THE ZERO LIMIT OF THERMAL DIFFUSIVITY FOR THE 2D DENSITY-DEPENDENT BOUSSINESQ EQUATIONS

This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.

The theoretical expressions of wood thermal diffusivity

From viewpoint of chemical element and microstructure of wood, this paper makes a discussion on thermal diffusivity of wood and two theoretical expressions of thermal diffusivity for the choral and radial directions were derived. The thermal diffusivities of the choral and radial directions for about 20 species of trees were calculated with the derived theoretical expressions and compared with the experimental values. The average error of the theoretical values of thermal diffusivity was 7.5% for choral direction and 6.2% for radial direction.

Thermal diffusivity of light-emitting diode packaging material determined by photoacoustic piezoelectric technique

Thermal property is one of the most important properties of light-emitting diode （LED）. Thermal property of LED packaging material determines the heat dissipations of the phosphor and the chip surface, accordingly having an influence on the light-emitting efficiency and the life-span of the device. In this paper, photoacoustic piezoelectric （PAPE） technique has been employed to investigate the thermal properties of polyvinyl alcohol （]？VA） and silicon dioxide, which are the new and the traditional packaging materials in white LED, respectively. Firstly, the theory of PAPE technique has been developed for two-layer model in order to investigate soft materials; secondly, the experimental system has been set up and adjusted by measuring the reference sample; thirdly, the thermal diffusivities of PVA and silicon dioxide are measured and analysed. The experimental results show that PVA has a higher thermal diffusivity than silicon dioxide and is a better packaging material in the sense of thermal diffusivity for white LED.

Influence of Annealing on the Grain Growth and Thermal Diffusivity of Nanostructured YSZ Thermal Barrier Coating

The nanostructured zirconia coatings were deposited by atmospherically plasma spraying. Scanning electron microscopy （SEM）, transmission electron microscopy （TEM） and X-ray diffraction were used to investigate the microstructure of the zirconia coatings. Thermal diffusivity values at normal temperatures have been evaluated by laser flash technique. Effect of annealing on the microstructure evolution of the zirconia coating has been performed. The grains and thermal diffusivity are increased with increasing annealing time and temperature. The grain growth is according to the GRIGC （the grain rotation induced grain coalescence） mechanism. The increase in thermal diffusivity is attributed to the grain growth and the decrease in porosity of nanostructured zirconia coatings.

Laser-induced thermal lens study of the role of morphology and hydroxyl group in the evolution of thermal diffusivity of copper oxide

The paper explores the evolution of thermal behavior of the material by studying the variations in thermal diffusivity using the single beam thermal lens(TL) technique. For this purpose, the decomposition of Cu(OH)_(2) into CuO is studied in a time range up to 120 h, by subjecting the sample to morphological, structural, and spectroscopic characterizations. The time evolution of thermal diffusivity can be divided into three regions for demonstrating the dynamics of the reaction. When the reaction is complete, the thermal diffusivity is also found to be saturated. In addition to the morphological modifications,from rods to flakes, the variations in the amount of hydroxyl group are attributed to be responsible for the enhancement of base fluid's thermal diffusivity by 165%. Thus the study unveils the role of hydroxyl groups in the thermal behavior of CuO.

Theoretical determination of thermal diffusivity of composite material

A very simple model based on the Quadrupole method was used in thetheoretical analysis of thermal diffusivity of composite materials of Cu-PVC, PVC-Cu-PVC, andCu-PVC-Cu. The use of MATLAB software with a return to real space using the Stehfest algorithm makesthe time of calculation very short. The thermal responses on the rear face of each consideredsample, which determine the thermal diffusivity were represented. A mathematical demonstration whichconfirmed the results was given. Thermal diffusivity determined from the rear face thermalresponses were compared with the results of the thermal diffusivity calculated by considering thecomposite materials to be homogeneous, and a discussion on the two kinds of results was provided.

