Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Steady-state heat transfer problems in heterogeneous solid are simulated by developing an adaptive extended isogeometric analysis(XIGA)method based on locally refined non-uniforms rational B-splines(LR NURBS).In the XIGA,the LR NURBS,which have a simple local refinement algorithm and good description ability for complex geometries,are employed to represent the geometry and discretize the field variables;and some special enrichment functions are introduced into the approximation of temperature field,thus the computational mesh is independent of the material interfaces,which are described with the level setmethod.Similar to the approximation of temperature field,a temperature gradient recovery technique for heterogeneous media is proposed,and based on the Zienkiewicz–Zhu recovery technique a posteriori error estimator is defined to automatically identify the locally refined regions.The convergence and performance properties of the developed method are verified by using three numerical examples.The numerical results show that(1)The convergence speed of the adaptive local refinement is faster than that of the uniform global refinement;(2)The convergence rate of the high-order basis functions is faster than that of the low-order basis functions;and(3)The existing inclusions change the local distributions of the temperature,and the extreme values of the temperature gradients take place around the inclusion interfaces.

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the trial function,and the penalty method is applied to enforce the boundary conditions,thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form.The influences of node distribution,weight functions,scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively,and these numerical solutions show that less computational resources are spent when using the IEFG method.

RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

Meshless Least-Squares Method for Solving the Steady-State Heat Conduction Equation

The meshless weighted least-squares (MWLS) method is a pure meshless method that com- bines the moving least-squares approximation scheme and least-square discretization. Previous studies of the MWLS method for elastostatics and wave propagation problems have shown that the MWLS method possesses several advantages, such as high accuracy, high convergence rate, good stability, and high com- putational efficiency. In this paper, the MWLS method is extended to heat conduction problems. The MWLS computational parameters are chosen based on a thorough numerical study of 1-dimensional problems. Several 2-dimensional examples show that the MWLS method is much faster than the element free Galerkin method (EFGM), while the accuracy of the MWLS method is close to, or even better than the EFGM. These numerical results demonstrate that the MWLS method has good potential for numerical analyses of heat transfer problems.

Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths(IHBs) or two common heat baths(CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steadystate with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation(RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime,the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures.We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong(weak) coupling regime, the heat current increases(decreases) with coupling strength increasing when the temperature of one bath is lower(higher) than the other, and the energy detuning leads to a positive(negative) effect when the temperature is low(high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.

FUNDAMENTAL SOLUTION BASED GRADED ELEMENT MODEL FOR STEADY-STATE HEAT TRANSFER IN FGM

A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials （FGMs）. The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element （FE） model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional FEM and boundary element method （BEM）. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.

Influence of heat treatment on microstructure,mechanical and corrosion behavior of WE43 alloy fabricated by laser-beam powder bed fusion

Magnesium(Mg)alloys are considered to be a new generation of revolutionary medical metals.Laser-beam powder bed fusion(PBF-LB)is suitable for fabricating metal implants withpersonalized and complicated structures.However,the as-built part usually exhibits undesirable microstructure and unsatisfactory performance.In this work,WE43 parts were firstly fabricated by PBF-LB and then subjected to heat treatment.Although a high densification rate of 99.91%was achieved using suitable processes,the as-built parts exhibited anisotropic and layeredmicrostructure with heterogeneously precipitated Nd-rich intermetallic.After heat treatment,fine and nano-scaled Mg24Y5particles were precipitated.Meanwhile,theα-Mg grainsunderwent recrystallization and turned coarsened slightly,which effectively weakened thetexture intensity and reduced the anisotropy.As a consequence,the yield strength and ultimate tensile strength were significantly improved to(250.2±3.5)MPa and(312±3.7)MPa,respectively,while the elongation was still maintained at a high level of 15.2%.Furthermore,the homogenized microstructure reduced the tendency of localized corrosion and favoredthe development of uniform passivation film.Thus,the degradation rate of WE43 parts was decreased by an order of magnitude.Besides,in-vitro cell experiments proved their favorable biocompatibility.

Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems

The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.

A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

Pre‑hatch thermal manipulation of embryos and post‑hatch baicalein supplementation mitigated heat stress in broiler chickens

Background High environmental temperatures induce heat stress in broiler chickens,affecting their health and pro-duction performance.Several dietary,managerial,and genetics strategies have been tested with some success in mitigating heat stress(HS)in broilers.Developing novel HS mitigation strategies for sustaining broiler production is critically needed.This study investigated the effects of pre-hatch thermal manipulation(TM)and post-hatch baica-lein supplementation on growth performance and health parameters in heat-stressed broilers.Results Six hundred fertile Cobb 500 eggs were incubated for 21 d.After candling on embryonic day(ED)10,238 eggs were thermally manipulated at 38.5℃ with 55%relative humidity(RH)from ED 12 to 18,then transferred to the hatcher(ED 19 to 21,standard temperature)and 236 eggs were incubated at a controlled temperature(37.5℃)till hatch.After hatch,180-day-old chicks from both groups were raised in 36 pens(n=10 birds/pen,6 replicates per treatment).The treatments were:1)Control,2)TM,3)control heat stress(CHS),4)thermal manipulation heat stress(TMHS),5)control heat stress supplement(CHSS),and 6)thermal manipulation heat stress supplement(TMHSS).All birds were raised under the standard environment for 21 d,followed by chronic heat stress from d 22 to 35(32–33℃ for 8 h)in the CHS,TMHS,CHSS,and TMHSS groups.A thermoneutral(22–24℃)environment was maintained in the Control and TM groups.RH was constant(50%±5%)throughout the trial.All the data were analyzed using one-way ANOVA in R and GraphPad software at P<0.05 and are presented as mean±SEM.Heat stress significantly decreased(P<0.05)the final body weight and ADG in CHS and TMHS groups compared to the other groups.Embryonic TM significantly increased(P<0.05)the expression of heat shock protein-related genes(HSP70,HSP90,and HSPH1)and antioxidant-related genes(GPX1 and TXN).TMHS birds showed a significant increment(P<0.05)in total cecal volatile fatty acid(VFA)concentration compared to the CHS birds.The cecal microbial analysis showed significant enrichment(P<0.05)in alpha and beta diversity and Coprococcus in the TMHSS group.Conclusions Pre-hatch TM and post-hatch baicalein supplementation in heat-stressed birds mitigate the detrimental effects of heat stress on chickens’growth performance,upregulate favorable gene expression,increase VFA produc-tion,and promote gut health by increasing beneficial microbial communities.

STEADY-STATE OPERATION ANALYSIS OF AN IDEAL HEAT INTEGRATED DISTILLATION COLUMN

A systematic approach for the steady-state operation analysis of chemical processes is pro-posed.The method affords the possibility of taking operation resilience into consideration during thestage of process design.It may serve the designer as an efficient means for the initial screening ofalternative design schemes.An ideal heat integrated distillation column(HIDiC),without any reboileror condenser attached,is studied throughout this work.It has been found that among the various va-riables concerned with the ideal HIDiC,feed thermal condition appears to be the only factor exertingsignificant influences on the interaction between the top and the bottom control loops.Maximuminteraction is expected when the feed thermal condition approaches 0.5.Total number of stages andheat transfer rate are essential to the system ability of disturbance rejection.Therefore,more stagesand higher heat transfer rate ought to be preferred.But,too many stages and higher heat transfer ratemay increase the load of the

Optimum Profiles of Endwall Contouring for Enhanced Net Heat Flux Reduction and Aerodynamic Performance

