Dynamic Thermoelastic Response of a Heated Thin Composite Plate Using the Dual-Phase-Lag Heat Conduction Model

This paper investigates the dynamic thermoelastic response of a heated thin composite plate. The plate is composed of a dominant matrix domain and an insert domain. A step-function heat source is generated within the matrix domain, causing the heating of the whole plate. The dual-phase-lag heat conduction model is used to determine the thermal behavior of the plate in the form of the spatial and time variations of the temperatures in both domains. The temperature of the matrix is used to evaluate the thermoelastic behavior of the plate in the form of the induced displacements and thermal stresses. The Laplace transformation technique combined with the Rieman-sum method is used to calculate the temperatures. The finite difference method is used to solve the governing equation of plate deflection and then calculate the thermal stresses. The resulting thermal stresses are found to be compressive and follow the same behavior as that of the temperature.     

Multifrequential AC modeling of the SThM probe behavior

The scanning thermal microscope is of current use for the determination of the thermal conductivity of material surfaces, with a submicrometer resolution. The determination of the parameters that have great importance in the probe response is clarified and an analytical approach in the multifrequency domain is compared with a finite element method and experimental results without contact.     

Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue

In this article, the parabolic (Pennes bioheat equation) and hyperbolic (thermal wave) bioheat transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The bioheat transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat transfer equations. The non-Fourier bioheat transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic bioheat transfer equations.     

GENERALIZED COUPLED THERMOELASTICITY OF DISKS BASED ON THE LORD–SHULMAN MODEL

A one-dimensional generalized thermoelasticity model of a disk based on the Lord–Shulman theory is presented. The dynamic thermoelastic response of the disk under axisymmetric thermal shock loading is studied. The effects of the relaxation time and coupling coefficient are studied. The Laplace transform method is used to transform the coupled governing equations into the space domain, where the Galerkin finite element method is employed to solve the resulting equations in the transformed domain. The dimensionless temperature, displacement, and stresses in the transformed domain are inverted to obtain the actual physical quantities using the numerical inversion of the Laplace transform method.     

形状记忆复合材料可展桁架在轨热分析

传统星载桁架结构需通过驱动器实现展开/收拢动作,应用形状记忆复合材料可突破该限制。对新型可展桁架各组件进行热控方案设计,基于I-DEAS/TMG软件建立热分析数值模型,对桁架各组件在轨外热流以及温度场变化进行计算分析。结果表明:最外端桁架在轨运行4个周期后其温度场呈周期性变化特征;不同多层隔热材料(multi-layer insulation material,MLI)表面辐射特性对内/外端纵杆温度影响明显;热控方案能实现有效的在轨温度控制。     

Advances in Studying Phonon Mean Free Path Dependent Contributions to Thermal Conductivity

The thermal conductivity of a material or device is dependent on its characteristic dimension. When the characteristic dimension is commensurate to the mean free paths of thermal energy carriers, the thermal conductivity decreases. The precise relationship between characteristic size and thermal conductivity, which depends on the distribution of energy carrier mean free paths in the material, is not straightforward to determine experimentally. The utility of this relationship has led many researchers to study the mean free path dependent contributions of thermal energy carriers to the thermal conductivity of materials, known as the thermal conductivity accumulation function. This review highlights a number of recent experimental results and techniques used to study the thermal conductivity accumulation function, including transient thermal grating, time domain thermoreflectance, and broadband frequency domain thermoreflectance. In these techniques, nondiffusive thermal transport is induced (i.e., thermal gradients occur over length scales comparable to energy carrier mean free paths) and an effective thermal conductivity of the material is determined. We conclude with our outlook on future directions for the field focused on improved interpretations of the experiments and new materials with unique mean free path distributions.     

Investigation of the thermal properties of a Li-ion pouch-cell by electrothermal impedance spectroscopy

Electrothermal impedance spectroscopy (ETIS), is introduced as a new measurement method and thermal parameters derived from a pouch-type lithium-ion cell are presented. ETIS is a valuable tool for (i) the determination of the thermal impedance and (ii) the validation of thermal models. The excitation signal applied to the cell during measurement does not cause a change in entropy, thus facilitating the parameter identification of a thermal model for heat conduction and thermal capacity.ETIS can be applied to measurements in time domain and in frequency domain. Both approaches are presented and a combination further improves measurement time and accuracy.     

Optimization of microchannel-based cooling systems

Abstract

In this article, microchannel systems for cooling applications such as in the thermal management of electronic equipment are investigated and optimized. Numerical simulations are carried out to study the conjugate heat transfer and flow behavior. The numerical model has been validated by comparing with analytical results. Two sets of design variables are evaluated: (Set I) Incoming flow rate and the number of channels and (Set II) Incoming flow rate and heat flux input. Response surfaces are used to represent the thermal and fluid behavior in the microchannel systems. Based on the polynomial response surface (PRS) modeling results, a multi-objective optimization problem is formulated to reduce both pumping power and thermal resistance. Two major practical concerns, hot-spot temperature and pressure difference, serve as optimization constraints. With varying weights on the two conflicting objectives, Pareto frontiers are obtained. It is also shown that an optimal configuration exists under pressure and temperature constraints. This study provides a feasible design domain and optimal solutions for microchannel-based cooling systems. The optimization process can also be applied to different applications of similar thermal systems.     

