Transient Heat Conduction Model Research Articles

Modeling Exposures of a Nylon-Cotton Fabric to High Radiant Heat Flux

American soldiers and marines involved in the recent conflicts in Iraq and Afghanistan have suffered increased incidence of burn injury, often as a direct result of exposure to improvised explosive devices. In this work, a one dimensional numerical pyrolysis model for transient heat conduction, incorporating material transformations described by chemical kinetics, is used to investigate the response of the standard 230 g/m2 Army Combat Uniform (ACU) fabric to high radiant heat fluxes in short duration thermal protection tests and long duration cone calorimeter tests. Thermal protection tests are performed using a Thermal Barrier Test Apparatus–an automated device, incorporating a closed-loop controlled IR radiant heat source, automated water cooled shutter, a fabric sample holder, an adjustable stage with a water cooled Schmidt-Boelter heat flux gauge and a PC based data acquisition system. Cone calorimeter tests are performed on fabric specimens at an exposure heat flux of 25 kW/m2. In thermal protection tests involving exposures of 90 kW/m2 for five seconds and 77 kW/m2 for four seconds, modeling indicated that desorption and evaporation of moisture content has an important effect, but melting of the nylon component and material decomposition had insignificant effects on the heat flux transmitted through the fabric back face. Modeling results for cone testing exhibited good agreement for time to ignition and duration of flaming combustion.

Effect of volume-fraction dependent agglomeration of nanoparticles on the thermal conductivity of nanocomposites: Applications to epoxy resins, filled by SiO2, AlN and MgO nanoparticles

A thermodynamic model for transient heat conduction in ceramic-polymer nanocomposites is proposed. The model takes into account particle’s size, particle’s volume fraction, and interface characteristics with emphasis on the effect of agglomeration of particles on the effective thermal conductivity of the nanocomposite. The originality of the present work is its basement on extended irreversible thermodynamics, combining nano- and continuum-scales without invoking molecular dynamics. The model is compared to experimental data using the examples of SiO2, AlN and MgO nanoparticles embedded in epoxy resin. The analysis is limited to spherical nanoparticles. The dependence of the degree of agglomeration with respect of the volume fraction of particles is also discussed and a power-law relation is established through a kinetic mechanism and experiments performed in our laboratory. This relation is used in our theoretical model, resulting into a good agreement with experiments. It is shown that the effective thermal conductivity may either increase or decrease with the degree of agglomeration.

Overflow-assisted laser machining of titanium alloy: surface characteristics and temperature field modeling

Underwater laser machining process is a promising method to cut materials with less thermal damage. A variation of underwater technique is overflow-assisted laser ablation. This process can introduce a higher thermal convection and more uniform water layer than the typical underwater method. Such characteristics can encourage the damage-free fabrication and also stabilize the laser ablation in water. In this study, cut profile and temperature distribution of workpiece induced by the overflow technique were investigated. Titanium alloy (Ti-6Al-4V) used as a work sample was grooved by a nanosecond pulse laser under different overflow conditions. The effects of laser power, laser repetition rate, and water flow velocity were experimentally and numerically examined. A clean and smooth cut surface can be fabricated when the overflow technique was used. Microcracks and porosities found on the laser-ablated area were also addressed in this study. The temperature field of titanium alloy under the different ablation conditions was simulated by using the finite difference computation. The transient heat conduction model was implemented together with the enthalpy method and temperature-dependent material properties. By using the developed model, the groove depths obtained from the experiment and simulation were in a good agreement.

