Effects of mechanical boundary conditions on thermal shock resistance of ultra-high temperature ceramics

The effects of mechanical boundary conditions, often encountered in thermalstructural engineering, on the thermal shock resistance (TSR) of ultra-high temperature ceramics (UHTCs) are studied by investigating the TSR of a UHTC plate with various types of constraints under the first, second, and third type of thermal boundary conditions. The TSR of UHTCs is strongly dependent on the heat transfer modes and severity of the thermal environments. Constraining the displacement of the lower surface in the thickness direction can significantly decrease the TSR of the UHTC plate, which is subject to the thermal shock at the upper surface. In contrast, the TSR of the UHTC plate with simply supported edges or clamped edges around the lower surface is much better.     

Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins with temperature-dependent thermal conductivity.     

装药弹体侵彻混凝土厚靶中的炸药摩擦起爆模型

基于炸药的热爆炸理论,采用炸药的热点温度（也称为临界起爆温度）作为起爆判据,分析了装药弹体在侵彻混凝土厚靶过程中的炸药安全性问题,建立了炸药摩擦起爆的热传导模型。对模型进行了量纲一化分析,得出量纲一热流率幅值Qm与炸药和弹壳界面量纲一温度峰值Tmax的关系,以及可在实际工程中应用的临界量纲一控制参数Qmc,同时得到了反映摩擦产生的热量在炸药与弹壳间分配比例关系的量纲一参数Ⅰ。结果表明,炸药装药和弹壳接触面间的强摩擦是形成热点、从而导致炸药早炸的一个重要因素。     

A new 1-D composite lumped model facilitates the algebraic calculation of local temperatures, mean temperatures, and total heat transfer in simple bodies

Estimates of spatio-temporal temperatures and total heat transfer in simple bodies (large plate, long cylinder and sphere) have been done in the past with the help of charts and recently by way of algebraic correlation equations; both avenues are valid for large times mostly, i.e., dimensionless times or Fourier numbers τ?≥?0.2. The imposing time restriction comes from the utilization of the truncated ‘one-term series’ because the Fourier infinite series diverge for very short times approaching zero. The central goal of this technical paper is to predict the mean, surface and center temperatures, as well as the total heat transfer in those simple bodies by implementing a 1-D composite lumped analysis united to a sound physics-based computational procedure. The effortless combined methodology is new. It brings forth a handful of compact algebraic equations covering the full gamma of Biot numbers (0?<?Bi?<?100) and all dimensionless times, 0?<?τ?<?∞.     

Stress boundary conditions for plate bending

The determination of the appropriate boundary conditions for a two-dimensional theory of elastic flat plates (and shells) consistent with the expected order of accuracy of the theory is both critical and challenging. The reciprocal theorem of elasticity will be applied in a novel way to obtain the appropriate stress boundary conditions for plate bending accurate to all order (with respect to the usual dimensionless thickness parameter) for plates of general edge geometry and loading. Kirchhoff’s two contracted stress boundary conditions are shown to be consistent with a leading term (thin plate) approximation theory, but the more general results obtained herein are needed for higher order theories.     

Fully Developed Forced Convection Heat Transfer in a Porous Channel with Asymmetric Heat Flux Boundary Conditions

An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between the lower or upper walls while the fluid is flowing in the channel.     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

Flow of colloidal suspension and irreversibility analysis with aggregation kinematics of nanoparticles in a microchannel

The current exploration focuses on the ethylene glycol (EG) based nanoliquid flow in a microchannel. The effectiveness of the internal heat source and linear radiation is reflected in the present investigation. The estimation of suitable thermal conductivity model has affirmative impact on the convective heat transfer phenomenon. The examination is conceded with the nanoparticle aggregation demonstrated by the MaxwellBruggeman and Krieger-Dougherty models which tackle the formation of nanolayer. These models effectively describe the thermal conductivity and viscosity correspondingly. The dimensionless mathematical expressions are solved numerically by the Runge Kutta Fehlberg approach. A higher thermal field is attained for the Bruggeman model due to the formation of thermal bridge. A second law analysis is carried out to predict the sources of irreversibility associated with the thermal system. It is remarked that lesser entropy generation is obtained for the aggregation model. The entropy generation rate declines with the slip flow and the thermal heat flux. A notable enhancement in the Bejan number is attained by increasing the Biot number. It is established that the nanoparticle aggragation model exhibits a higher Bejan number in comparision with the usual flow model.     