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

Numerical techniques are used to study the receptivity to small-amplitude thermal disturbances of the boundary layer flow of air which is induced by a heated vertical flat plate. The fully elliptic nonlinear, time-dependent Navier–Stokes and energy equations are first solved to determine the steady state boundary-layer flow, while a linearised version of the same code is used to determine the stability characteristics. In particular we investigate (i) the ultimate fate of a localised thermal disturbance placed in the region near the leading edge and (ii) the effect of small-scale surface temperature oscillations as means of understanding the stability characteristics of the boundary layer. We show that there is a favoured frequency of excitation for the time-periodic disturbance which maximises the local response in terms of the local rate of heat transfer. However the magnitude of the favoured frequency depends on precisely how far from the leading edge the local response is measured. We also find that the instability is advective in nature and that the response of the boundary layer consists of a starting transient which eventually leaves the computational domain, leaving behind the large-time time-periodic asymptotic state. Our detailed numerical results are compared with those obtained using parallel flow theory.     

Non-iterative estimation of temperature-dependent thermal conductivity without internal measurements

In this work a direct integration method is proposed to estimate temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal measurements. By approximating the spatial temperature distribution in the domain as a third-order polynomial of position and by integrating the heat conduction equation over the spatial and temporal domain, the present method estimates the thermal conductivity directly. Also, this method does not require any prior information on the functional form of the thermal conductivity. Some illustrative examples are examined to verify the proposed approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for sophisticated algorithms usually based on iterative refinement scheme.     

THERMOELASTIC TRANSIENT RESPONSE OF MULTILAYERED HOLLOW CYLINDER WITH INITIAL INTERFACE PRESSURE

This article deals with the transient response of one-dimensional axisymmetric quasi-static coupled thermoelastic problems with initial interface pressure. The initial interface pressure in a multilayered cylinder caused by the heat-assembling method is considered as an initial condition for the thermoelastic equilibrium problem. The Laplace transform and finite difference methods are used to analyze problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained using the matrix similarity transformation and inverse Laplace transform. We obtained solutions for the temperature and thermal stress distributions in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder.     

Topological Shape Optimization of Heat Conduction Problems using Level Set Approach

ABSTRACT

A topological shape optimization method for heat conduction problems is developed using a level set method. The level set function obtained from the “Hamilton-Jacobi type” equation is embedded into a fixed initial domain to implicitly represent thermal boundaries and obtain the finite-element response and adjoint sensitivity. The developed method minimizes the thermal compliance, satisfying the constraint of allowable volume by varying the implicit boundary. During optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition. The newly developed method shows no numerical instability and makes it easy to represent topological shape variations.     

A shortcut to inverse Fourier transforms: Approximate reconstruction of transient heating curves from sparse frequency domain data

Frequency domain (AC) analysis, and associated phasor notation, offers a powerful and systematical way for dynamic thermal characterisation. The complex thermal impedance Z_th(jω) plays a central role and can be obtained from analytical calculation, numerical simulation and experimental measurements. Relevant associated time domain information, such as the transient heating curve, can be derived through inverse Fourier transform (IFT). However, IFT is known to suffer from aliasing, instabilities and other artifacts. In this work we propose an alternative method that bypasses the IFT but still allows approximate reconstruction of the heating curve based on the impedance spectrum. The technique is particularly useful in cases where only truncated or sparse (low-resolution) AC data is available. It simply consists of plotting the magnitude of the impedance |Z_th(jω)| (or transfer impedance for locations outside of the active junction) versus ω^?1 as time scale. Very reasonable results, with relative errors in the order of 10%, are achieved, while the transformation is extremely simple to perform. We develop a mathematical proof for increasingly complex situations, ranging from the simple case of one single thermal time constant to a generic thermal system characterised by an arbitrary continuous time constant spectrum. Additional illustration and validation of the method is provided by practical case studies. Finally, we develop an extension to the evaluation of the impulse response and related transients. In that context the proposed method produces accurate results as well, and outperforms IFT related techniques.     

