DPL Model Analysis of Non—Fourier Heat Conduction Restricted by Continuous Boundary Interface

IntroductionAs widely known, the hahonal Fourier law isbased on a large quantity of regular heat transfer (i.e. thethermal bine scale is comparatively lOng and the heatflux density is comparatively small) experiments and it'sjust a phenomenological descriphon of regular thermalProcesses. The Fourier law itself mpes an infinitespeed of Propagation of thermal distUrbance, indicatingthat a local change in tempera~ causes aninstantaneous per'tUrbation in the temperatore at eachPOint in the medi…     

Thermal stress analysis of a parabolic inhomogeneity under uniform remote heat flux and uniform temperature change

Abstract

We study the distributions of temperature and thermal stresses within a parabolic inhomogeneity when the surrounding matrix is subjected to a system of uniform remote heat flux. Our analysis indicates that: in general, the temperature and the thermal stresses inside the inhomogeneity are linear functions of the two in-plane Cartesian coordinates; and, in particular, the normal stress perpendicular to the axis of symmetry of the parabola is uniform within the inhomogeneity. When the inhomogeneity-matrix system undergoes a uniform temperature change, the normal stress parallel to the axis of symmetry of the parabola is uniform inside the inhomogeneity whereas the other two in-plane stress components are zero inside the inhomogeneity.     

A study on the performance of a geothermal heat exchanger under coupled heat conduction and groundwater advection

Being environmental friendly and with the potential of energy-efficiency, more and more ground-source heat pump (GSHP) systems are being widely used. However, the influence of groundwater advection on the performance of the geothermal heat exchanger (GHE) in a GSHP is not still clearly known. In this paper, the configuration of a vertical dual-function GHE used in an integrated soil cold storage and ground-source heat pump (ISCS&GSHP) system, which charged cold energy to soil at night and produced chilled water in daytime in summer, and hot water for heating in winter, is firstly presented. This is then followed by a report on a mathematical model for the GHE considering the impact of the coupled heat conduction and groundwater advection on the heat transfer between the GHE and its surrounding soil. The GHE model developed was then integrated into a previously developed simulation program for an ISCS&GSHP system, and the operating performances of the GHE in an ISCS&GSHP system having a vertical dual-function GHE have been studied by simulation and reported. These simulation results, firstly seen in open literature, are much helpful to the design of a GHE buried in soil and widely used in GSHP systems or ISCS&GSHP systems.     

An experimental and theoretical study of the nonlinear heat conduction in dry porous media

Heat transfer in porous media is important in various engineering fields, including contaminated soil incineration. Most heat transfer models are theoretical in nature. Consequently, this study was undertaken to perform both theoretical and experimental studies of heat transfer in two different sand matrices. A mathematical model based on Fourier's law of heat conduction for a one‐dimensional system with the variable thermal conductivity was developed. The experimental part included heating sand samples placed in a small reactor within an infrared furnace. The transient temperature profiles of the sand layers were monitored by thermocouples. The bulk thermal conductivity was estimated to be linearly proportional to the temperature. The temperature profiles predicted by the model of heat conduction with a variable bulk thermal conductivity was compared by the observed temperatures in Quartz and Sea sands matrices up to 1300 K. Copyright © 1999 John Wiley & Sons, Ltd.     

An investigation on thermoelastic interactions under an exact heat conduction model with a delay term

The present work is concerned with a very recently proposed heat conduction model: an exact heat conduction model with a single delay term. A generalized thermoelasticity theory was proposed by Roy Choudhuri based on the heat conduction law with three-phase-lag effects for the purpose of considering the delayed response in time due to the microstructural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in Hadamard sense. Quintanilla has recently proposed to reformulate this heat conduction model as an alternative heat conduction theory with a single delay term and subsequently, Leseduarte and Quintanilla investigated the spatial behavior of the solutions for this theory and they extended the results to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction with one delay term. In the present work, we consider the thermoelasticity theory based on this newly proposed heat conduction model and investigate a problem of thermoelastic interactions. State-space approach is used to formulate the problem and the formulation is then applied to a problem of an isotropic elastic half-space with its plane boundary subjected to sudden increase in temperature and zero stress. The integral transform method is applied to obtain the solution of the problem. A detailed analysis of analytical results is provided by finding the short-time approximated solutions of different field variables analytically and comparing the results of the present model with the corresponding results reported for other existing theories. An attempt has also been made to illustrate the problem and numerical values of field variables are obtained for a particular material. Results are analyzed with different graphs. To the best of the author\textquoteright s knowledge, this thermoelastic model is not yet investigated by any researcher in this direction.     

High-order approximations of three-phase-lag heat conduction model: Some qualitative results

This article deals with some high-order approximations of the three-phase-lag heat transfer model aiming, at first, to identify the restrictions that make them well-posed consistence. Consequently, a first result about the uniqueness and continuous dependence of the solutions with respect to the given initial data and to the supply term is established for the related initial boundary value problems. Subsequently, to provide a more comprehensive analysis of the model, some further spatial decay results are established, this time conveniently relaxing the hypotheses about the delay times and the thermal conductivities. More precisely, a theorem of influence domain is proved for the wave propagating models and an exponential decaying estimate of Saint-Venant type is established for the diffusive models.     

Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model

In this article, the size-dependent behavior of micro-beams with the thermoelastic damping (TED) phenomenon is studied. The coupled thermoelasticity equations are derived on the basis of the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model. By solving these coupled equations simultaneously, a closed-form expression for the TED parameter in micro-beams is presented which considers the small-scale effects incorporation. Then, the effect of various parameters on TED in micro-beams, such as micro-beam height, the type of material, boundary conditions, and aspect ratio is investigated. The results show that the influence of utilizing non-classical continuum and thermoelasticity theories on the amount of TED and the critical thickness is significant in small scales.     

A new numerical method to simulate the non-Fourier heat conduction in a single-phase medium

Many non-equilibrium heat conduction processes can be described by the macroscopic dual-phase lag model (DPL model). In this paper, a numerical method, which combines the dual reciprocity boundary element method (DRBEM) with Laplace transforms, is constructed to solve such mathematical equation. It is used to simulate the non-Fourier phenomenon of heat conduction in a single-phase medium, then numerically predict the differences between the thermal diffusion, the thermal wave and the non-Fourier heat conduction under different boundary conditions including pulse for one- and two-dimensional problems. In order to check this numerical method's reliability, the numerical solutions are still compared with two known analytical solutions.     

Study on heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source

Abstract

A hybrid numerical method for heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source was studied. A weighted residual equation of heat conduction was considered under thermal boundary conditions. In order to calculate temperature distribution of functionally graded plate with variable gradient parameters, the Fourier transform and inverse Fourier transform were applied and the temperature field was obtained under the H(t) heat source. Results show that the influences of the gradient parameters on temperature distribution are dramatic. But with the increase of gradient parameters, the influences of parameters on the temperature distribution are gradually reduced. When the gradient parameters reach a certain critical value, the temperature does not change anymore. By comparing the temperature distribution of the upper and lower surfaces, it is seen that the temperature presents a gentle downward trend with the increase of the heat source distance, while the temperature does not change with the time in farther distance from heat source. Also, the results show that the influence of the heat source has only partial and limited influence on the temperature, which is in accordance with St. Venant’s Principle. The law of the temperature distribution of the lower surface varies with the gradient parameters, which is also discussed, an optimal gradient parameter with the thermal insulation effect of the functionally graded plate is obtained.     

热渗耦合作用下U型埋管换热器的数值模拟

针对土壤耦合热泵地下U型换热埋管,建立了管内流体以及换热器周围土壤热渗耦合物理数学模型。所建模型考虑了U型管的实际形状,土壤考虑为饱和多孔介质,管内湍流流动采用R ea lizab le k-ε模型。采用F luen t软件对模型进行模拟计算,得到了管内流体以及周围土壤温度分布。分析了土壤中水的渗流对传热过程的影响,并对考虑渗流作用时不同土壤物性对单根U型垂直埋管换热器周围土壤温度场进行了模拟计算与分析。     

A transcritical CO2 heat pump for simultaneous water cooling and heating: Test results and model validation

Working prototype of a transcritical CO₂ heat pump system for simultaneous cooling and heating of water is designed and developed based on numerical simulation studies. System behaviour and performance of the system have been studied experimentally for various operating parameters such as system pressure, water mass flow rate, water inlet temperature and expansion valve opening. Finally, the system simulation model predictions have been validated by the test data. Test results show the effect of water mass flow rate to be modest for both evaporator and gas cooler, whereas the effect of water temperature at the inlet to the gas cooler on system performance is significant. The expansion valve opening has a significant effect as well near the full valve closing condition (up to 20°). Validation of the simulation model shows reasonably good agreement (a maximum deviation of 15%) with the test data exhibiting fairly similar trends. Copyright © 2008 John Wiley & Sons, Ltd.     

不同加热方式下环路热管蒸发器可视化研究

针对环路热管内部工质相变及流动换热问题,设计了环路热管蒸发器中心通道可视化实验平台,研究了不同加热方式对热管内工质状态和传热特性的影响。结果表明：加热方式直接影响热管10W启动过程,双面加热启动速度最快。相同热载荷时,不同加热方式下环路热管热阻及蒸发器中心通道内液面高度和成核情况存在差异。10W - 40W热载荷时,随着热载荷的增大,三种加热方式的传热热阻均在减小。40W-50W热载荷时,顶部加热方式下的热管性能出现恶化,底部加热传热性能出现停滞,仅双面加热性能稳定并有提高趋势。随着热负荷的增加,蒸发器中心通道内气液界面升高、气泡的产生变得更加剧烈,蒸发器通过吸液芯向储液器的漏热量增加,进而影响环路热管的性能。     

一维非稳态导热过程(火用)传递的规律及计算

对平壁在导热第三类边界下的一维非稳态导热过程中的Yong传递进行计算，并将导温系数在定值与变值下的计算结果加以比较，以非稳态条件下Yong传递的时空分布规律进行分析。结果表明，Yong流密度随时间按指数规律递减，而Yong传递数却按指数曲线递增。在密度和比热近似不变的条件下，导温系数对温度场分布、Yong传递系数及Yong流密度有决定性的影响。     

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.     