Effect of Ocean Thermal Diffusivity on Global Warming Induced by Increasing Atmospheric CO_2

A global mean ocean model including atmospheric heating, heat capacity of the mixed layer ocean, and vertical thermal diffusivity in the lower ocean, proposed by Cess and Goldenberg (1981), is used in this paper to study the sensitivity of global warming to the vertical diffusivity. The results suggest that the behaviour of upper ocean temperature is mainly determined by the magnitude of upper layer diffusivity and an ocean with a larger diffusivity leads to a less increase of sea surface temperature and a longer time delay for the global warming induced by increasing CO2 than that with smaller one. The global warming relative to four scenarios of CO2 emission assumed by Intergovernmental Panel of Climate Change (IPCC) is also estimated by using the model with two kinds of thermal diffusivities. The result shows that for various combinations of the CO2 emission scenarios and the diffusivities, the oceanic time delay to the global warming varies from 15 years to 70 years.

A Numerical Solution of Heat Equation for Several Thermal Diffusivity Using Finite Difference Scheme with Stability Conditions

The heat equation is a second-order parabolic partial differential equation, which can be solved in many ways using numerical methods. This paper provides a numerical solution that uses the finite difference method like the explicit center difference method. The forward time and centered space (FTCS) is used to a problem containing the one-dimensional heat equation and the stability condition of the scheme is reported with different thermal conductivity of different materials. In this study, results obtained for different thermal conductivity of distinct materials are compared. Also, the results reveal the well-behavior properties of the materials in good agreement.

Effects of Diesel Concentration on the Thermal Conductivity,Specific Heat Capacity and Thermal Diffusivity of Diesel-Contaminated Soil

High energy consumption is a serious issue associated with in situ thermal desorption(TD)remediation of sites contaminated by petroleum hydrocarbons(PHs).The knowledge on the thermophysical properties of contaminated soil can help predict accurately the transient temperature distribution in a remediation site,for the purpose of energy conservation.However,such data are rarely reported for PH-contaminated soil.In this study,by taking diesel as a representative example for PHs,soil samples with constant dry bulk density but different diesel mass concentrations ranging from 0% to 20% were prepared,and the variations of their thermal conductivity,specific heat capacity and thermal diffusivity were measured and analyzed over a wide temperature range between 0℃ and 120℃.It was found that the effect of diesel concentration on the thermal conductivity of soil is negligible when it is below 1%.When diesel concentration is below 10%,the thermal conductivity of soil increases with raising the temperature.However,when diesel concentration becomes above 10%,the change of the thermal conductivity of soil with temperature exhibits the opposite trend.This is mainly due to the competition between soil minerals and diesel,because the thermal conductivity of minerals increases with temperature,whereas the thermal conductivity of diesel decreases with temperature.The analysis results showed that,compared with temperature,the diesel concentration has more significant effects on soil thermal conductivity.Regardless of the diesel concentration,with the increase of temperature,the specific heat capacity of soil increases,while the thermal diffusivity of soil decreases.In addition,the results of a control experiment exhibited that the relative differences of the thermal conductivity of the soil samples containing the same concentration of both diesel and a pure alkane are all below 10%,indicating that the results obtained with diesel in this study can be extended to the family of PHs.A theoretical prediction model was proposed based on cubic fractal and thermal resistance analysis,which confirmed that diesel concentration does have a significant effect on soil thermal conductivity.For the sake of practical applications,a regression model with the diesel concentration as a primary parameter was also proposed.

Microstructure and thermal properties of dissimilar M300–CuCr1Zr alloys by multi-material laser-based powder bed fusion

Multi-material laser-based powder bed fusion (PBF-LB) allows manufacturing of parts with 3-dimensional gradient and additional functionality in a single step. This research focuses on the combination of thermally-conductive CuCr1Zr with hard M300 tool steel.Two interface configurations of M300 on CuCr1Zr and CuCr1Zr on M300 were investigated. Ultra-fine grains form at the interface due to the low mutual solubility of Cu and steel. The material mixing zone size is dependent on the configurations and tunable in the range of0.1–0.3 mm by introducing a separate set of parameters for the interface layers. Microcracks and pores mainly occur in the transition zone.Regardless of these defects, the thermal diffusivity of bimetallic parts with 50vol% of CuCr1Zr significantly increases by 70%–150%compared to pure M300. The thermal diffusivity of CuCr1Zr and the hardness of M300 steel can be enhanced simultaneously by applying the aging heat treatment.

