for the density and compressional stress relationships to thermal conductivity observed in the in-situ measurements in Apollo 15 and 17 Heat Flow Experiments.

Laminar-to-Turbulent Transition Flow inside a Heated Circular Tube

The natural transition flow and convective heat transfer inside an electrically heated circular tube are analyzed. The transition flow is treated as a composition of fully developed laminar and turbulent flows by assuming the fluctuating velocity in radial direction exists as if the flow is fully turbulent. The composite ratios are used to define the composite flow, and they fluctuate in transition flow. The criterion of minimum entropy production is used to derive an equation which can describe how transition evolves. It is pointed out that the fluctuations of the composite ratios govern the transition behavior. One fluctuation function is given to attain agreements with measurements including those obtained in heat transfer and flow experiments.

Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations

Semiconductor alloys exhibit a strong dependence of effective thermal conductivity on measurement frequency. So far this quasi-ballistic behaviour has only been interpreted phenomenologically, providing limited insight into the underlying thermal transport dynamics. Here, we show that quasi-ballistic heat conduction in semiconductor alloys is governed by L\'evy superdiffusion. By solving the Boltzmann transport equation (BTE) with ab initio phonon dispersions and scattering rates, we reveal a transport regime with fractal space dimension $1 < \alpha < 2$ and superlinear time evolution of mean square energy displacement $\sigma^2(t) \sim t^{\beta} (1 < \beta < 2)$. The characteristic exponents are directly interconnected with the order $n$ of the dominant phonon scattering mechanism $\tau \sim \omega^{-n} (n>3)$ and cumulative conductivity spectra $\kappa_{\Sigma}(\tau;\Lambda)\sim (\tau;\Lambda)^{\gamma}$ resolved for relaxation times or mean free paths through simple relations $\alpha = 3-\beta = 1 + 3/n = 2 - \gamma$. The quasi-ballistic transport inside alloys is no longer governed by Brownian motion, but instead dominated by L\'evy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental $\alpha$ values for InGaAs and SiGe, determined through TR analysis with a novel L\'evy heat formalism, match ab initio BTE predictions within a few percent. Our findings lead to a deeper and more accurate quantitative understanding of the physics of nanoscale heat flow experiments.

Thermal Property Measurements of Stratigraphic Units with Modeled Implications for Expected Performance of Vertical Ground Source Heat Pumps

Ground temperature and lithology influence ground source heat pump (GSHP) performance; however, typical design for residential systems uses estimated handbook values that are not necessarily representative of local geology. The incorporation of true ground temperature and thermal property measurements into design models would yield a more optimal design and thus decrease life cycle cost. A two-part study was conducted, first focusing on recording thermal properties of specific lithofacies in a particular region (Wisconsin, USA), then modeling how these measurements could change expected GSHP design and performance in a typical residential setting. Representative sedimentary, igneous, and metamorphic rocks from Wisconsin were characterized using guarded-comparative-longitudinal heat flow experiments (ASTM E1225), calorimetry, and weight-volume assessments. X-ray diffraction was also performed on some samples to assess the effect of mineralogy. Across all rock types, thermal conductivity ranged from 1.84 to 6.71 W m−1 K−1, and specific heat capacity ranged from 713 to 891 J kg−1 K−1. The indexed values were used to construct a hypothetical vertical heat exchange loop penetrating vertically consecutive Paleozoic strata. The hypothetical loop was examined using the rate of system temperature drop under full load as a measure of performance during the heating season. Expected system performance was compared between commonly cited thermal conductivity values of their general lithologies (e.g. sandstone, dolomite, shale) and the laboratory-measured thermal properties of the specific formations. Thermal conductivity indexed by general lithology proved to be insufficient as a design parameter to generate accurate assessments of GSHP performance.

