Thermal shock fracture of a crack in a functionally gradient half-space based on the memory-dependent heat conduction model

In the present study, we consider a thermoelastic half-space made of a functionally gradient material with an insulated crack, which is subjected to a thermal impact. The memory-dependent heat conduction model is adopted for analysis. By using the Fourier and Laplace transforms, the thermoelastic problem is formulated in terms of singular integral equations which can be solved numerically. Effects of the time delay, kernel function, and nonhomogeneity parameters on the temperature and stress intensity factor are analyzed. Our results are also compared with those based on the Fourier and CV heat conduction models, which can be viewed as two special cases of the present model. In conclusion, the memory-dependent derivative and nonhomogeneity parameters play an essential role in controlling the heat transfer process.     

A problem of generalized magneto-thermoelastic thin slim strip subjected to a moving heat source

The generalized thermoelastic theory with thermal relaxation, in the context of Lord and Shulman theory, is used to investigate the magneto-thermoelastic problem of a thin slim strip placed in a magnetic field and subjected to a moving plane of heat source. The generalized magneto-thermoelastic coupled governing equations are formulated. By means of the Laplace transform and numerical Laplace inversion, the governing equations are solved. Numerical calculations for the considered variables are performed and the obtained results are presented graphically. The effects of moving heat source speed and applied magnetic field on temperature, stress and displacement are studied. It is found from the graphs that the temperature, thermally induced displacement and stress in the strip are found to decrease at large heat source speed, and the magnetic field significantly influences the variations of non-dimensional displacement and stress. However, it has no effect on the non-dimensional temperature.     

热传导的微极固体和流体介质界面上波的传播

研究微极广义热弹性固体半空间和热传导微极流体半空间界面上波的传播.讨论微极广义热弹性固体半空间和热传导微极流体半空间之间平面界面上,斜向入射平面波的反射和透射现象.假设入射波穿过微极广义热弹性固体,射向平面界面后传播.得到了封闭形式的、不同反射和透射波的波幅比,它们是入射角、频率的函数,并为介质的弹性性质所影响.对一些特定的类型,显示出微极和热松弛对波幅比的影响.还从本文的研究中推演出一些早期工作的结果.     

Thermoelastic instability of functionally graded coating with arbitrarily varying properties considering contact resistance and frictional heat

Using the homogeneous multi-layered model, this paper studies the thermoelastic instability (TEI) of the functionally graded material (FGM) coating with arbitrary varying properties considering the frictional heat and thermal contact resistance. A homogeneous half-plane slides on an FGM coated half-plane at the out-of-plane direction under a uniform pressure. The perturbation method and transfer matrix method are used to deduce the characteristic equation of the TEI problem, which is then solved to obtain the relationship between the critical sliding speed and critical heat flux. The effects of the gradient index and varying form of material properties of the FGM coating on the stability boundaries are examined. The results show that FGM coating can adjust the thermoelastic contact stability of sliding systems.     

Temperature and displacement fields in brake and clutch systems with thermoelastic instabilities

In brake and clutch systems kinetic energy is converted into thermal energy. Experiments show that the corresponding temperature field can develop unstable periodic structures. The temperature field couples to the displacement field by thermal expansion. Local pressure maxima in the frictional plane and the corresponding maxima in heat generated cause thermoelastic instabilities (TEI). A model describing both effects covers layers of thermoelastic materials for all necessary mechanical components of the system. The set of field equations of each layer can analytically be solved by separation of constants. These solutions must fulfill the boundary conditions e.g. in the sliding plane. A stability discussion yields whether TEI appear or not. As a study a brake system is analyzed comprising two pads pressed against a rotating disk with cooling channels inside. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An extended thermal-medium crack model

It is important to investigate the effects of heat conduction of crack interior on thermoelastic fields of a cracked material. In this paper, an extended thermal-medium crack model is proposed to address the influences of the thermal conductivity inside an opening crack on the induced thermoelastic fields. Then the problem of a penny-shaped crack in a transversely isotropic material is investigated under applied mechanical and uniform heat flow loadings. Based on the Hankel transform technique, the governing partial differential equations are transformed to ordinary differential equations, then to a system of coupled dual integral equations. The thermoelastic fields around the penny-shaped crack are obtained explicitly by solving the derived dual integral equations. Numerical results are reported to show the influences of the thermal conductivity of crack interior on partial insulation coefficient, temperature change across crack and thermal stress intensity factor. As compared to the known thermal-medium crack model, the proposed one exhibits more applicability.     