Treatment of the interfacial temperature jump condition with non-Fourier heat conduction effects

Transient energy transport with non-Fourier heat conduction effects in a two-layer structure of dissimilar materials subject to ultra-fast laser heating is studied using the proper interfacial temperature jump condition. The solution obtained is compared with solutions available in literature that use diffusion-type interfacial conditions in conjunction with non-Fourier heat conduction effects. The dual-phase lag heat conduction model is used in this work as it includes both the temporal and spatial non-Fourier effects. It is found that the diffusion-type interfacial temperature jump condition with non-Fourier heat conduction models can lead to discrepancies and erroneous trends in theoretical predictions. Moreover, a comparison between the functional forms of the two solutions obtained utilizing both interfacial conditions shows that implementing the proper interfacial temperature jump condition does not add any complexity to the solution obtained. This study – implementing the proper interfacial temperature jump condition – is further extended to show the strong effects of the thermal contact conductance and the surface layer thickness on the transient thermal response of a two-layer material in a semi-infinite domain subject to ultra-fast laser heating processes in terms of the reflectivity change of the surface layer, the temperature distribution in the two-layer structure as well as the temporal variation of the interfacial temperature difference.     

Decay of the timoshenko beam with thermal effect and memory boundary conditions

In this paper, we study the general decay of solutions for a Timoshenko beam with thermal effect and memory conditions working at the boundary. We show that the dissipation produced by the memory effect is independent of the present values of temperature gradient, and is sufficiently strong to produce a general decay result obtained without imposing the condition of equal-speed propagation. The usual exponential and polynomial decay rate are only special cases of the obtained result. This result improves earlier one in the literature on the stability of Timoshenko beam with or without thermal effect obtained under the condition of equal-speed propagation.     

BEHAVIOR OF THERMOELASTIC THICK PLATE UNDER LATERAL LOADS

A mathematical model has been developed and solved for predicting the response of a thick thermoelastic axisymmetric solid plate subjected to sudden lateral mechanical and thermal loads. The governing equations of motion and heat conduction have been solved by using Laplace and Fourier transform methods to predict the response of the plate in the physical time domain. A modified Bessel function solution with complex argument is directly used. The model is also formulated and solved with the help of the finite element method (FEM). The results for radial and axial displacements and temperature change have been computed numerically and illustrated graphically for different theories of generalized thermoelasticity. The comparison of exact analysis with that of FEM is also discussed. Excellent agreement is found between the finite element analysis and analytical and classical solutions.     

Transient Response of a Serpentine Finned-Tube Cross-Flow Heat Exchanger to a Step Change in Inlet Temperature

Abstract

An analysis of the thermal response of a finned-tube, liquid-to-gas cross-flow heat exchanger due to a step change in the liquid inlet temperature is performed. Closed-form solutions for the liquid and gas temperatures as functions of space and time are obtained via the Laplace transform technique for both small and large arguments of the modified Bessel function of the first kind. Using four physically important dimensionless parameters, the response of the liquid and average gas outlet temperatures are studied and presented in the time domain. The analysts is extended to a single-row serpentine coil geometry by accounting for U-tube bends. Using a typical heat exchanger geometry, the effects of the tube bends are shown to be significant. Relevant applications include automotive and HVAC heat exchangers and systems.     

Analysis for Thermal Conductance Effect on the Interfacial Thermal Stresses of Anisotropic Composites

The present work applies the regularized boundary integral equations that are newly developed to treat the thermoelastic field in thin anisotropic media. For the anisotropic thermal field, a direct domain mapping technique is applied with a unique interface condition that considers the heat conductance relation. By incorporating the heat conductance effect, the paper investigates how interfacial thermal stresses between generally anisotropic materials vary with the heat conductance coefficient. Accounting for the thermal conductance effect, the paper presents the complete algorithm for computing the thermal as well as the subsequent elastic fields on interfaces between dissimilarly adjoined anisotropic composites.     

基于VB的电站燃煤锅炉热力计算通用程序设计

重点介绍了热力计算程序解决锅炉炉型通用性、计算方法通用性、受热面布置通用性、工质流程通用性的思想与实现方法 ,简单介绍了基于VB开发平台的电站燃煤系列锅炉 (1 3 0t/h～ 1 0 2 5t/h)热力计算通用程序的主要内容 ,展示和介绍了程序的主界面及程序的系统组成与计算流程。该程序对42 0t/h再热燃煤锅炉的示例计算表明 :程序具有较好的用户界面 ,热力计算数据的输入和输出处理及程序的维护与扩展十分方便 ,整体热力计算速度较快 ,需 1min左右 ,但内存管理不如C、VC优越     

Non-iteration estimation of thermal conductivity using finite volume method

The finite volume approach is developed for the inverse estimation of thermal conductivity in one-dimensional domain. The differential governing equation of heat conduction is converted to a system of linear equations in matrix form using the temperature data and heat generation at the discrete grid points as well as surface heat flux. The unknown thermal conductivities are obtained by solving the system equations directly. The features of the present method are that no prior information about the functional form of the thermal conductivity is required and no iterations in the calculation process are needed. The accuracy and robust of the present method are verified by comparing examples of inverse estimation of spatially and temperature-dependent thermal conductivities with the exact solutions.