Thermal characterization of carbon nanotube fiber by time-domain differential Raman

Most conventional Raman thermometry for thermal properties measurement is on steady-state basis, which utilizes either Joule heating effect or two lasers configurations coupled with increased complexity of system or measurement uncertainty. In this work, a new comprehensive approach including both transient and steady-state Raman method is proposed for thermal properties measurement of micro/nanowires. The transient method employs a modulated (pulsed) laser for transient heating and Raman excitation, and is termed time-domain differential Raman. The average elevated temperature during the transient heating period is probed simultaneously based on Raman thermometry. Thermal diffusivity can be readily determined by fitting normalized temperature rise against heating time with a transient heat conduction model. On the other hand, thermal conductivity can be obtained in the steady-state measurement by adjusting modulation settings. To verify this method, a carbon nanotube (CNT) fiber is measured with the thermal diffusivity of 1.74−0.20+0.20×10−5 m2/s and the thermal conductivity of 34.3−0.4+0.4 W/m K. The relatively low thermal transport values stem from numerous CNT-glue matrix and CNT–CNT thermal contact resistances. Compared with the conventional steady-state Raman method, the transient method requires no detailed laser absorption value and no temperature coefficient calibration. It can be easily applied to study transient thermal transport in materials.

Machining with Internally Cooled Toolholder Using a Phase Change Fluid

The cutting fluid application is the most usual method for cooling the cutting tool, however it is harmful to the environment and to the human being health, besides it represents a significative part of the production costs. One recent alternative method for eliminating the cutting fluid in machining employ a toolholder with internal cooling, but to make it efficient and economically viable, it is necessary to study the behavior of thermal energy in its interior in order to get better efficiency in heat removal from the cutting tool. This study proposes to develop a model of three-dimensional transient heat conduction, discretized by a non-uniform mesh, to estimate the temperature and heat flux at any point of the set of cutting tool and toolholder. The calibration of the virtual model of the set was made using the finite element method, correlating it with experimental tests of turning by using thermocouple to mensure the temperatures on the body of the toolholder along the time. The results show that it is possible to obtain a close correlation of the model with the experimental results.

Non-probabilistic set-theoretic models for transient heat conduction of thermal protection systems with uncertain parameters

Thermal protection systems (TPS) play a key role in the development of hypersonic aircrafts and the performance of TPS is directly in connection with its temperature field, thus a number of analytical and experimental studies have been conducted to study heat transfer analysis. Due to the existence of uncertain parameters in the temperature field, it is imperative to adopt the approaches involving uncertainty analysis to obtain reliable results. The non-probabilistic set-theoretic models, compared with the probabilistic approach, only require a small amount of experimental samples to process the study of uncertainties. Interval analysis method (IAM), classical convex model (CCM) and novel convex model (NCM) are applied to quantify uncertain parameters in TPS and then combined with finite elemental differential equation of transient thermal analysis to study the effects of uncertain parameters on temperature field response by means of Taylor series expansion. Moreover, the thermal responsive bounds in both CCM and NCM are yielded by the Lagrange multiplier method. A ceramic TPS is performed to illustrate the application of the present method and the results show that NCM can reduce the space of temperature field responses. Besides, the non-probabilistic set-theoretic methods can serve for the design of TPS.

Experimental Study and Thermal Analysis on the Buckling of Friction Components in Multi-Disc Clutch

A full-scale multi-disc clutch test bench was set up and some sliding experiments were conducted to investigate the temperature evolution processes in low and high lubrication regimes. Friction discs with single friction lining were used and arranged back-to-back in order to preserve possible evidences of buckling. Temperatures were measured with thermocouples from four different radii on the mid-plane of the separator disc. Two different kinds of temperature variation processes with obvious critical points of cone shape buckling were obtained. These temperatures can be divided into three effective stages that represent different deformation status of the discs in these experiments. The temperature fields in the contacting separator disc and friction disc were studied through a transient heat conduction model, and the results show that the temperatures measured by the thermocouples from the separator disc can represent the average temperatures in both of the separator disc and friction disc for a long sliding time. By comparing the computational critical moments of the friction components with the experimental results, the capability of the curved beam model for predicting the critical moments of cone buckling was validated.