Characterization of rock thermophysical properties and factors affecting thermal conductivity−A case study of Datong Basin,China

Rock thermal physical properties play a crucial role in understanding deep thermal conditions,modeling the thermal structure of the lithosphere,and discovering the evolutionary history of sedimentary basins.Recent advancements in geothermal exploration,particularly the identification of high-temperature geothermal resources in Datong Basin,Shanxi,China,have opened new possibilities.This study aims to characterize the thermal properties of rocks and explore factors influencing thermal conductivity in basins hosting high-temperature geothermal resources.A total of 70 groups of rock samples were collected from outcrops in and around Datong Basin,Shanxi Province.Thermal property tests were carried out to analyze the rock properties,and the influencing factors of thermal conductivity were studied through experiments at different temperature and water-filled states.The results indicate that the thermal conductivity of rocks in Datong,Shanxi Province,typically ranges from 0.690 W/(m·K)to 6.460 W/(m·K),the thermal diffusion coefficient ranges from 0.441 mm^(2)/s to 2.023 mm^(2)/s,and the specific heat capacity of the rocks ranges from 0.569 KJ/(kg·℃)to 1.117 KJ/(kg·°C).Experimental results reveal the impact of temperature and water saturation on the thermal conductivity of the rock.The thermal conductivity decreases with increasing temperature and rises with high water saturation.A temperature correction formula for the thermal conductivity of different lithologies in the area is proposed through linear fitting.The findings from this study provide essential parameters for the assessment and prediction,development,and utilization of geothermal resources in the region and other basins with typical high-temperature geothermal resource.

Dual-wavelength flash Raman mapping method for measuring thermal diffusivity of the suspended nanowire

In this paper,we present a dual-wavelength flash Raman(DFR)mapping method for measuring the thermal diffusivity of a suspended nanowire.A heating pulse is used to heat the nanowire sample,and a probing pulse of different wavelength is used to measure the increase in temperature.The laser absorption coefficient can be eliminated by normalization,and the thermal diffusivity of the sample can be extracted from the normalized temperature increase.An infinite heat conduction model is used in this method to avoid the influence of boundary thermal resistance.By changing the position of the probing laser center,the measurement sensitivity of thermal diffusivity can be further improved.The position of maximum sensitivity is influenced by the thermal diffusivity of the nanowire,width of the heating pulse,radius of the heating laser spot,and characteristic length of the sample.To comprehensively analyze the influences of the various parameters,obtain the best measurement conditions,and attain maximum sensitivity,we propose a dimensionless physical model to analyze the heat conduction of the suspended nanowire.Based on the analysis of the best dimensionless parameters,the corresponding appropriate measurement conditions can be determined.Sensitivity analysis shows that when the radius of the heating laser spot is 1%of the length of the nanowire,the sensitivity of the DFR mapping method can be more than four times that of the concentric DFR method for measuring the thermal diffusivity of the nanowire.

Electronic and thermal properties of Ag-doped single crystal zinc oxide via laser-induced technique

The doping of ZnO has attracted lots of attention because it is an important way to tune the properties of ZnO.Postdoping after growth is one of the efficient strategies.Here,we report a unique approach to successfully dope the single crystalline ZnO with Ag by the laser-induced method,which can effectively further post-treat grown samples.Magnetron sputtering was used to coat the Ag film with a thickness of about 50 nm on the single crystalline ZnO.Neodymium-doped yttrium aluminum garnet(Nd:YAG)laser was chosen to irradiate the Ag-capped ZnO samples,followed by annealing at700℃for two hours to form ZnO:Ag.The three-dimensional(3D)information of the elemental distribution of Ag in ZnO was obtained through time-of-flight secondary ion mass spectrometry(TOF-SIMS).TOF-SIMS and core-level x-ray photoelectron spectroscopy(XPS)demonstrated that the Ag impurities could be effectively doped into single crystalline ZnO samples as deep as several hundred nanometers.Obvious broadening of core level XPS profiles of Ag from the surface to depths of hundred nms was observed,indicating the variance of chemical state changes in laser-induced Ag-doped ZnO.Interesting features of electronic mixing states were detected in the valence band XPS of ZnO:Ag,suggesting the strong coupling or interaction of Ag and ZnO in the sample rather than their simple mixture.The Ag-doped ZnO also showed a narrower bandgap and a decrease in thermal diffusion coefficient compared to the pure ZnO,which would be beneficial to thermoelectric performance.

