Periodic heat conduction in a solid homogeneous finite cylinder

Analytic solution of the steady periodic, non-necessarily harmonic, heat conduction in a homogeneous cylinder of finite length and radius is given in term of Fourier transform of the fluctuating temperature field. The solutions are found for quite general boundary conditions (first, second and third kind on each surface) with the sole restriction of uniformity on the lateral surface and radial symmetry on the bases. The thermal quadrupole formalism is used to obtain a compact form of the solution that can be, with some exception, straightforwardly extended to multi-slab composite cylinders. The limiting cases of infinite thickness and infinite radius are also considered and solved.     

POINT SOURCE OF HEAT IN AN ELASTOPLASTIC MEDIUM

Abstract

An infinite elastoplastic medium (Tresca's criterion) is loaded with a spherically symmetrical time-dependent temperature distribution. The thermal expansion induced by changes in temperature can lead to the generation of plastic zones. It is shown that relatively simple formulas can be used to calculate the boundaries of the plastic zones for any temperature distribution. The cases of increasing and decreasing plastic zones are considered. These formulas are applied to the case of a constant point source of heat acting during a finite or infinite interval of time.     

Improving parameter estimates obtained from thermal response tests: Effect of ambient air temperature variations

This paper presents a method of subtracting the effect of atmospheric conditions from thermal response test (TRT) estimates by using data on the ambient air temperature. The method assesses effective ground thermal conductivity within 10% of the mean value from the test, depending on the time interval chosen for the analysis, whereas the estimated value can vary by a third if energy losses outside the borehole are neglected. Evaluating the same test data using the finite line-source (FLS) model gives lower values for the ground thermal conductivity than for the infinite line-source (ILS) model, whether or not heat dissipation to ambient air is assumed.     

Melting evaluation of a thermal energy storage unit with partially filled metal foam*

This paper introduces a novel strategy on enhancing melting heat transfer for a shell-and-tube unit by partially filling porous foam. A series of filling ratios for metal foam are studied regarding thermal energy charging performance. A two-dimensional axial-symmetric model is established and verified by comparing of temperature with experimental data, obtaining satisfactory agreement between the two methods. The characteristics of the melting process such as melting fraction, temperature response and uniformity, heat storage and velocity field are analyzed in detail. The results show that the appropriate reduction of the metal foam filling ratio in the upper part can significantly promote the heat storage process due to mainly the enhanced natural convection effect. By comparing 17 cases with different filling ratios, an optimal filling ratio of 0.89 is recommended to achieve a 10.5% higher heat storage efficiency than the one with fully filled condition. The temperature uniformity first increases and then decreases with metal foam filling ratios. The best temperature uniformity is achieved for the filling ratio of 0.95. The case with a filling ratio of 0.89 possesses the shortest energy charging time at the expense of reducing the temperature uniformity. Compared with the fully filled metal foam, a better energy storage process was achieved with less metal foam material.     

Optimisation of zinc oxide nanorods for use in dye sensitised solar cells

Abstract

Zinc oxide nanorods were fabricated via a low temperature hydrothermal method on fluorine doped tin oxide (FTO) substrates. The concentrations of hexamethylenetetramine (HMT) and polyethyleneimine (PEI) were optimised to give nanorods with an aspect ratio of ～110. Post-growth thermal annealing and nitrogen plasma treatment led to significant enhancement of the UV emission peak (380 nm) and suppression of the deep level emission peak (600 nm). Although the post-growth treatments did not appear to affect the crystallinity of the ZnO nanorods, the efficiency of dye sensitised solar cells constructed following the post-growth thermal treatments saw a decrease in efficiency.     

