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.

Numerical simulation based on two-directional freeze and thaw algorithm for thermal diffusion model

Freeze-thaw processes significantly modulate hydraulic and thermal char- acteristics of soil. The changes in the frost and thaw fronts （FTFs） affect the water and energy cycles between the land surface and the atmosphere. Thus, the frozen soil com- prising permafrost and seasonally frozen soil has important effects on the land surface hydrology in cold regions. In this study, a two-directional freeze and thaw algorithm is incorporated into a thermal diffusion equation for simulating FTFs. A local adaptive variable-grid method is used to discretize the model. Sensitivity tests demonstrate that the method is stable and FTFs can be tracked continuously. The FTFs and soil tempera- ture at the Qinghai-Tibet Plateau D66 site are simulated hourly from September 1, 1997 to September 22, 1998. The results show that the incorporated model performs much better in the soil temperature simulation than the original thermal diffusion equation, showing potential applications of the method in land-surface process modeling.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Composition Variation of Borax Salt during the Process of Vanadizing by Thermal Diffusion

Vanadium pentoxide, borax, boron carbide and sodium fluoride were used to grow vanadium carbide coating on surface of Crl2 steel at 950℃ by TD process. The coating of vanadium carbide （VC） extended the serve-life period of Crl2 steel as punching die. Kinetics of vanadium carbide coating growth was brought forward and verified by comparison of the mathematical model with the experimental results. The thickness of coating was illustrated by SEM. The chemical constituent of coating and remnants were tested by X-ray diffraction （XRD） and X-ray energy dispersive spectroscopy （EDS）. To increase the thickness, rare earth silicon powder （FeSiRe23） was added to the borax salt bath. The analysis of XRD revealed that FeSiRe23 increased the depth of vanadium car-bide coating as reducing agent and catalysis.

Segregation of Molten Salt on Chromizing in Thermal Diffusion Process

The segregation of thermal diffusion salt bath chromizing process was analyzed. The experimental chromizing ingredients were prepared by the four groups A, B, C, and D. In order to study the segregation status of this case, the cooling molten salt in the crucible was removed by drilling from the heart core of molten salt. The core of molten salt was analyzed by X-ray fluorescence spectroscopy and XRD. Through the analysis, we can conclude that the Cr element deposited in the bottom was 4.51 times than the top. Chloride added to the molten salt will reduce segregation. Meantime we proposed some measures to overcome the segregation problem.

Thermal Diffusion Effect on MHD Heat and Mass Transfer Flow past a Semi Infinite Moving Vertical Porous Plate with Heat Generation and Chemical Reaction

The objective of present work is to study the thermo diffusion effect on an unsteady simultaneous convective heat and mass transfer flow of an incompressible, electrically conducting, heat generating/absorbing fluid along a semi-infinite moving porous plate embedded in a porous medium with the presence of pressure gradient, thermal radiation field and chemical reaction. It is assumed that the permeable plate is embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. It is also assumed that the free stream consists of a mean velocity, temperature and concentration over which are super imposed an exponentially varying with time. The equations of continuity, momentum, energy and diffusion, which govern the flow field, are solved by using a regular perturbation method. The behavior of the velocity, temperature, concentration, Skin-friction, rate of heat transfer and rate of mass transfer has been discussed for variations in the physical parameters. An increase in both Pr and R results a decrease in thermal boundary layer thickness. However, concentration decreases as Kr, Sc increase but it increases with an increase in both So and δ.

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow. An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow, saltating grains, and a kind of electrostatic force exerted on the grains are considered in this theoretical model. The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown groan flow is quite obvious and very similar to the effect of the electrostatic force on the evolution. Not only the time for the entire system to reach a steady state （called the duration time）, the transport rate of grains, the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.

Phase field modeling of the ring-banded spherulites of crystalline polymers: The role of thermal diffusion

The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established to investigate the emergence and formation mechanism of the ring-banded spherulites of crystalline polymers. The model consists of a nonconserved phase field representing the phase transition and a temperature field describing the diffusion of the released latent heat. The corresponding model parameters can be obtained from experimentally accessible material parameters.Two-dimensional calculations are carried out for the ring-banded spherulitic growth of polyethylene film under a series of crystallization temperatures. The results of these calculations demonstrate that the formation of ring-banded spherulites can be triggered by the self-generated thermal field. Moreover, some temperature-dependent characteristics of the ring-banded spherulites observed in experiments are reproduced by simulations, which may help to study the effects of crystallization temperature on the ring-banded structures.

Preparation and Property of Chromium Carbide Thermal Diffusion Coating on Cold Working Die Materials

Thermal diffusion （TD） salt bath chromizing of cold working dies was studied. Firstly, it obtained an ideal salt bath formula by comparing with a variety of formulas, and then obtained the influence rule of coating thickness based on studying of some process parameters. The microstructure morphologies and phase structures of the TD chromizing coating were investigated by X-ray diffraction （XRD）, energy-dispersive spectrometry （EDS） and other modern analysis methods. Meanwhile, it carried out a system of testing and analysis of coating, such as hardness, wear resistance, etc.

