The Effects of Nonuniform Thermal Boundary Condition on Thermal Stress Calculation of Water-Cooled W/Cu Divertors

The thermal boundary condition has very important effects on the accuracy of thermal stress calculation of a water-cooled W/Cu divertor. In this paper, phase-change heat transfer was simulated based on the Euler homogeneous phase model, and local differences of liquid physical properties were considered under one-sided high heating conditions. The steady-state temperature field and thermal stress field under nonuniform thermal boundary conditions were obtained through numerical calculation. By comparison with the case of traditional uniform thermal boundary conditions, the results show that the distribution of thermal stress under nonuniform thermal boundary conditions exhibits tbe same trend as that under uniform thermal boundary conditions, but is larger in value. The maximum difference of maximum von Mises stress is up to 42% under the highest heating conditions. These results provide a valuable reference for the thermal stress caleulat.ion of water-cooled W/Cu divertors.

Quantitative Visualization of the Thermal Boundary Layer of Forced Convection on a Heated or Cooled Flat Plate with a 30°Leading Edge Using a Mach-Zehnder Interferometer

This study focuses on the experimental measurements of the heat transfer coefficient over a flat plate with a 30° leading edge. Under forced convection by a hot/cold air and flow over a cooled/heated flat plate, the thermal boundary layer and its thickness are quantitatively visualized and measured using a Mach-Zehnder interferometer. In addition, the variation in the local heat transfer coefficient is evaluated experimentally with respect to the air flow velocity and temperature. Differences within the heat transfer performance between the plates are confirmed and discussed. As a result, the average heat transfer performance is about the same for the heated plate and the cooled plate under all air velocity conditions. This contrasts with the theoretical prediction in the case of low air velocity, the reason considered was that the buoyancy at the 30° leading edge blocked air from flowing across the surface of the plate.

Measurement of thermal boundary conductance between metal and dielectric materials using femtosecond laser transient thermoreflectance technique

The thermal boundary conductance of Al/SiO2, Al/Si, Au/SiO2, and Au/Si are measured by a femtosecond laser transient thermoreflectance technique. The distinct differences of the interfacial thermal conductance between these samples are observed. For the same metal film, the thermal boundary conductance between metal and substrate decreases with the thermal conductivity of the substrate. The measured results are explained with the phonon diffusion mismatch model by introducing a phonon transmission coefficient across the interface.

Numerical Study of Thermal Boundary Layer on a Continuous Moving Surface in Power Law Fluids

This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.

An Analysis of the Characteristics of the Thermal Boundary Layer in Power Law Fluid

This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.

Reduced thermal boundary conductance in GaN-based electronic devices introduced by metal bonding layer

Achieving high interface thermal conductance is one of the biggest challenges in the nanoscale heat transport of GaN-based devices such as light emitting diodes(LEDs),and high electron mobility transistors(HEMTs).In this work,we experimentally measured thermal boundary conductance(TBC)at interfaces between GaN and the substrates with AuSn alloy as a commonly-used adhesive layer by time-domain thermoreflectance(TDTR).We find that the TBCs of GaN/Ti/AuSn/Ti/Si,GaN/Ti/AuSn/Ti/SiC,and GaN/Ti/AuSn/Ti/diamond,are 16.5,14.8,and 13.2 MW·m^(-2)·K^(-1)at room temperature,respectively.Our measured results show that the TBC of GaN/Ti/AuSn/Ti/SiC interface is inferior to the TBC of pristine GaN/SiC interface,due to the large mismatch of phonon modes between AuSn/Ti and substrates,shown as the difference of Debye temperature of two materials.Overall,we measured the TBC at interface between GaN and thermal conductive substrates,and provided a guideline for designing the interface between GaN and substrate at HEMT from a thermal management point of view.