干熄炉内传热和流体流动的数学模型

干熄焦工艺具有节能和环保双重效益，其基本原理是利用循环惰性气体冷却焦炭。根据多孔介质理论，采用非达西流和非局域热平衡方法，建立了干熄炉内流体流动和传热的数学模型，并采用基于非正交同位网格的SIMPLE方法求解对流扩散方程，通过数值求值，得到了干熄炉内气体速度，压降以及气体和焦炭的温度分布规律，计算结果表明熄焦过程解决焦炭温度偏析的关键是改善布料时焦炭粒度分布的均匀性。     

Maximum power of an endoreversible intercooled Brayton cycle

This paper describes an application of finite‐time thermodynamics to optimize the power output of endoreversible intercooled Brayton cycles coupled to two heat reservoirs with infinite thermal capacitance rates. The effects of intercooling on the maximum power and maximum‐power efficiency of an endoreversible Brayton cycle are examined. With appropriate temperature ratios of turbines and compressors being used, the maximum power output of an endoreversible intercooled Brayton cycle can be higher than that of an endoreversible simple Brayton cycle without lowering the thermal efficiency. New diagrams for maximum power, maximum‐power thermal efficiency, and optimum temperature ratios of turbines and compressors are reported. Copyright © 2000 John Wiley & Sons, Ltd.     

Generalized thermoelasticity of a piezoelectric layer

In the present research, the response of a one-dimensional piezoelectric layer is investigated using the generalized thermoelasticity theory of Lord and Shulman. The layer is subjected to thermal shock on one surface. Three coupled equations, namely, motion equation, energy equation and Maxwell equation in terms of displacement, temperature, and electric potential are established. Using the proper transformation, the mentioned equations are given in a dimensionless form. These equations are discretized by means of the generalized differential quadrature method and traced in time by means of the Newmark time marching scheme. Numerical examples are provided to show the propagation and reflection of thermal, mechanical and electrical waves in a layer. It is shown that under the Lord and Shulman theory, temperature propagates with a finite speed, similar to mechanical displacement wave. However, the electric displacement and potential propagate with infinite speed.     

Effect of uniform heat flux on stress distribution around a triangular hole in anisotropic infinite plates

The presence of a hole in an anisotropic plate under uniform heat flux causes thermal stress around the hole. In this study, on the basis of two-dimensional thermoelastic theory and using Lekhnitskii’s complex variable technique, the stress analysis of an anisotropic infinite plate with a circular hole under a uniform heat flux is developed to the plate containing a triangular hole. For this purpose, an infinite plate containing a triangular hole is mapped to the outside of a unit circle using a conformal mapping function. Stress and displacement distributions around the triangular holes in an anisotropic infinite plate are investigated in thermal steady-state condition. The plate is under uniform heat flux at infinity and Neumann boundary conditions and thermal-insulated condition on the hole boundary are considered. The rotation angle of the hole, fiber angle, the angle of heat flux, bluntness, and the aspect ratio of hole size are investigated in the present study. The accuracy of the analytical results is also confirmed by finite element analysis.     

A method to measure time lag constants of heat conduction equations

Technique based on frequency response is suggested for the measuring of time lag constants in heat conduction problem. Steady state temperature distribution at a semi infinite medium subjected to periodic heat flux for non-Fourier, Dual Phase Lag, and T wave models are found and thermal impedances are acquired. The time lags of these models can be found by measuring thermal impedance. Because of the difficulties concerning generating and measuring high frequencies, it is focused on the minimum required frequency to achieve a suitable accuracy. Some notes and a procedure are proposed to determine time lags of mentioned models with desired accuracy.     

TRANSIENT THERMOELASTIC PROBLEM FOR AN INFINITE PLATE CONTAINING A PENNY-SHAPED CRACK AT AN ARBITRARY POSITION

This article deals with the transient thermoelastic problem for an infinite plate containing a penny-shaped crack that is parallel to the surfaces of the plate but at an arbitrary position of the plate. The transient thermal stresses are set up by the heat generation on the surfaces and the sudden heat exchange on the surfaces. By using the finite difference method for the time variable, the analytical solution for spatial variables can be obtained. The numerical results for the temperature and stress intensity factor are obtained, and results are shown in graphs.     