Successfully utilized non-axisymmetric endwalls to enhance turbine efficiencies(aerodynamic and turbine inlet temperatures)by controlling the characteristics of the secondary flow in a blade passage.This is accomplished by steady-state numerical hydrodynamics and deep knowledge of the field of flow.Because of the interaction between mainstream and purge flow contributing supplementary losses in the stage,non-axisymmetric endwalls are highly susceptible to the inception of purge flow exit compared to the flat and any advantage rapidly vanishes.The conclusions reveal that the supreme endwall pattern could yield a lowering of the gross pressure loss at the design stage and is related to the size of the top-loss location being productively lowered.This has led to diminished global thermal exchange lowered in the passage of the vane alone.The reverse flow adjacent to the suction side corner of the endwall is migrated farther from the vane surface,as the deviated pressure spread on the endwall accelerates the flow and progresses the reverse flow core still downstream.The depleted association between the tornado-like vortex and the corner vortex adjacent to the suction side corner of the endwall is the dominant mechanism of control in the contoured end wall.In this publication,we show that the non-axisymmetric endwall contouring by selective numerical shape change method at most prominent locations is advantageous in lowering the thermal load in turbines to augment the net heat flux reduction as well as the aerodynamic performance using multi-objective optimization.

Optimal synthesis of heat-integrated distillation configurations using the two-column superstructure

In the realm of the synthesis of heat-integrated distillation configurations,the conventional approach for exploring more heat integration possibilities typically entails the splitting of a single column into a twocolumn configuration.However,this approach frequently necessitates tedious enumeration procedures,resulting in a considerable computational burden.To surmount this formidable challenge,the present study introduces an innovative remedy:The proposition of a superstructure that encompasses both single-column and multiple two-column configurations.Additionally,a simultaneous optimization algorithm is applied to optimize both the process parameters and heat integration structures of the twocolumn configurations.The effectiveness of this approach is demonstrated through a case study focusing on industrial organosilicon separation.The results underscore that the superstructure methodology not only substantially mitigates computational time compared to exhaustive enumeration but also furnishes solutions that exhibit comparable performance.

Low-energy-consumption temperature swing system for CO_(2) capture by combining passive radiative cooling and solar heating

Temperature-swing adsorption(TSA)is an effective technique for CO_(2) capture,but the temperature swing procedure is energy-intensive.Herein,we report a low-energy-consumption system by combining passive radiative cooling and solar heating for the uptake of CO_(2) on commercial activated carbons(CACs).During adsorption,the adsorbents are coated with a layer of hierarchically porous poly(vinylidene fluoride-co-hexafluoropropene)[P(VdF-HFP)HP],which cools the adsorbents to a low temperature under sunlight through radiative cooling.For desorption,CACs with broad absorption of the solar spectrum are exposed to light irradiation for heating.The heating and cooling processes are completely driven by solar energy.Adsorption tests under mimicked sunlight using the CACs show that the performance of this system is comparable to that of the traditional ones.Furthermore,under real sunlight irradiation,the adsorption capacity of the CACs can be well maintained after multiple cycles.The present work may inspire the development of new temperature swing procedures with little energy consumption.

Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices

In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.

Time-lagged Effects of the Spring Atmospheric Heat Source over the Tibetan Plateau on Summer Precipitation in Northeast China during 1961–2020:Role of Soil Moisture

The spring atmospheric heat source(AHS)over the Tibetan Plateau(TP)has been suggested to affect the Asian summer monsoon and summer precipitation over South China.However,its influence on the summer precipitation in Northeast China(NEC)remains unknown.The connection between spring TP AHS and subsequent summer precipitation over NEC from 1961 to 2020 is analyzed in this study.Results illustrate that stronger spring TP AHS can enhance subsequent summer NEC precipitation,and higher soil moisture in the Yellow River Valley-North China region(YRVNC)acts as a bridge.During spring,the strong TP AHS could strengthen the transportation of water vapor to East China and lead to excessive rainfall in the YRVNC.Thus,soil moisture increases,which regulates local thermal conditions by decreasing local surface skin temperature and sensible heat.Owing to the memory of soil moisture,the lower spring sensible heat over the YRVNC can last until mid-summer,decrease the land–sea thermal contrast,and weaken the southerly winds over the East Asia–western Pacific region and convective activities over the South China Sea and tropical western Pacific.This modulates the East Asia–Pacific teleconnection pattern,which leads to a cyclonic anomaly and excessive summer precipitation over NEC.