Evaluation of Haney-Type Surface ThermalBoundary Conditions Using a CoupledAtmosphere and Ocean Model

A coupled atmosphere-ocean model developed at the Institute for Space Studies at NASA Goddard Space Flight Center (Russell et al., 1995) was used to verify the validity of Haney-type surface thermal boundary condition, which linearly connects net downward surface heat fluxQ to air/sea temperature difference ΔT by a relaxation coefficientk. The model was initiated from the National Centers for Environmental Prediction (NCEP) atmospheric observations for 1 December 1977, and from the National Ocean Data Center (NODC) global climatological mean December temperature and salinity fields at 1°x 1° resolution. The time step is 7.5 minutes. We integrated the model for 450 days and obtained a complete model-generated global data set of daily mean downward net surface fluxQ, surface air temperatureT A, and sea surface temperatureT O. Then, we calculated the cross-correlation coefficients (CCC) betweenQ and ΔT. The ensemble mean CCC fields show (a) no correlation betweenQ and ΔT in the equatiorial regions, and (b) evident correlation (CCC≥0.7) betweenQ and ΔT in the middle and high latitudes. Additionally, we did the variance analysis and found that whenk=120 W m?2K?1, the two standard deviations, σQ and σκδT , are quite close in the middle and high latitudes. These results agree quite well with a previous research (Chu et al., 1998) on analyzing the NCEP re-analyzed surface data, except that a smaller value ofk (80 W m?2K?1) was found in the previous study. Key words Air-sea coupled system - Ocean surface fluxes - Surface thermal boundary condition

THERMAL BOUNDARY LAYER IN CFB BOILER RISER

Measurement of temperature profiles of gas-solid two-phase flow at different heights in commercial-scale circulating fluidized bed （CFB） boilers was carried out. Experimental results showed that the thickness of thermal boundary layer was generally independent of the distance from the air distributor, except when close to the riser outlet. Through analysis of flow and combustion characteristics in the riser, it was found that the main reasons for the phenomena were： 1 ） the hydrodynamic boundary layer was thinner than the thermal layer and hardly changed along the CFB boiler height, and 2） both radial and axial mass and heat exchanges were strong in the CFB boiler. Numerical simulation of gas flow in the outlet zone confirmed that the distribution of the thermal boundary layer was dominated by the flow field characteristics.

Study on the Thermal internal Boundary Layer and Dispersion of Air Pollutant in Coastal Area by Numerical Simulation

In this paper, a scheme on a mesoscale dispersion modeling system was set up. The modeling system was used tostudy the turbulence structure of TIBL and dispersion features under shoreline tlimigation situation. The modelingsystem has successfully solved the problem of meteorological input of stochastic dispersion models and exploited anew approach to comprehensive application of this kind of dispersion models.

Fourth-Order Compact Formulation for the Resolution of Heat Transfer in Natural Convection of Water-Cu Nanofluid in a Square Cavity with a Sinusoidal Boundary Thermal Condition

In the present work, we numerically study the laminar natural convection of a nanofluid confined in a square cavity. The vertical walls are assumed to be insulated, non-conducting, and impermeable to mass transfer. The horizontal walls are differentially heated, and the low is maintained at hot condition (sinusoidal) when the high one is cold. The objective of this work is to develop a new height accurate method for solving heat transfer equations. The new method is a Fourth Order Compact (F.O.C). This work aims to show the interest of the method and understand the effect of the presence of nanofluids in closed square systems on the natural convection mechanism. The numerical simulations are performed for Prandtl number ( ), the Rayleigh numbers varying between and for different volume fractions varies between 0% and 10% for the nanofluid (water + Cu).

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

Uncertainties of thermal boundaries and soil properties on permafrost table of frozen ground in Qinghai-Tibet Plateau

In the permafrost regions of the Qinghai-Tibet Plateau(QTP),the permafrost table has a significant effect on the stability of geotechnical engineering.The thermal boundaries and soil properties are the key factors affecting the permafrost table.Complex geological environments and human activities can lead to the uncertainties of thermal boundaries and soil properties.In this paper,an array of field experiments and Monte Carlo(MC)simulations of thermal boundaries and soil properties are carried out.The coefficient of variation(COV),scale of fluctuation(SOF),and autocorrelation distance(ACD)of uncertainties of thermal boundaries and soil properties are investigated.A stochastic analysis method of the probabilistic permafrost table is then proposed,and the statistical properties of permafrost table on the QTP are computed by self-compiled program.The proposed stochastic analysis method is verified with the calculated and measured temperature observations.According to the relationship between ACD and SOF for the five theoretical autocorrelation functions(ACFs),the effects of ACF,COV,and ACD of soil properties and the COV of thermal boundaries on the permafrost tables are analyzed.The results show that the effects of different ACFs of soil properties on the standard deviation(SD)of permafrost table depth are not obvious.The SD of permafrost table depth increases with time,and the larger the COVs of thermal boundaries and soil properties,the deeper the SD of permafrost table;the longer the ACD of soil properties,the shallower the SD of permafrost table.This study can provide a reference for the stability analysis of geotechnical engineering on the QTP considering the uncertainties of thermal boundaries and soil properties.