Cool-down time of solid oxide fuel cells intended for transpotation application

To provide answers to the concern as to how quickly the temperature of solid oxide fuel cells (SOFCs) for transportation application will drop, a thermal analysis of the cool-down time of an SOFC stack during vehicle idle or stand-by has been carried out. Because a large amount of thermal energy is stored in high-temperature SOFC stacks, it is important to select suitable thermal insulations to reduce heat loss. Three typical kinds of thermal insulating materials have been selected in the present calculations. The results indicate that a high-performance, vacuum-multifoil thermal insulation can be applied to significantly reduce heat loss and to maintain temperature uniformity across a cell stack. Consequently, the cool-down time from 1000 to 800°C is extended from 2 h (with a 5 cm thick conventional material) to about 31 h (with a 1 cm thick high-performance material).     

Numerical Technique for Resolving the Dual Phase Lag Heat Conduction in Thin Film Metal

Abstract

In this article, a three-time level finite difference scheme is used to resolve the dual phase lag’s (DPL) heat conduction in a micro scale gold film subjected to spontaneous temperature boundary conditions without knowing the heat flux. Finite difference analog of DPL equation on applying to the intermediate grid points of the computational domain results into a system of linear, algebraic equations which can be solved using Thomas’ algorithm to finally obtain the transient temperature solution distributions in the film. The solution predicted by the DPL model is compared with that obtained by the single-phase Cattaneo–Vernotte’s model. Further, the way in which non-Fourier’s temperature distributions affected by the diffusion due to the increase in Heat Conduction Model numbers agree with the predecessor’s published results. The results by both the models revealed a finite thermal wave speed in the film contrasting the infinite speed of heat propagation as stated by the classical Fourier’s thermal model. Low spatial step and higher order finite difference schemes are recommended for better accurate numerical results of the non-Fourier’s temperature distributions occurring in the very short transient period between the instants of the suddenly applied spatial temperature gradient and the reaching of the steady state conditions.     

General solution of one-dimensional,time dependent coupled heat flow systems

A new, powerful method of analysis, involving the combined use of finite integral transform and finite element techniques, is presented for the solution of time dependent heat flow systems composed of many one-dimensional elements connected through the nodes. This method leads to an eigenvalue problem which is not of the conventional Sturm-Liouville type. A procedure for the determination of the eigenvalues is described. The solution obtained is in the form of an infinite series and contains quasi-steady and transient terms. The general solution obtained can be applied in the mathematical modelling of many engineering applications such as the determination of the penetration of the daily temperature cycle into buildings, the analysis of heat transfer in array of extended surfaces in compact heat exchangers, and many others.     

Control of temperature uniformity during the manufacture of stable thin-film photovoltaic devices

The production of stable thin-film photovoltaic cells requires tight control of temperature uniformity within the glass substrates during the vacuum deposition process. Though traditional approaches such as radiation shielding and channeling more power to outer lamps result in substantial improvements in temperature uniformity they fail in meeting the stringent requirement of less than 1 °C variation across the substrate required to guarantee the long-term stability of the devices. The problem becomes especially acute while scaling up to larger commercially-viable panel sizes. To this end, a finite element thermal model of a commercial-scale deposition station has been developed and optimized with the target of achieving the desired temperature uniformity of 1 °C. The effects of improvements such as radiation shielding, addition of radiation spreader, contouring of radiation spreader and optimizing power distribution among the radiation lamps have been studied. A new lamp configuration has been proposed for attaining the desired uniformity levels.     

Comparison of vacuum glazing thermal performance predicted using two- and three-dimensional models and their experimental validation

Thermal performance of vacuum glazing predicted by using two-dimensional (2-D) finite element and three-dimensional (3-D) finite volume models are presented. In the 2-D model, the vacuum space, including the pillar arrays, was represented by a material whose effective thermal conductivity was determined from the specified vacuum space width, the heat conduction through the pillar array and the calculated radiation heat transfer between the two interior glass surfaces within the vacuum gap. In the 3-D model, the support pillar array was incorporated and modelled within the glazing unit directly. The predicted difference in overall heat transfer coefficients between the two models for the vacuum window simulated was less than 3%. A guarded hot box calorimeter was used to determine the experimental thermal performance of vacuum glazing. The experimentally determined overall heat transfer coefficient and temperature profiles along the central line of the vacuum glazing are in very good agreement with the predictions made using the 2-D and 3-D models.     