Thermal conductivity of transition metal containing type-I clathrates

ABSTRACTConcerning a materials ability to convert heat to electrical energy, the electrical power factor S2/ρ as well as the thermal conductivity at elevated temperatures are of special interest. Since Flash experiments measure the thermal diffusivity and standard steady-state heat-flow experiments are inaccurate at elevated temperatures due to radiation errors inherent to this technique, direct and accurate thermal conductivity data on type-I clathrate single crystals at elevated temperatures are scarce in literature. Here we report 3ω thermal conductivity data on single crystalline Ba8Cu5.09Ge40.91 (BCG), La1.23Ba6.99Au5.91Si39.87, and Ce1.06Ba6.91Au5.56Si40.47 in the temperature range between 80 and 330 K, and specific heat data on BCG between 2 and 300 K. The comparison of our room temperature phonon thermal conductivity data (κph) to results on transition metal (TM) free type-I clathrates in terms of the guest free space (Rfree) suggests a stronger dependence of κph on Rfree for the clathrates containing TM elements.

The hydration of alite: a time-resolved quantitative X-ray diffraction approach using theG-factor method compared with heat release

The classical external-standard method derived from the work of O'Connor &amp; Raven [Powder Diffr.(1988),3, 2–6] was used to examine the hydration of the major phase, alite, of ordinary Portland cements at different temperatures and different water/alite ratios. In order to estimate the accuracy of the method, heat-flow curves were calculated from the alite dissolution curves obtained from X-ray diffractionin situexperiments. The heat-flow curves calculated in this way were compared with heat-flow curves recorded using a calorimeter. It is shown that the calculated curves agree well with the curves obtained from heat-flow experiments.

Lunar heat flow experiments: Science objectives and a strategy for minimizing the effects of lander-induced perturbations

Reliable measurements of the Moon's global heat flow would serve as an important diagnostic test for models of lunar thermal evolution and would also help to constrain the Moon's bulk abundance of radioactive elements and its differentiation history. The two existing measurements of lunar heat flow are unlikely to be representative of the global heat flow. For these reasons, obtaining additional heat flow measurements has been recognized as a high priority lunar science objective. In making such measurements, it is essential that the design and deployment of the heat flow probe and of the parent spacecraft do not inadvertently modify the near-surface thermal structure of the lunar regolith and thus perturb the measured heat flow. One type of spacecraft-related perturbation is the shadow cast by the spacecraft and by thermal blankets on some instruments. The thermal effects of these shadows propagate by conduction both downward and outward from the spacecraft into the lunar regolith. Shadows cast by the spacecraft superstructure move over the surface with time and only perturb the regolith temperature in the upper 0.8m. Permanent shadows, such as from thermal blankets covering a seismometer or other instruments, can modify the temperature to greater depth. Finite element simulations using measured values of the thermal diffusivity of lunar regolith show that the limiting factor for temperature perturbations is the need to measure the annual thermal wave for 2 or more years to measure the thermal diffusivity. The error induced by permanent spacecraft thermal shadows can be kept below 8% of the annual wave amplitude at 1m depth if the heat flow probe is deployed at least 2.5m away from any permanent spacecraft shadow. Deploying the heat flow probe 2m from permanent shadows permits measuring the annual thermal wave for only one year and should be considered the science floor for a heat flow experiment on the Moon. One way to meet this separation requirement would be to deploy the heat flow and seismology experiments on opposite sides of the spacecraft. This result should be incorporated in the design of future lunar geophysics spacecraft experiments. Differences in the thermal environments of the Moon and Mars result in less restrictive separation requirements for heat flow experiments on Mars.

An Application of the Modified PID Control System for Heat Flow Experiment

The Proportional-Integral-Derivative (PID) controller structure is the most widely used in industrial applications thanks to its structural simplicity and applicability in solving practical control problems. It is not, however, almighty. Yamada and Hagiwara proposed design modified PID controllers to make control for any plant stable and make admissible sets of P, I, and D parameters mutually independent. Applying modified PID control to practical plants requires that the influence of disturbance in the plant be considered. In many cases, this disturbance is unknown, making it difficulty to attenuate. Although designs have been proposed for modified PID control to attenuate unknown disturbances, little has been done in examining the attenuation of unknown disturbances. We demonstrate the effectiveness of modified PID control in attenuating unknown disturbances for temperature control in heat flow experiments.