Topological structure bifurcation of temperature field of deformable drop in Marangoni migration

The unsteady processes of the Marangoni migration of deformable liquid drops are simulated numerically in a wider range of Marangoni number(up to Ma = 500) in the present work.A steady terminal state can always be reached,and the scaled terminal velocity is a monotonic function decreasing with increasing Marangoni number,which is generally in agreement with corresponding experimental data.The topological structure of flow field in the steady terminal state does not change as the Marangoni number increases,while bifurcation of the topological structure of temperature field occurs twice at two corresponding critical Marangoni numbers.A third critical value of Marangoni number also exists,beyond which the coldest point jumps from the rear stagnation to inside the drop though the topological structure of the temperature field does not change.It is found that the inner and outer thermal boundary layers may exist along the interface both inside and outside the drop if Ma>70.But the thickness decreases with increasing Marangoni number more slowly than the prediction of potential flow at large Marangoni and Reynolds numbers.

Thermal internal boundary layer and its effects on air pollutants during summer in a coastal city in North China

The thermal internal boundary layer（TIBL） is associated with coastal pollution dispersion,which can result in high concentrations of air pollutants near the surface of the Earth. In this study, boundary layer height data which were obtained using a ceilometer were used to assess the effect of the TIBL on atmospheric pollutants in Qinhuangdao, a coastal city in North China.A TIBL formed on 33% of summer days. When a TIBL formed, the sunshine duration was 2.4 hr longer, the wind speed was higher, the wind direction reflected a typical sea breeze, and the boundary layer height was lower from 9：00 LT to 20：00 LT compared to days without a TIBL. If no TIBL formed, the average concentrations of PM2.5 and PM10 decreased with increasing boundary layer height. However, when a TIBL was observed, the average concentrations of PM2.5 and PM10 increased with increasing boundary layer height. Because the air from the sea is clean, PM2.5 and PM10 concentrations reached minimums in the daytime at 16：00 LT. After16：00 LT, the PM2.5 and PM10 concentrations increased rapidly on days when a TIBL formed,which indicated that the TIBL leads to the rapid accumulation of atmospheric pollutants in the evening. Therefore, the maximum concentrations of particulate matters were larger when a TIBL formed compared to when no TIBL was present during the night. These results indicate that it is suitable for outdoor activities in the daytime on days with a TIBL in coastal cities.

First-Principles Study of the High-Temperature Behaviors of the Willemite-Ⅱ and Post-Phenacite Phases of Silicon Nitride

The structural and elastic properties of the recently-discovered wⅡ- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa,respectively.The α→wⅡ phase transition can be observed at 18.6 GPa and 300 K.The β→δ phase transformation occurs at pressures of 29.6,32.1,35.9,39.6,41.8,and 44.1 GPa when the temperatures are100,200,300,400,500,and 600 K,respectively.The results show that the interactions among the N-2s,Si-3s,3p bands（lower valence band） and the Si-3p,N-2p bands（upper valence band） play an important role in the stabilities of the wⅡ and S phases.Moreover,several thermodynamic parameters（thermal expansion,free energy,bulk modulus and heat capacity） of δ-Si3N4 are also obtained.Some interesting features are found in these properties.δ-Si3N4 is predicted to be a negative thermal expansion material.The adiabatic bulk modulus decreases with applied pressure,but a majority of materials show the opposite trend.Further experimental investigations with higher precisions may be required to determine the fundamental properties of wⅡ- andδ-Si3N4.