Dynamic test strategy for diagnosing a heat pipe cooling module

This article experimentally develops a dynamic test strategy for efficiently diagnosing a heat pipe cooling module in order to improve the time-consuming conventional steady-state test. The first step is to investigate the performance of a heat pipe by measuring its thermal resistance, and the next step is to examine the influence of the parameters on the temperature response of the heat pipe cooling module. The experimental parameters include the press force, preheating temperature, heating power, and starting time of the fan. The results show that the thermal performance of a heat pipe, the contact condition between the heat pipe and the base plate, and the heat dissipation ability of a heat sink, are diagnosed within 30 seconds. During the dynamic test, both the startup and the ability to reach uniformity of temperature of the heat pipe can be observed. In addition, the temperature response of a heat pipe cooling module based on a lumped model matches the experimental data.     

Forced convective mixing in a zero boil-off cryogenic storage tank

This paper presents the results of a study of fluid flow and heat transfer of liquid hydrogen in a cryogenic storage tank with a heat pipe and an array of pump-nozzle units. A forced flow is directed onto the evaporator section of the heat pipe to prevent the liquid from boiling off when heat leaks through the tank wall insulation from the surroundings. An axisymmetric computational model was developed for the simulation of convective heat transfer in the system. Steady-state velocity and temperature fields were solved from this model by using the finite element method. Forty five configurations of geometry and velocity were considered. As the nozzle fluid speed increases, the values of the maximum, average, and spatial standard deviation of the temperature field decrease nonlinearly. Parametric analysis indicates that overall thermal performance of the system can be significantly improved by reducing the gap between the nozzle and the heat pipe, while maintaining the same fluid speed exiting the nozzle. It is also indicated that increased inlet tube length of the pump-nozzle unit results in slightly better thermal performance. Increased heat pipe length also improves thermal performance but only for low fluid speed.     

Thermal effects in packaging high power light emitting diode arrays

The package and system level temperature distributions of a high power (>1 W) light emitting diode (LED) array have been investigated using numerical heat flow models. For this analysis, a thermal resistor network model was combined with a 3D finite element submodel of an LED structure to predict system and die level temperatures. The impact of LED array density, LED power density, and active versus passive cooling methods on device operation were calculated. In order to help understand the role of various thermal resistances in cooling such compact arrays, the thermal resistance network was analyzed in order to estimate the contributions from materials as well as active and passive cooling schemes. Finally, an analysis of a ceramic packaging architecture is performed in order to give insight into methods to reduce the packaging resistance for high power LEDs.     

Long-term performance of BHE (borehole heat exchanger) fields with negligible groundwater movement

The long-term performance of double U-tube BHE (borehole heat exchanger) fields is investigated by finite element simulations, performed through the software package COMSOL Multiphysics (^©COMSOL, Inc.), for grounds in which the effects of groundwater movement are negligible. Six time periodic heat loads with period of 1 year are examined, with either full compensation, or partial compensation or no compensation of winter heating with summer cooling. A single BHE surrounded by infinite ground and the following BHE field configurations are analyzed: a single line of infinite BHEs, two staggered lines of infinite BHEs, a square field of infinite BHEs. For each BHE field configuration, four different distances between adjacent BHEs and two values of the ground thermal conductivity are considered. The undisturbed ground temperature is assumed equal to 14 °C, and −5 °C is prescribed as the lowest allowed temperature for the working fluid. For each BHE field geometry, heat load and ground thermal conductivity, plots of the minimum annual value of the fluid temperature for a period of 50 years are reported, and the pairs “distance – heat load” which keep the fluid temperature above the prescribed limit are evidenced.