Thermal Diffusion in Masson Pine Wood

In order to analyze the effects of the temperature gradient on moisture movement during the highly intensive microwave-vacuum drying, thermal diffusion of Masson pine wood was studied. Internal distribution of temperature and moisture in Masson pine samples sealed by epoxy resin and aluminum foil was measured, the magnitude of thermal diffusion was calculated and the influencing factors of thermal diffusion were discussed. Results showed that with the transfer of moisture toward the low temperature in wood, opposite temperature and moisture gradient occurred. The initial moisture content （MC）, temperature and time are important factors affecting this process; the thermal diffusion is in proportion to wood temperature, its initial moisture and time. The temperature and distance from hot surface is strongly linearly correlated, and the relationship between MCs at different locations and distance from the hot end surface changes from logarithmically form to exponentially form with the increase in experimental time.

Combined Effects of Thermal Diffusion and Diffusion-Thermo Effects on Transient MHD Natural Convection and Mass Transfer Flow in a Vertical Channel with Thermal Radiation

We study the nonlinear coupled evolution equations which model the transient MHD natural convection and mass transfer flow of viscous, incompressible and electrically conducting fluid between two infinite vertical plates in the presence of the transversal magnetic field, thermal radiation, thermal diffusion and diffusion-thermo effects. Both analytical and numerical methods are used for this study.

A Three-Dimensional Prediction Method for Thermal Diffusion

A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.

A_(2)B_(7)-type La-Mg-Ni alloys prepared by Mg thermal diffusion for improved hydrogen storage performance

A novel approach based on thermal diffusion was used to achieve controllable Mg content in A_(2)B_(7)-type La-Mg-Ni-based alloys.The formation mechanism of the A_(2)B_(7)-type phase as a result of the thermal diffusion process and the effect of Mg content on hydrogen storage performance were investigated.X-ray diffraction(XRD)patterns and Rietveld refinement results showed that increased Mg transformed the LaNi_(5)phase in the La_(0.74)Sm_(0.03)Y_(0.23)Ni_(4.32)Al_(0.04)precursor alloy into a superlattice structure.Scanning electron microscopy(SEM)images showed that Mg was evenly distributed in the alloy bulk.Mg in the superlattice significantly inhibited the phase decomposition of the superlattice structure during the hydrogen absorption/desorption cycles.An A_(2)B_(7)-type La_(0.57)Sm_(0.02)Y_(0.18)Mg_(0.23)Ni_(3.38)Al_(0.03)alloy composed of Gd_(2)Co_(7)and Ce_(2)Ni_(7)phases was successfully synthesized.The pressure-composition isotherm profiles showed that the alloy had a hydrogen storage capacity as high as 1.73 wt%,with good cycling stability.After 50 cycles of hydrogen absorption/desorption,the alloy retained a hydrogen storage capacity of 1.45 wt%,with a capacity retention rate of up to 84.28%.The Mg thermal diffusion process thus provides a new approach for the controlled preparation of La-Mg-Ni-based alloys.

Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

Anti-corrosion performance of Si-surface-alloying NdFeB magnets obtained with magnetron sputtering and thermal diffusion

Si alloying in the surface layer of NdFeB magnets was realized by thermal diffusion combined with magnetron sputtering.The surface composition,phase structure and morphology of NdFeB(S-Si)specimens were characterized by an X-ray diffractometer,an X-ray photoelectron spectrometer and a field emission scanning electron microscope,respectively.The corrosion resistance of bare NdFeB(S-Si)was analyzed by static full immersion corrosion test and electrochemical experiments.Effects of sputtering and thermal diffusion on the microstructure and corrosion resistance of the surface layer were studied.Results show that surface alloying layer can effectively improve the corrosion resistance of bare NdFeB with the optimized static total immersion corrosion test time in NdFeB(1S-Si)-800 of 36 h,which is much longer than that of the pristine NdFeB(less than 0.5 h).The E_(corr)of NdFeB(1S-Si)-800 positively shifts from-1.05 to-0.92 V,indicating that the corrosion tendency is obviously lower.The J_(corr)is1.45×10^(-6)A/cm^(2)which is 2 orders of magnitude lower than that of the pristine NdFeB(5.25×10^(-4)A/cm^(2)).The intergranular composite oxides existing in Nd-rich phase contribute to the enhancement of corrosion resistance of Si-surface-alloying NdFeB.

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.

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles:an analytical study

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion,vicious,and Darcy dissipation is studied.The first region consists of a clear fluid,and the second one is filled with a nanofluid saturated with a porous medium.The behaviors of Cu-H_(2)O,In-H_(2)O,and Au-H_(2)O nanofluids are analyzed.The transport properties are assumed to be constant.The coupled non-linear equations of the flow model are transformed into the dimensionless form,and the solutions for the velocity,temperature,and concentration are obtained by the regular perturbation technique.Investigations are carried out on the flow characteristics for various values of the material parameters.The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number,solutal Grashof number,and Brinkman number while decrease with the porosity parameter and solid volume fraction.

Directional region control of the thermal fractal diffusion of a space body

We present a directional region control （DRC） model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.

Global Well-Posedness for the 3D Tropical Climate Model without Thermal Diffusion

this paper,we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion.Firstly,we establish the global regularity for this system with fractional diffusionα=β=5/4.Secondly,by adding only a damp term,we obtain the global well-posedness for small initial data.