Variation in the surface heat flux on the north and south slopes of Mount Qomolangma

The distinctive conditions present on the north and south slopes of Mount Qomolangma,along with the intricate variations in the underlying surfaces,result in notable variations in the surface energy flux patterns of the two slopes.In this paper,data from TESEBS(Topographical Enhanced Surface Energy Balance System),remote sensing data from eight cloud-free scenarios,and observational data from nine stations are utilized to examine the fluctuations in the surface heat flux on both slopes.The inclusion of MCD43A3 satellite data enhances the surface albedo,contributing to more accurate simulation outcomes.The model results are validated using observational data.The RMSEs of the net radiation,ground heat,sensible heat,and latent heat flux are 40.73,17.09,33.26,and 30.91 W m^(−2),respectively.The net radiation flux is greater on the south slope and exhibits a rapid decline from summer to autumn.Due to the influence of the monsoon,on the north slope,the maximum sensible heat flux occurs in the pre-monsoon period in summer and the maximum latent heat flux occurs during the monsoon.The south slope experiences the highest latent heat flux in summer.The dominant flux on the north slope is sensible heat,while it is latent heat on the south slope.The seasonal variations in the ground heat flux are more pronounced on the south slope than on the north slope.Except in summer,the ground heat flux on the north slope surpasses that on the south slope.

A coupled thermo-mechanical peridynamic model for fracture behavior of granite subjected to heating and water-cooling processes

Thermal damage and thermal fracture of rocks are two important indicators in geothermal mining projects.This paper investigates the effects of heating and water-cooling on granite specimens at various temperatures.The laboratory uniaxial compression experiments were also conducted.Then,a coupled thermo-mechanical ordinary state-based peridynamic(OSB-PD)model and corresponding numerical scheme were developed to simulate the damage of rocks after the heating and cooling processes,and the change of crack evolution process was predicted.The results demonstrate that elevated heating temperatures exacerbate the thermal damage to the specimens,resulting in a decrease in peak strength and an increase in ductility of granite.The escalating occurrence of thermal-induced cracks significantly affects the crack evolution process during the loading phase.The numerical results accurately reproduce the damage and fracture characteristics of the granite under different final heating temperatures(FHTs),which are consistent with the test results in terms of strength,crack evolution process,and failure mode.

Personal Thermal Management by Radiative Cooling and Heating

Maintaining thermal comfort within the human body is crucial for optimal health and overall well-being.By merely broadening the setpoint of indoor temperatures,we could significantly slash energy usage in building heating,ventilation,and air-conditioning systems.In recent years,there has been a surge in advancements in personal thermal management(PTM),aiming to regulate heat and moisture transfer within our immediate surroundings,clothing,and skin.The advent of PTM is driven by the rapid development in nano/micro-materials and energy science and engineering.An emerging research area in PTM is personal radiative thermal management(PRTM),which demonstrates immense potential with its high radiative heat transfer efficiency and ease of regulation.However,it is less taken into account in traditional textiles,and there currently lies a gap in our knowledge and understanding of PRTM.In this review,we aim to present a thorough analysis of advanced textile materials and technologies for PRTM.Specifically,we will introduce and discuss the underlying radiation heat transfer mechanisms,fabrication methods of textiles,and various indoor/outdoor applications in light of their different regulation functionalities,including radiative cooling,radiative heating,and dual-mode thermoregulation.Furthermore,we will shine a light on the current hurdles,propose potential strategies,and delve into future technology trends for PRTM with an emphasis on functionalities and applications.