Time Dependent Surface Heat Transfer in Light Weight Aggregate Cement Based Materials

Surface temperature changes of building materials affect the calculation of heat flow and thus the energy use in heating and cooling. The surface heat transfer coefficient , limiting the heat flow between material surface and ambient air is normally taken as a constant. In this study we propose a time-dependent function . We estimate from unidirectional heat flow experiments with transient and steady-state conditions. Using temperature measurements and the conservation of energy at the surface including convective and irradiative boundary conditions, the value of was obtained both using Finite Difference and Taylor Polynomials methods. Numerical solutions of temperature distribution as function of time were improved with the obtained -functions compared to with constant . There were no clear difference between on different materials, and the final values observed were in the order of magnitude expected from the literature.

Thermal disturbances caused by lander shadowing and the measurability of the martian planetary heat flow

A measurement of the martian planetary heat flow requires the determination of the subsurface temperature gradient, which is affected by surface insolation. I investigate the propagation of thermal disturbances caused by lander shadowing and derive measurement requirements for in situ heat flow experiments. I find that for short term measurements spanning 180 sol, a measurement depth of at least 2 m is needed to guarantee a stable thermal environment directly underneath the lander for Moon-like thermal conductivities of 0.02 W m - 1 K - 1 . For extremely large conductivities of 0.1 W m - 1 K - 1 , this depth needs to be increased to 4 m, but if the probe can be deployed outside the lander structure, the respective depths can be decreased by 1 m. For long term measurements spanning at least a full martian year heat flow perturbations are smaller than 5% below a depth of 3 m directly underneath the lander. Outside the lander structure, essentially unperturbed measurements may be conducted at depths of 0.5 and 1.5 m for thermal conductivities of 0.02 and 0.1 W m - 1 K - 1 , respectively.

Processing of LiBH 4 from its elements by ball milling method

Investigations of alternative renewable energy resources continue, with many studies concentrating on hydrogen storage. However, there are a few problems such as storage, transportation, delivery to the user and usage safely, to be addressed to facilitate commercialization and wide usage of the hydrogen. The absorbed form within the metal hydrides seems to be the best solution of this problem. Since Li is the lightest metal, it has the advantage as the stored amount of hydrogen mass ratio. LiBH 4 production process was investigated using elemental Li, B and H 2. Spex type ball milling with tungsten carbide, stainless steel and zirconia type vessels, was used to mix the different amount of Li and B under argon atmosphere. X-ray diffraction pattern demonstrated that the LiB was obtained. A system was designed to provide a hydrogen atmosphere of 60 bars to force hydrogen into the LiB structure. FTIR analysis strongly indicated the LiBH 4 compound when the mol ratio of B/Li is 0.214. Thermal decomposition and heat flow experiments performed simultaneously with DSC and TGA techniques also indicate hydrogen-rich structure showing greater mass loss. One gram of lithium borohydride sample released 1423 ml of hydrogen with Ni catalyst while NiO caused 1972.94 ml of hydrogen gas desorption, equaling to 90% of the theoretical yield of commercial LiBH 4. Indicating that, hydrogen of water can be obtained by either Ni or NiO catalysts.

The present status of the Japanese Penetrator Mission: LUNAR-A

The scientific objective of the LUNAR-A Japanese Penetrator Mission is to explore the lunar interior by seismic and heat-flow experiments. Two penetrators containing two-component seismometer and heat-flow probes will be deployed from a spacecraft onto the lunar surface, one on the nearside and the other on the farside of the moon. The data obtained by the penetrators will be transmitted to the ground station by way of the LUNAR-A mother spacecraft orbiting at an altitude of about 200 km. The seismic observations are expected to provide key data on the size of the lunar core, as well as data on the deep mantle structure. The heat-flow measurements at two different sites will also provide important data on the thermal structure and bulk concentrations of heat-generating elements in the Moon. These data will provide much stronger geophysical constraints on the origin and evolution of the Moon than has ever been obtained. The LUNAR-A mission was supposed to be launched in 2004. However, a malfunction of spacecraft subsystem and technical issues for penetrator system occurred during the course of the qualification level test. Therefore, further improvements and some modifications were considered to be required for reliability and robustness. The development of the mother spacecraft was temporarily suspended, while we have put a three-year program into effect to solve the penetrator technology issues.