Thermoelastic bending of orthotropic plates acted on by concentrated heat sources with arbitrary heat transfer

The thermoelastic problem is solved for an infinite thin orthotropic plate acted on by internal heat sources. Arbitrary heat transfer is assumed between the plate and its surroundings. Results from a numerical study are presented. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 96–102, 1999.     

New closed-form Green function and integral formula for a thermoelastic quadrant

In this study a new Green’s function and a new Green-type integral formula for a boundary value problem (BVP) in thermoelastostatics for a quadrant are derived in closed form. On the boundary semi-straight-lines twice mixed homogeneous mechanical boundary conditions (one boundary semi-straight-line is free of loadings and normal displacements and tangential stresses are prescribed on the other one) are prescribed. The thermoelastic displacements are subject by a heat source applied in the inner points of the quadrant and by mixed non-homogeneous boundary heat conditions (on one boundary semi-straight-line the temperature is prescribed and the heat flux is given on the other one). When thermoelastic Green’s function is derived the thermoelastic displacements are generated by an inner unit point heat source, described by δ Dirac’s function. All results are obtained in elementary functions that are formulated in a special theorem. A closed-form solution for a particular BVP of thermoelastostatics for a quadrant also is included. Using the proposed approach it is possible to extend the obtained for quadrant results to any other canonical Cartesian domain.     

Near-wall gas-droplet flows with liquid-film formation

A self-consistent asymptotic theory of a near-wall aerodisperse flow with the formation of a liquid film due to inertial deposition of liquid droplets on the body surface is constructed. With the reference to the examples of low-speed mist flows near plane and curvilinear solid surfaces, asymptotically different situations are analyzed. The two-fluid equations of the mist flow are solved simultaneously with the equations of the liquid film, on the outer edge of which the distributed mass, momentum, and energy fluxes (found from the solution of the outer problem) are specified. It is shown that depending on the values of governing parameters the flow in the film should be described by either boundary-layer or creeping-flow equations in the layer with a priori unknown thickness. For the film on the frontal surface of a blunt body, the film thickness and the friction and heat transfer coefficients are found numerically. The conditions in which the presence of the film significantly reduces the heat fluxes are determined and the possibility of the realization of steady-state flow regimes in the film is demonstrated. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic equations of thermoelastic Cosserat rods

A thermoelastic Cosserat rod with a heat flux along its length is modeled after reviewing a simple Cosserat rod model. Extended Kirchhoff constitutive relations that include thermal effects, and the associated heat conduction equation, are derived using the first law of thermodynamics. The rate of internal dissipation of the Cosserat rod is estimated by the Clausius–Duhem inequality. Nonlinear dynamic equations of the thermoelastic Cosserat rod, which extend the simple Cosserat rod model, are obtained. Dynamic equations of a planar thermoelastic Cosserat rod, the Timoshenko thermoelastic beam, and the planar Euler–Bernoulli thermoelastic beam are derived as a special case within the framework of the thermoelastic Cosserat rod.     

Wave propagation in an initially stressed transversely isotropic thermoelastic solid half-space

The governing equations of thermoelasticity of transversely isotropic solid with initial stresses are formulated at uniform temperature. These equations are solved analytically in two-dimensions to show the existence of three plane quasi waves, namely, Quasi-Longitudinal (QL), Thermal (T-mode) and Quasi-Transverse (QT) waves. Reflection from a thermally insulated stress free surface of an initial stressed transversely isotropic thermoelastic solid half-space is studied. A particular model is chosen for the numerical computations of the propagation speeds, attenuation coefficients and reflection coefficients. Effects of initial stress parameter and thermal disturbances are observed on speeds of propagation, attenuation coefficients and reflection coefficients.     

温差影响下的局部滑移接触行为的研究

针对不同温度装配件间接触界面的局部滑移问题,建立了三维稳态热弹性局部滑移接触的半解析求解模型.基于热弹性理论与热传导方程,构建了半空间受热流载荷和力载荷作用下的频响函数并建立了相应的影响系数矩阵.借助离散卷积-快速Fourier变换等数学工具,实现了针对高温压头与热弹性半空间局部滑移接触问题的高效求解.接触界面间的热量传递满足Fourier热传导定律,并且黏/滑状态由Coulomb定律确定.基于该半解析模型分析了不同荷载及温差对表面法向压力分布、摩擦力分布、刚体位移及接触区黏/滑演化行为的影响.研究结果表明,当法向荷载和切向荷载一定时,温差的上升会导致接触区域的减小,引起接触面法向压力及摩擦力的峰值增大,并且会显著影响黏着区与滑移区的分布情况.     