Thermal Conductivity and Thermal Diffusivity of Ferrosilite under High Temperature and High Pressure

Orthopyroxene is an important constitutive mineral in the crust and the upper mantle.Its thermal properties play a key role in constructing the thermal structure of the crust and the upper mantle.In this study,we developed a new method to synthesize polycrystalline ferrosilite,one end-member of orthopyroxene,via the reaction of FeO+SiO_(2)→FeSiO_(3).We found that the P-T condition of 3 GPa and 1273 K is suitable to synthesize dense ferrosilite samples with low porosity.We employed the transient plane-source method to investigate the thermal conductivityκand thermal diffusivity D of synthetic ferrosilite at 1 GPa and 293-873 K,of which,κ=1.786+1.048×10^(3)T^(-1)-9.269×10^(4)T^(-2) and D=0.424+0.223×10^(3)T^(-1)+1.64×10^(4)T^(-2).Our results suggest phonon conduction should be the dominant mechanism at P-T conditions of interest since the thermal conductivity and the thermal diffusivity of ferrosilite both decrease with increasing temperature.The calculated heat capacity of ferrosilite at 1 GPa increases with temperature,which increases with increasing temperature with about 10%per 100 K(<500 K)and 4%per 100 K(>500 K).Iron content of an asteroid significantly influences its thermal evolution history and temperature distribution inside.It is expected that the mantle temperature of the Fe-rich asteroid will be higher and the Fe-rich asteroid's cooling history will be longer.

Study of the Thermal Characteristics of a Geomaterial:Case of SavèGranites in the Republic of Benin

This work focuses on the valorization of local materials.The rock that is granite,a material used in construction thanks to its mechanical resistance,is the subject of our study.The granite of the commune of Savè,made it possible to appreciate the thermal behavior of this rock studied with a view to its use as a building material.To this end,a thermal diffusivity measurement test was carried out on this material.Thus,we made samples which were then connected to a data acquisition box via thermocouples.A Python script is used to ensure the collection of temperature values over time.From this thermal diffusivity test carried out on the granite taken from the Savèbreasts,we obtained an average diffusivity a=5.84×10^(-6)m^(2)/s.As a result,the thermal effusivity and the heat capacity of the material were determined having respectively the value 1,351.09 J/(K·m^(2)·s^(1/2))and 547,945.21 J/(m^(3)·K).These different results highlight a thermal characterization of Savègranites as a relevant material in the design and construction of an energy-efficient eco-housing.

Thermal Characterization of Concrete and Cement Mortar from Construction Sites and Industrial Production Units in the City of Ouagadougou with a View to Standardization in Energy Certification

The present study allowed to carry out a thermal characterization of concrete and cement mortar. Thermal tests were carried out with the KD2 Pro device, on concrete and mortar samples taken from twenty-six (26) construction sites of office buildings and two (2) industrial production units in the city of Ouagadougou. The tests were carried out on rectangular specimens after four weeks (4) of conservation on the site of construction or production of materials. This study seeks to determine the thermal properties of the materials, in particular the thermal conductivity, the thermal diffusivity and the thermal capacity of the samples, in the real conditions of execution of the buildings and environment. The thermal conductivity varies from 1.413 to 1.965 W/m·K, 0.940 - 1.658 W/m·K and 0.703 - 1.149 W/m·K respectively for concrete, cinder block mortar and plaster mortar. Regarding the other properties, especially the capacity and thermal diffusivity, the values vary respectively, from 1070.59 - 1974.67 kJ/kg·K and (3.74 - 6.70) × 10-7 m2/s for concrete, from 1123.69 - 1586.81 kJ/kg·K and (3.38 - 5.65) × 10-7 m2/s for plaster mortar and 1202.51 - 1736.01 kJ/kg·K and (3.82 - 7.36) × 10-7 m2/s for the mortar of building blocks. The conductivity, capacity and thermal diffusivity of industrial mortar vary from 1.019 - 1.229 W/m·K, 792.18 - 1862.58 J/kg·K and (2.75 - 6.80) × 10-7 m2/s, respectively. Only the correlations made between the thermal properties and the density of the samples of the plaster mortar, give good relations namely R2 = 0.9308 for the thermal conductivity, R2 = 0.7823 for the thermal capacity and R2 = 0.9272 for the thermal diffusivity. This study contributes to the establishment of a thermal regulation in Burkina Faso for the adoption of the West African Economic and Monetary Union (WAEMU) Directive 05 on energy efficiency in buildings.