热环境对超高温陶瓷材料抗热震性能的影响

基于超高温陶瓷材料相关材料参数对温度的敏感性,以现有的抗热震断裂评价理论为基础,通过考虑温度对超高温陶瓷材料物理性能的影响,探讨了热震温度范围内热应力衰减系数、表面热传递系数、热冲击初始环境温度等热环境参数对抗热冲击阻力参数、断裂临界温差和断裂临界温度的影响.      

THERMAL BUCKLING ANALYSIS OF CIRCULAR PLATE EMBEDDED IN AN INFINITE ELASTIC PLATE 1)

分析了嵌入无限大弹性板中的圆板在变温时的热屈曲问题。由于圆板的热膨胀系数与无限大弹性板的热膨胀系数不同,温度变化时圆板中会产生压应力。当压应力达到其临界值时,圆板会发生热屈曲。首先,基于弹性力学平面应力问题的基本理论,得到圆板和无限大弹性板的应力和位移;然后建立圆板热屈曲的控制微分方程,求得临界屈曲温度的解析解和数值解,着重讨论圆板和无限大弹性板的材料物性参数的关系对圆板临界屈曲温度的影响。     

Hydrodynamic instability in fluid layers with uniform volumetric energy sources

Linear and energy theory stability criteria are presented for fluid layers of infinite horizontal extent heated internally by a uniform volumetric energy source. The thermal coupling between the layer and its environment is modeled by a general mixed boundary condition in both the conduction state and the disturbance temperature. Rigid-rigid, free-free, free-rigid, and rigid-free boundaries are considered in the computations. For a fixed ratio of upper surface Biot number to that at the lower surface, decreasing the Biot number is strictly destabilizing for both linear and energy theory criteria. A region of possible subcritical instability is found; its size is strongly dependent on Biot number and becomes small for small values of lower surface Biot number and large Biot number ratio. For two rigid surfaces and an upper and lower surface Biot number of 47.5, mean energy transport measurementswithin the convecting layer indicate a critical Reyleigh number close to that predicted by linear theory. Subcritical instability is not observed when finite amplitude disturbances are introduced at a Rayleigh number between the critical values predicted by the linear theory and the energy theory.     

弹性地基上多孔功能梯度材料矩形板的自由振动与临界屈曲载荷分析

多孔功能梯度材料(FGM)构件的特性与孔隙率和孔隙分布形式有密切关系。本文基于经典板理论,考虑不同孔隙分布形式时修正的混合率模型,研究Winkler弹性地基上四边受压多孔FGM矩形板的自由振动与临界屈曲载荷特性。首先利用Hamilton原理和物理中面的定义推导Winkler弹性地基上四边受压多孔FGM矩形板自由振动的控制微分方程并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程和边界条件进行变换,得到计算无量纲固有频率和临界屈曲载荷的代数特征方程。将问题退化为孔隙率为零时的FGM矩形板并与已有文献进行对比以验证其有效性。最后计算并分析了梯度指数、孔隙率、地基刚度系数、长宽比、四边受压载荷及边界条件对多孔FGM矩形板无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

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激光直接成形中,几何参数、材料属性和工艺参数等众多参量均会对残余应力造成影响,需 要进行系统分析. 采用量纲分析的方法,分别提取表征几何、传热和变形的3类关键无 量纲参数,并结合三维瞬态有限元分析模型来研究这些无量纲参数对热致残余应力的影响规 律. 研究表明,选用热膨胀系数、屈服应力较小的材料,残余应力会较小;工艺控制中,可 通过降低热散失、增大激光功率和提升预热温度来减小残余应力,其中预热的效果最好.     

多孔介质平板通道强迫对流中热局部非平衡时的热应力

根据微观不可压饱和多孔介质热-力-流相互作用的一般理论,在固相骨架小变形的假定下,考虑固相和流相相互作用的粘性耗散,研究了多孔介质平板通道强迫对流热局部非平衡的热应力问题.建立了问题的热-力数学模型,根据饱和多孔介质的平衡方程,在固相骨架只存在横向位移的假定下,求解了固相骨架的位移和相应的热应力,数值考察了各种物性参数对热应力分布的影响,讨论了热局部平衡模型的适用性.     