Lumped models for transient thermal analysis of multilayered composite pipeline with active heating

In this study, improved lumped parameter models were proposed for transient thermal analysis of multilayered composite pipeline with active heating, which is essential for flow assurance design and operating strategies of deepwater subsea pipelines. Improved lumped models for transient heat conduction in multilayered composite pipelines were based on two-points Hermite approximations for integrals. The transient energy equation for the bulk temperature of the produced fluid was transformed into a set of ordinary differential equations in time by using a finite difference method. The coupled system of ordinary differential equations for average temperatures in the solids and bulk temperature of the fluid at each longitudinal discretization point along the pipeline was solved by using an ODE solver. With the proposed method, we analyzed the transient heat transfer in stainless steel-polypropylene-stainless steel sandwich pipes (SP) with active electrical heating. Convergence behaviors of the average temperature of each layer and the bulk temperature of the produced fluid calculated by using the improved lumped models (H0,0/H1,1 and H1,1/H1,1 approximations) against the number of grid points along the pipelines were presented. Case studies were performed to investigate the effect of the linear rate of power input and the average velocity on the bulk temperature distribution of the produced fluid.

Rewetting of Hot Vertical Surfaces by a Falling Liquid Film

In this work, a transient heat conduction model is developed for rewetting a hot wall surface by a falling liquid film. In the model, the heat conduction in the rewetted wall is assumed to be two-dimensional. Convection heat transfer from the hot surface to rewetting fluid is considered negligible in the dry surface region ahead of the wet front. The numerical solution indicates that the rewetting process is mainly controlled by two-dimensional heat conduction in the rewetted wall, even for the walls of low Biot number, especially at low initial temperatures. The effects of Biot number and initial wall temperature on the rewetting velocity are investigated. Comparison of the results with previous studies is presented.

A thermal–metallurgical model of laser beam welding simulation for carbon steels

A coupled thermal–metallurgical model is developed to predict the temperature fields and spatial distribution of volume fraction of phases during laser beam welding of 1020, 1045, and 1060 steels. The classical transient heat conduction model is used to calculate the temperature fields during laser beam welding. For phase transformation, the austenization, the austenite-to-pearlite/ferrite transformation, the austenite-to-bainite transformation, and the austenite-to-martensite transformation are modeled respectively. All of these transformation models are solved by the finite element method (FEM) based on the simulated temperature fields. The thermal properties of the three steels are determined by the linear interpolation base of the phase fractions, and thermal properties for each pure phase. The temperature fields and spatial distribution of phases are predicted by 3D finite element method (FEM) code which is developed by the authors to solve the thermal–metallurgical models. In addition, comparison between the coupled model and the pure conduction model without considering phase transformations is carried out to study the influence of phase transformation on temperature fields during welding. According to the comparison, the temperature of the coupled model is higher than the pure conduction model in the temperature region above 1000 °C, but the temperature profiles are very similar at the temperature region under 1000 °C. The predicted volume fractions of 1020 and 1060 steels are close to experimental results. However, there is an obvious difference between predicted and experimental results of the phase fraction of 1045 steels.

Modelling of transient heat conduction with diffuse interface methods

We present a survey on different numerical interpolation schemes used for two-phase transient heat conduction problems in the context of interface capturing phase-field methods. Examples are general transport problems in the context of diffuse interface methods with a non-equal heat conductivity in normal and tangential directions to the interface. We extend the tonsorial approach recently published by Nicoli M et al (2011 Phys. Rev. E 84 1–6) to the general three-dimensional (3D) transient evolution equations. Validations for one-dimensional, two-dimensional and 3D transient test cases are provided, and the results are in good agreement with analytical and numerical reference solutions.

Temperature and Heat Flux Measurement on Hot Models in Short-Duration Facilities

An electrical preheating technique applied to a carbon-based model in an impulse facility has previously demonstrated surface temperatures around 2500 K, but the measurement of heat flux at such elevated surface temperatures was not previously achieved. A technique for fast-response surface temperature measurement of an electrically preheated carbon-phenolic model using an indium gallium arsenide detector with in situ calibration via a visible/near-infrared spectrometer is assessed through application in a short-duration cold-flow hypersonic wind tunnel. The method is reliable: the scatter in temperatures determined from successive acquisitions of the spectrometer data had a standard deviation of 3 K at a mean temperature of about 1500 K; the standard deviation of the Indium gallium arsenide detector results from the visible/near-infrared spectrometer data was 11 K at a temperature of about 1100 K after the termination of the hypersonic flow. The surface temperature history from the Indium gallium arsenide detector was analyzed using a one-dimensional transient heat conduction model to deduce the surface heat flux. Good agreement with an engineering correlation for stagnation point heat flux is demonstrated; however, uncertainties are large (), as the thermal properties of the particular carbon-phenolic material were not available. The method is suitable for application in impulse facilities, but the effusivity () for the heat shield material will need to be accurately defined for reliable deduction of surface heat flux.