Study on thermal diffusivity of materials by laser photothermal reflection technique

A method of measuring thermal diffusivity of materials at room temperature by photothermal reflection technique is described. An intensity-modulated Ar+ laser beam is used as incident light. The beam is focused to about 1 mm diameter spot and illuminates the sample surface. HgCdTe infrared detector is used to receive photothermal signal. By using this technique, the photothermal signals are experimentally measured as the function of different frequencies. The thermal diffusivities can be obtained by fitting the experimental data. On the other hand, the thermal diffusivities of one-way composite and orthogonal symmetric arranged composites Al2O3/Al are measured in transverse, longitudinal and arbitrary directions. The results show that the diffusivity of one-way material decreases with the increase of the measurement angle; the diffusivity of orthogonally arranged material almost keeps the same when measurement angle changes.

Procedure for determining the number of thermal diffusion columns in square cascade for separation of Ne stable isotopes

The thermal diffusion column represents one method of separating stable isotopes.This method is advantageous for smallscale operations because of the simplicity of the apparatus and small inventory,especially in gas-phase operations.Consequently,it has attracted attention for its applicability in tritium and noble gas separation systems.In this study,the R cascade was used to design and determine the number of columns.A square cascade was adopted for the final design because of its flexibility,and calculations were performed to separate 20Ne and 22Ne isotopes.All the R cascades that enriched the Ne isotopes by more than 99%were investigated,the number of columns was determined,and the square cascade parameters were optimized using the specified columns.Additionally,a calculation code“RSQ_CASCADE”was developed.A unit separation factor of three was considered,and the number of studied stages ranged from 10 to 20.The results showed that the column separation power,relative total flow rate,and required number of columns were linearly related to the number of stages.The separation power and relative total flow decreased and the number of columns increased as the stage number increased.Therefore,a cascade of 85 columns is recommended to separate the stable Ne isotopes.These calculations yielded a 17-stage square cascade with five columns in each stage.By changing the stage cut,feed point,and cascade feed flow rate,the best parameters for the square cascade were determined according to the cascade and column separation powers.As the column separation power had a maximum value in cascade feed 50,it was selected for separating Ne isotopes.

Exploration of regional surface average heat flow from meteorological and geothermal series

We attempt to compute the Surface Average Heat Flow （SAHF） from long-term temperature observations of one hundred seventy-seven observational points at the depths of 0.8, 1.6, and 3.2 m, which were relatively evenly distributed in China's Mainland. We first employ Fourier transformation to remove the influence of atmospheric temperature variations from the observation series, which are classified into the type of the steady-state temperature monotonously increasing with depth （type I） and other three types. Then we compare our results obtained from the data of type I, of which the values are thought to equal to those of the mean borehole heat flow, with those obtained from traditional heat flow observations mainly distributed in North China Craton. In computations of the SAHF at the observation stations, we deduce the thermal diffusivity and volumetric specific heat of the soil by employing harmonic solutions of the heat conduction equation for the same moisture group as the first step, and then we determine the SAHF using Fourier＇s law. Our results indicate that the SAHF derived from shallow earth geothermal data can reflect the heat flow field to a large extent.

Variability of Soil Moisture and Its Relationship with Surface Albedo and Soil Thermal Parameters over the Loess Plateau

Data from July 2006 to June 2008 observed at SACOL （Semi-Arid Climate and Environment Observatory of Lanzhou University, 35.946°N, 104.137°E, elev. 1961 m）, a semi-arid site in Northwest China, are used to study seasonal variability of soil moisture, along with surface albedo and other soil thermal parameters, such as heat capacity, thermal conductivity and thermal diffusivity, and their relationships to soil moisture content. The results indicate that surface albedo decreases with increases in soil moisture content, showing a typical exponential relation between the surface albedo and the soil moisture. The heat capacity, the soil thermal diffusivity, and soil thermal conductivity show large variations between Julian day 90-212 and 450-578. The soil thermal conductivity is found to increase as a power function of soil moisture. Soil heat capacity and soil thermal diffusivity increase with increases in soil moisture. The SACOL observed soil moisture are also used to validate the AMSR-E/AQUA retrieved soil moisture and there is good agreement between them. The analysis of the relationship between satellite retrieved soil moisture and precipitation suggests that the variability of soil moisture depends on the variation of precipitation over the Loess Plateau.