瞬态热冲击下层合材料板界面的热弹性行为

基于带有两个热松弛时间的G-L广义热弹性理论, 利用有限元方法研究了零阻抗理想界面层合板在瞬态热冲击诱导的位移、应力和温度等通过界面时的热弹性行为. 通过比较不同层中材料的比热容、热导系数、热松弛时间和密度等对界面处的位移、应力和温度的影响, 研究了不同材料参数对复合材料热力学行为影响, 发现不同材料参数将导致热穿过界面时界面处温度、位移和应力发生突变, 研究结果可以为由热引起的层合板挠曲变形提供理论依据.      

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

The 1-D heat transfer through a flat plate exposed to out of phase step changes in the free stream temperatures

 The thermal response of an infinite flat plate is considered, when the temperatures of both the surrounding fluids undergo step changes. The configuration is a simplified model for the heat transfer through the separating wall in the isochoric countercurrent heat exchanger (ICHE). The step changes appear with a time delay. The plate temperature, surface heat fluxes and accumulated energy perturbations are evaluated for both the thermally thick and thin cases and the corresponding results are compared. The results show a significant influence of the delay time and a smaller one for the Biot numbers, especially when their sum exceeds the value of 0.1. Received on 19 December 2000 / Published online: 29 November 2001     

Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system

This paper studies the fracture behavior of a thermoelastic cylinder subjected to a sudden temperature change on its outer surface within the framework of non-classical heat conduction.The heat conduction equation is solved by separation of variable technique.Closed form solution for the temperature field and the associated thermal stress are established.The critical parameter governing the level of the transient thermal stress is identified.Exact expression for the transient stress intensity factor is obtained for a crack in the cylinder.The difference between the non-classical solutions and the classical solution are discussed.It is found that the traditional classical heat conduction considerably underestimates the transient thermal stress and thermal stress intensity factor.     

A simplified model of heat transfer in heat exchangers and stack plates of thermoacoustic refrigerators

A simplified model of heat transfer was developed to investigate the thermal behavior of heat exchangers and stack plates of thermoacoustic devices. The model took advantage of previous results describing the thermal behavior of the thermoacoustic core and heat transfer in oscillating flow to study the performance of heat exchangers attached to the core. The configuration considered is a flat tube (with a working fluid flowing in the tube) of the thickness of the stack plate attached to both ends of the stack plate. Geometrical and operational parameters as well as thermophysical properties of the heat exchangers, transport fluids in the heat exchangers, stack plate and the thermoacoustic working fluid were organized into dimensionless groups that allowed accounting for their impact on the performance of the heat exchangers. Two types of thermal boundary conditions were considered: constant temperature and constant heat flux along the heat exchanger tubes. Numerical simulations were carried out with the model introduced in the paper. The temperature distributions and heat fluxes near the edge of the stack plate were found to be nonlinear. The influence of system parameters on the thermal performance of the heat exchangers was analyzed.This article is dedicated to Prof. D. Mewes, whose knowledge, creativity, enthusiasm and dedication to engineering science was an inspiration to me and to many students, scientists, engineers and colleagues all over the world (C. Herman).     

Hydrodynamic instability in a porous layer saturated with a heat generating fluid

Critical Rayleigh numbers determined by linear stabiliy theory are presented for porous-fluid layers of infinite horizontal extent heated internally by a uniform volumetric energy source in the fluid. The thermal coupling between the layer and its environment is represented by a general mixed boundary condition for both the conduction state and the disturbance temperature. Rigid-rigid, rigid-constant pressure, and constant pressure-rigid boundaries are considered in the computations. For a fixed ratio of upper surface Biot number to that at the lower surface, decreasing the Biot number is strictly destabilizing for values of this ratio greater than or equal to one. A layer with a rigid upper surface is generally the most stable; however, a layer with a rigid upper surface and a constant pressure lower surface exhibits the largest values of critical Rayleigh numbers for large values of Biot number.