A comparison of two equivalent solutions of the diffusion equation

Plane radial flow of water in a closed aquifer towards a circular well or heat flow through a homogeneous conducting solid from a circular hole to infinity are well known problems that were solved long ago. The solution is expressed in terms of an integral of ordinary Bessel functions. A new solution, which is expressed in terms of an integral of modified Bessel functions, is derived by means of Laplace transformation instead of integration of Green's function. One particular choice of the Bromwich contour in the invers transformation, which appears unnecessarily complicated, gives a solution the integral of which converges much more rapidly than the corresponding integral that is given in the literature. In contrast with the classical solution, the new one gives an explicit expression for the transient part. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 657–671, 1999     

Efficient Simulation of Short Fibre Reinforced Composites

In this paper we present a way how short fibre reinforced composites, produced by injection moulding, can be simulated in a linear thermoelastic setting, with an stationary heat equation. The main problem is the unknown stochastic fibre orientation. The only information known about this orientation field are the first moments of its distribution. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Simulation of Short Fibre Reinforced Composites

In this paper we present a way how short fibre reinforced composites, produced by injection moulding, can be simulated in a linear thermoelastic setting, with an instationary heat equation. The main problem is the unknown stochastic fibre orientation. The only information known about this orientation field are the first moments of its distribution. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal control of Huygens mock up probe in Earth atmosphere: Thermo‐fluid dynamic simulation and mission data

A mock up of Huygens probe with 76 channels acquisition has been developed at University of Padova and successfully flown with a stratospheric space balloon from Italian Space Agency Base in Trapani on May 30th 2002. Temperature sensors have monitored temperature profiles in critical points of electronics, batteries and structure during raise at 40 km altitude, floating and parachuted descent. A thermal model of the probe has been implemented taking into consideration incoming external fluxes (solar direct, albedo and radiative heat fluxes), internal heat fluxes generation and convective heat transfer with atmosphere as a function of probe altitude. For the evaluation of convective fluxes and probe spinning rates an algebraic turbulent model, developed by the present authors, has been employed. This model is suitable to predict effects such as flow curvature and separation and solid boundary rotations. Simulation results have been utilized during project phase to optimize thermal paths in order to keep critical components in the allowable temperature range and for post flight analysis of mission data. These data show that passive thermal control of the probe has performed as expected contributing to a extremely successful scientific flight.     

Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.     

在重力作用下的上覆无限热弹性流体对广义热弹性固体转动的影响

计及上覆无限热弹性流体的重力作用,沿界面有不同的外力作用时,研究广义热弹性固体的旋转变形问题.在Laplace和Fourier域内,通过积分变换,得到了位移、应力及温度分布的表达式.然后在物理域内,应用数值逆变换方法,得到这些分量的值,并讨论了该问题的一些特例.结果以图形方式给出,显示了介质的旋转以及重力作用的影响.     

Coupled fluid-solid thermal interaction modeling for efficient transient simulation of biphasic water-steam energy systems

This paper proposes a fluid-solid coupled finite element formulation for the transient simulation of water-steam energy systems with phase change due to boiling and condensation. As it is commonly assumed in the study of thermal systems, the transient effects considered are exclusively originated by heat transfer processes. A homogeneous mixture model is adopted for the analysis of biphasic flow, resulting in a nonlinear transient advection-diffusion-reaction energy equation and an integral form for mass conservation in the fluid, coupled to the linear transient heat conduction equation for the solid. The conservation equations are approximated applying a stabilized Petrov-Galerkin FEM formulation, providing a set of coupled nonlinear equations for mass and energy conservation. This numerical model, combined with experimental heat transfer coefficients, provides a comprehensive simulation tool for the coupled analysis of boiling and condensation processes. For the treatment of enthalpy discontinuities traveling with the flow, a novel explicit-implicit time integration method based on Crank-Nicolson scheme is proposed, analyzing its accuracy and stability properties. To reduce problem size and enhance numerical efficiency, a modal superposition method with balanced truncation is applied to the solid equations. Finally, different example problems are solved to demonstrate the capabilities, flexibility and accuracy of the proposed formulation.