Convection heat loss from cavity receiver in parabolic dish solar thermal power system: A review

The convection heat loss from cavity receiver in parabolic dish solar thermal power system can significantly reduce the efficiency and consequently the cost effectiveness of the system. It is important to assess this heat loss and subsequently improve the thermal performance of the receiver. This paper aims to present a comprehensive review and systematic summarization of the state of the art in the research and progress in this area. The efforts include the convection heat loss mechanism, experimental and numerical investigations on the cavity receivers with varied shapes that have been considered up to date, and the Nusselt number correlations developed for convection heat loss prediction as well as the wind effect. One of the most important features of this paper is that it has covered numerous cavity literatures encountered in various other engineering systems, such as those in electronic cooling devices and buildings. The studies related to those applications may provide valuable information for the solar receiver design, which may otherwise be ignored by a solar system designer. Finally, future development directions and the issues that need to be further investigated are also suggested. It is believed that this comprehensive review will be beneficial to the design, simulation, performance assessment and applications of the solar parabolic dish cavity receivers.     

Analytical approach with Laplace transform to the inverse problem of one‐dimensional heat conduction transfer: Application to second and third boundary conditions

An analytical method using Laplace transformation has been developed for one‐dimensional heat conduction. This method succeeded in explicitly deriving the analytical solution by which the surface temperature for the first kind of boundary condition can be well predicted. The analytical solutions for the surface temperature and heat flux are applied to the second and third of the boundary conditions. These solutions are also found to estimate the corresponding surface conditions with a high degree of accuracy when the surface conditions smoothly change. On the other hand, when these conditions erratically change such as the first derivative of temperature with time, the accuracy of the estimation becomes slightly less than that for a smooth condition. This trend in the estimation is similar irrespective of any kind of boundary condition. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 29–41, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10069     

A novel analytical solution of the non-uniform convective boundary conditions problem for heat conduction in cylinders

The problem of heat conduction in a still cylinder exposed to non‐uniform convective conditions on both inner and outer surfaces has been addressed by a method based on the series solution and a novel analytic solution is derived to predict the temperature field in the cylinder. Compared to previous available results this method allows a simpler implementation and its almost straightforward extension to multilayered cylinders represents one of the main advantages over more complex numerical solutions. As an example of application the effect of the non-uniform distribution of heat transfer coefficients on the solid temperature field and the heat transferred is analysed, as function of the fluid flow regime, the Biot number and the cylinder thickness.     

Three-dimensional numerical study of heat transfer characteristics in the receiver tube of parabolic trough solar collector

The solar energy flux distribution on the outer wall of the inner absorber tube of a parabolic solar collector receiver is calculated successfully by adopting the Monte Carlo Ray-Trace Method (MCRT Method). It is revealed that the non-uniformity of the solar energy flux distribution is very large. Three-dimensional numerical simulation of coupled heat transfer characteristics in the receiver tube is calculated and analyzed by combining the MCRT Method and the FLUENT software, in which the heat transfer fluid and physical model are Syltherm 800 liquid oil and LS2 parabolic solar collector from the testing experiment of Dudley et al., respectively. Temperature-dependent properties of the oil and thermal radiation between the inner absorber tube and the outer glass cover tube are also taken into account. Comparing with test results from three typical testing conditions, the average difference is within 2%. And then the mechanism of the coupled heat transfer in the receiver tube is further studied.     

Development and validation of a coupled heat and mass transfer model for green roofs

This paper describes a dynamic model of transient heat and mass transfer across a green roof component. The thermal behavior of the green roof layers is modeled and coupled to the water balance in the substrate that is determined accounting for evapotranspiration. The water balance variations over time directly impact the physical properties of the substrate and the evapotranspiration intensity. This thermal and hydric model incorporates wind speed effects within the foliage through a new calculation of the resistance to heat and mass transfer within the leaf canopy. The developed model is validated with experimental data from a one-tenth-scale green roof located at the University of La Rochelle. A comparison between the numerical and the experimental results demonstrates the accuracy of the model for predicting the substrate temperature and water content variations. The heat and mass transfer mechanisms through green roofs are analyzed and explained using the modeled energy balances, and parametric studies of green roof behavior are presented. A surface temperature difference of up to 25 °C was found among green roofs with a dry growing medium or a saturated growing medium. Furthermore, the thermal inertia effects, which are usually simplified or neglected, are taken into account and shown to affect the temperature and flux results. This study highlights the importance of a coupled evapotranspiration process model for the accurate assessment of the passive cooling effect of green roofs.