Investigations of high-pressure and high-temperature behaviors of the newly-discovered willemite-Ⅱ and post-phenacite silicon nitrides

Using the first-principles method of the plane-wave pseudo-potential, the structural properties of the newly-discovered willemite-Ⅱ Si3N4 （wⅡ phase） and post-phenacite Si3N4 （δ phase） are investigated. The α phase is predicted to undergo a first-order α→wⅡ phase transition at 18.6 GPa and 300 K. Within the quasi-harmonic approximation （QHA）, the α→wⅡ phase boundary is also obtained. When the well-known β→γ transition is suppressed by some kinetic reasons, the β→δ phase transformation could be observed in the phase diagram. Besides, the temperature dependences of the cell volume,thermal expansion coefficient, bulk modulus, specific heat, entropy and Debye temperature of the involved phases are determined from the non-equilibrium free energies. The thermal expansion coefficients of wⅡ-Si3N4 show no negative values in a pressure range of 0-30 GPa, which implies that the wⅡ-Si3N4 is mechanically stable. More importantly, the δ-Si3N4 is found to be a negative thermal expansion material. Further experimental investigations may be required to determine the physical properties of wⅡ- and δ-Si3N4 with higher reliability.

Analytical solution and numerical simulation of the thermal entrance region problem for laminar flow through a circular pipe

In this paper,the assumptions implicited in Leveque’s approximation are re-examined,and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution.By defining a similarity variable,the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region.This report gives justification for the similarity variable via scaling analysis,details the process of converting to a similarity form,and presents a similarity solution.The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order(RK4)method.Finally,other important thermal results obtained from this analysis,such as;approximate Nusselt number in the thermal entrance region was discussed in detail.A comparison with the previous study available in literature has been done and found an excellent agreement with the published data.

Thermal studies of individual Si/Ge heterojunctions--The influence of the alloy layer on the heterojunction

Phonon transport across an interface is of fundamental importance to applications ranging from electronic and optical devices to thermoelectric materials.The phonon scattering by an interface can dramatically suppress the thermal transport,which can benefit thermoelectric applications but create problems for the thermal management of electronic/optical devices.In this aspect,existing molecular dynamics simulations on phonon transport across various interfaces are often based on estimates of atomic structures and are seldom compared with measurements on real interfaces.In this work,planar Si/Ge heterojunctions formed by film-wafer bonding are measured for the interfacial thermal resistance (R_(K)) that is further compared with predictions from existing simulations and analytical models.The twist angle between a 70-nm-thick Si film and a Ge wafer is varied to check the influence of the crystal misorientation.Detailed transmission electron microscopy studies are carried out to better understand the interfacial atomic structure.It is found that the alloyed interfacial layer with mixed Si and Ge atoms dominates the measured thermal resistance(R_(K)).Some oxygen impurities may also help to increase RK due to the formation of glassy structures.Following this,RK reduction should be focused on how to minimize the interdiffusion of Si and Ge atoms during the formation of a Si/Ge heterojunction.

A reined global-local approach for evaluation of singular stress ield based on scaled boundary inite element method

A reined global-local approach based on the scaled boundary inite element method（SBFEM） is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the irst step imposed along the whole boundary including the side-faces. Beneiting from the semi-analytical nature of the SBFEM, the singular stress ield can be predicted accurately without highly reined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.

Lattice Thermal Conductivity of Boron Nitride Nanoribbon from Molecular Dynamics Simulation

The lattice thermal conductivity of boron nitride nanoribbon（BNNR） is calculated by using equilibrium molecular dynamics（EMD） simulation method. The Green–Kubo relation derived from linear response theory is used to acquire the thermal conductivity from heat current auto-correlation function（HCACF）. HCACF of the selected BNNR system shows a tendency of a very fast decay and then be followed by a very slow decay process,finally,approaching zero approximately within 3 ps. The convergence of lattice thermal conductivity demonstrates that the thermal conductivity of BNNR can be simulated by EMD simulation using several thousands of atoms with periodic boundary conditions. The results show that BNNR exhibit lower thermal conductivity than that of boron nitride（BN） monolayer,which indicates that phonons boundary scatting significantly suppresses the phonons transport in BNNR. Vacancies in BNNR greatly affect the lattice thermal conductivity,in detail,only 1% concentration of vacancies in BNNR induce a 60% reduction of the lattice thermal conductivity at room temperature.