Modelling the non-equilibrium two-phase flow during depressurisation of CO2 pipelines

The development, testing and validation of a two-fluid transient flow model for simulating outflow following the failure of high pressure CO2 pipelines is presented. Thermal and mechanical non-equilibrium effects during depressurisation are accounted for by utilising simple constitutive relations describing inter-phase mass, heat and momentum transfer in terms of relaxation to equilibrium. Pipe wall/fluid heat exchange on the other hand is modelled by coupling the fluid model with a finite difference transient heat conduction model. The two-fluid transient flow model's performance is tested by comparison of the predicted transient pressure and temperature profiles along the pipeline against those based on the simplified homogeneous equilibrium model (HEM) as well as real data captured during the full bore rupture of a 260m long, 233mm internal diameter pipeline containing CO2 at 36bara and 273°C. The two-fluid model is found to produce a reasonably good degree of agreement with the experimental data throughout the depressurisation process. The HEM based flow model on the other hand performs well only near the rupture plane and during the early stages of the depressurisation process.

Reducing surface cracking in hot charged HSLA cast slabs by surface quenching prior to hot charging – experimental study on heat transfer behaviour

Surface quenching of cast slabs between casting and hot charging to prevent the occurrence of surface cracks in high strength low-alloy steel slabs has been investigated. In order to accurately control the quenching process and obtain the desired cooling rate, an experimental study on the heat transfer behaviour of a high temperature slab cooled by a water nozzle was performed. The surface temperature and heat transfer flux were calculated using a two-dimensional transient inverse heat conduction model, based on the finite element method. The effect of the water flowrate and inclination of the spray on the heat transfer is discussed. Based on a regression analysis of the experimental data, the heat transfer coefficient is provided as a function of slab temperature and water flow density. A surface quenching trial with a water flowrate of 46 m3 h−1 was conducted in a steel mill. Good correlation was found between the temperature predicted using the proposed heat transfer coefficient and the temperature measured during the surface quenching process.

Formation heating by steam circulation in a horizontal wellbore

Abstract A two-dimensional transient heat conduction model is developed that predicts heat transfer from a horizontal wellbore to the formation during a steam circulation process. The model takes into account the partial penetration of the wellbore, which is not included in previously developed analytical models applicable for reservoir heating. This inclusion makes the problem mathematically challenging as the inner boundary condition of the problem becomes non-homogenous. The governing heat conduction equation is solved for an infinite acting reservoir and semi-analytical solutions for the heat flux from the wellbore and temperature distribution in the formation are obtained using a combination of Laplace and finite Fourier cosine transforms. The average formation temperature and the heat flow across the wellbore are calculated and the results are presented. This analysis has applications in thermal stimulation of oil wells with low injectivity, where it is required to preheat the formation prior to steam injection.

Development of three dimensional transient numerical heat conduction model with growth of oxide scale for steel billet reheat simulation

This paper presents development of numerical heat conduction model for prediction of transient three dimensional temperature field in the billet. The model is applied to billet heating process in the reheat furnace. The discretization of governing equation is done by control volume approach and implicit scheme of finite difference method. The model captures various time dependent boundary conditions corresponding to the billet reheat in the reheat furnace, in addition to this it also accounts for the growth of oxide scale layer on the billet surfaces during reheat simulations. The set of discretized equations is solved using own developed MATLAB® code. The proposed model is capable of predicting the temperature field in the billet and scale growth on the billet surfaces. The model is validated with analytical results and published experimental results. The results obtained through the model simulations are in concurrence with the anticipated trend. The proposed methodology of numerical modeling will be helpful for the temperature and scale growth predictions, which are vital for a variety of reasons like energy efficiency, process optimization, roll force calculations, carbon segregation control and product microstructure control, etc.