Soil Heat Flux Plates: Heat Flow Distortion and Thermal Contact Resistance

Persistent concern regarding surface energy balance closure encourages increased scrutiny of potential sources of error. Laboratory and field experiments addressed heat flow distortion and thermal contact resistance errors during measurement of soil heat flux (G) using the flux plate technique. Steady‐state, one‐dimensional heat flow experiments determined flux plate thermal conductivities (λm) and measured the effect of air gaps and thermal heat sink coatings on plate performance. Use of measured instead of manufacturer‐specified λm and plate dimensions in a heat flow distortion correction improved the consistency but not the average disagreement between imposed sand G and corrected plate heat flux density (Gm). Consistent underestimates of G in dry sand by 20 to 25% after heat flow distortion correction was attributed to thermal contact resistance effects. A convex air gap 0.1 to 1.32 mm thick across 5.9% of the plate face area reduced Gm by up to 9.7%. A thin layer of a thermal heat sink compound with λ 0.18 W m−1 K−1 greater than the plate λm (1.0 W m−1 K−1) did not increase Gm in a clay soil but increased Gm by ∼6% in quartz sand. A 6.5% increase in Gm was also observed for plates treated with the same heat sink compound in a silt loam soil under field conditions. Thermal contact resistance errors are probably &lt;10% in moist, medium‐textured soils and can be minimized by careful plate installation. Relatively greater errors in Gm may occur due to thermal contact resistance in dry sand and due to heat flow distortion when soil λ &gt;&gt; λm

Lunar-A mission: Outline and current status

The scientific objective of the Lunar-A, Japanese Penetrator Mission, is to explore the lunar interior by seismic and heat-flow experiments. Two penetrators containing two seismonieters (horizontal and vertical components) and heat-flow probes will be deployed from a spacecraft onto the lunar surface, one on the near-side and the other on the far-side of the moon. The data obtained by the penetrators will be transmitted to the earth station via the Lunar-A mother spacecraft orbiting at an altitude of about 200km. The spacecraft of a cylindrical shape, 2.2 m in maximum diameter and 1.7 m in height, is designed to be spin-stabilized. The spacecraft will be inserted into an elliptic lunar orbit, after about a half-year cruise during which complex manoeuvering is made using the lunar-solar gravity assist. After lunar orbit insertion, two penetrators will be separated from the spacecraft near perilune, one by one, and will be landed on the lunar surface. The final impact velocity of the penetrator will be about 285 m/sec; it will encounter a shock of about 8000 G at impact on the lunar surface. According to numerous experimental impact tests using model penetrators and a lunar-regolith analog target, each penetrator is predicted to penetrate to a depth between 1 and 3 m, depending on the hardness and/or particle-size distribution of the lunar regolith. The penetration depth is important for ensuring the temperature stability of the instruments in the penetrator and heat flow measurements. According to the results of the Apollo heat flow experiment, an insulating regolith blanket of only 30cm is sufficient to dampen out about 280 K lunar surface temperature fluctuation to <3 K variation. The seismic observations are expected to provide key data on the size of the lunar core, as well as data on deep lunar mantle structure. The heat flow measurements at two penetrator-landing sites will also provide important data on the thermal structure and bulk concentrations of heat-generating elements in the Moon. These data will provide much stronger geophysical constraints on the origin and evolution of the Moon than has been obtained so far. Currently, the Lunar-A system is being reviewed and a more robust system for communication between the penetrators and spacecraft is being implemented according to the lessons learned from Beagle-2 and DS-2 failures. More impact tests for penetrators onto a lunar regolith analogue target will be undertaken before its launch.