Evolutive Housing System: Refurbishment with new technologies and unsteady simulations of energy performance

Abstract The aim of the present paper is to evaluate the energy performance in unsteady-state conditions of an Evolutive House. The original design was presented by two important architects, Renzo Piano and Peter Rice, in 1978. The house has two large glass walls in the east and west facades. Experimental investigation and numerical analysis were carried out in a prototype of the house realized in Perugia. The air temperature, the surface temperature of floors, the global solar radiation, the relative humidity were measured. Simulations were performed using both Energy Plus and TRNSYS software. Simulation models were tested and validated with experimental data considering a new weather database compiled for Perugia. The analysis compares different scenarios in terms of energy demand, such as the substitution of the glazing and the use of innovative packaged solutions. Innovative glazing systems filled with silica aerogel were investigated as a solution for energy saving in buildings. Results show that an important energy saving was obtained for all the proposed glazings (about 60–70%). The simulation codes’ results are in good agreement, but some differences are due to the different approach in the evaluation of the solar irradiance on tilted surfaces and to the transient heat conduction model.

Mathematical model and sensor development for measuring energy transfer from wildland fires

Current practices for measuring high heat flux in scenarios such as wildland forest fires use expensive, thermopile-based sensors, coupled with mathematical models based on a semi-infinite-length scale. Although these sensors are acceptable for experimental testing in laboratories, high error rates or the need for water cooling limits their applications in field experiments. Therefore, a one-dimensional, finite-length scale, transient-heat conduction model was developed and combined with an inexpensive, thermocouple-based rectangular sensor, to create a rapidly deployable, non-cooled sensor for testing in field environments. The proposed model was developed using concepts from heat conduction and with transient temperature boundary conditions, to avoid complicated radiation and convection conditions. Constant heat flux and tree-burning tests were respectively conducted using a mass loss cone calorimeter and a propane-fired radiant panel to validate the proposed analytical model and sensor as well as test the sensor in a simulated forest fire setting. The sensor was mounted directly beside a commercial Schmidt–Boelter gauge to provide data for comparison. The proposed heat flux measurement method provided results similar to those obtained from the commercial heat flux gauge to within one standard deviation. This suggests that the use of a finite-length scale model, coupled with an inexpensive thermocouple-based sensor, is effective in estimating the intense heat loads from wildland fires.

Convective Heat Transfer between Covered Kiln Wall and Material Bed

According to kiln structure and material movement features, the transient heat conduction model of material bed and the contact heat transfer model at the interface of covered kiln wall and material bed are built. Considering their contribution to the convective heat transfer of material bed, the convective heat transfer coefficient between covered kiln wall and material bed is proposed, and its formula is obtained, with which the convective heat transfer between covered kiln wall and material bed can be calculated conveniently, so the heat transfer prediction within the rotary kiln can be done more easily.

Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales

One of the current practices for measuring heat flux during flash fire testing, forest fires, and other industrial cases focuses on the use of semi-infinite models to predict the heat flux during exposure through surface temperature measurements on simulated skin sensors. For short time frames, these models can be shown to have acceptable accuracy. However, when considering longer time exposures at reduced heat fluxes, such as with firefighters in a forest fire, the accuracy of these models could be brought into question. A one-dimensional, finite length scale, transient heat conduction model was developed using a Green's function approach on a rectangular sensor. The model was developed using transient temperature boundary conditions to avoid the use of complicated radiation and convection conditions at each boundary. For comparison, a semi-infinite model utilizing the same boundary condition on the exposed face was solved using both the Laplace transform method and Green's function method. Experimental data was obtained during exposure to a cone calorimeter. All measurements were taken for a minimum duration of 2 min. This temperature data was used to develop appropriate curves for the boundary conditions and validate the analytical models. It was found that the temperature obtained from the one-dimensional transient heat conduction model based on Green's functions agreed well with the experimental results over longer exposure times, and with reduced error when compared with the semi-infinite model. This suggests that modeling the problem on a finite-length scale will produce more accurate or more conservative temperature and heat flux results over extended periods of exposure in high heat load applications.