Three-dimensional Transient Heat Research Articles

Importance of the experimental investigation of a concasting technology

The solidification and cooling of a continuously cast billet, slab or cylinder, generally of a concasting and the simultaneous heating of the mold is a very complicated problem of three-dimensional (3D) transient heat and mass transfer. The solving of such a problem is impossible without numerical models of the temperature field of the concasting itself which it is being processed through the concasting machine (caster). The application of the numerical model requires systematic experimentation and measurement of operational parameters on a real caster as well as in the laboratory. The measurement results, especially temperatures, serve not only for the verification of the exactness of the model, but mainly for optímization of the process procedure: real process → input data → numerical analyses → optimization → correction of real process. The most important part of the investigation is the measurement of the temperatures in the walls of the mold and the surface of the slab in the zones of secondary and tertiary cooling.

A Numerical Method for Analysing Heat Conduction in Composites Containing Encapsulated Phase Change Materials

In this study, a three-dimensional transient heat transfer model in a three-phase composite system is established to investigate effects of temperature reduction in a composite system due to the use of encapsulated phase change material (PCM). The entire composite system is composed of cement matrix material, PCM, and hollow metal microspheres (HMSs) which are introduced to accelerate the phase change efficiency of the PCM and to simultaneously hold the liquid phase of the PCM. The present transient heat transfer model is numerically solved via finite element technique for investigating the transient thermal performance of the three-phase composite system. The temperature distribution on the specific area is compared to that in the pure cement material and the two-phase composite system without metal shell for demonstrating the ability of temperature adjustment of the PCM. Finally, effects of the spatial distribution of HMS on the temperature variation in the three-phase composite system is further investigated to provide comprehensive understanding on energy adjustment of this composite system.

A mesh-free Monte-Carlo method for simulation of three-dimensional transient heat conduction in a composite layered material with temperature dependent thermal properties

A new solution for the three-dimensional transient heat conduction from a homogeneous medium to a non-homogeneous multi-layered composite material with temperature dependent thermal properties using a mesh-free Monte-Carlo method is proposed. The novel contributions include a new algorithm to account for the impact of thermal diffusivities from source to sink in the calculation of the particles’ step length (particles are represented as bundles of energy emitted from each source), and a derivation of the three-dimensional peripheral integration to account for the influence of material properties around the sink on its temperature. Simulations developed using the proposed method are compared against both experimental measurements and results from a finite element simulation.

Performance analysis of pulsed flow control method for radiant slab system

We present a novel pulsed flow control method (PFM) using a two-position valve to regulate the capacity of radiant slab systems. Under PFM, the on-time duration of the valve is short (compared to all prior work, e.g. 4-minute), and fixed, while the off-time varies. We present a novel, open-source, finite difference model that assesses three-dimensional transient slab heat transfer, accounting for the transient heat storage of the pipe fluid. Sensitivity analysis results indicate the dominant factors influencing energy performance of the PFM are: on-time duration; pipe diameter; and spacing. We experimentally validated both the new control strategy and model in full-scale laboratory experiments. Compared with previous intermittent control strategies (with on-time durations over 30 min), at 50% part load the PFM reduces 27% required water flow rate and increases supply to return water temperature differential. Compared with the variable temperature control method, at 50% part load the PFM reduces 24% required water flow rate. The energy performance of PFM is comparable to that of a conventional variable flow rate control. However, it has more accurate capacity control, achieves a more uniform surface temperature distribution, and reduces initial investment by substituting two-position for modulating valves, thus showing promise for engineering applications.

A triple reciprocity method in Laplace transform boundary element method for three-dimensional transient heat conduction problems

In this paper, a boundary element method employing the Laplace transform is developed to solve the three-dimensional transient heat conduction problems. The fundamental solution for the modified Helmholtz equation is adopted in order to derive the basic integral equations. Due to the effects of initial temperature and heat generation, the domain integrals appearing in the integral equation will degrade the advantages of boundary element method. Therefore, a new triple reciprocity formulation in Laplace domain is proposed to convert the domain integrals into boundary integrals. The higher order fundamental solutions required in the triple reciprocity method can be obtained from the original fundamental solution by multiplying a constant term, which leads to a much simpler formulation in the Laplace domain. Then, the inverse transformation can be used to obtain the solutions in the time domain. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. In summary, the triple reciprocity formulation is a useful approach to capture the transient heat conduction responses.

Transient behavior of a multi-tubular cavity solar thermochemical reactor

A three-dimensional transient heat transfer model is presented to predict the start-up operation of a multi-tubular cavity reactor under concentrated irradiation in a solar furnace. The reactor consists of a cavity containing nine absorber tubes, through which a suspension of CeO2 in Argon flows. An iterative splitting scheme coupling a Continuous Random Walk, a Finite Volume, and a Ray-Tracing Monte Carlo methods, is implemented to estimate the temperature gradients in the tubes and gas-particle media. The radiation heat transfer among the tubes and cavity walls is considered, as well as conduction and convection in the tubes and the particle suspension. During the initial heating stage, gradients are mainly angular, while in steady-state they are primarily axial. The former may cause tube bending or cracking, and strategies to reduce them are examined. In particular, different heating ramps were simulated, which was found to reduce these initial thermal gradients.

Transient Analysis of Nonuniform Heat Input Propagation Through a Heat Sink Base

For thermal management architectures wherein the heat sink is embedded close to a dynamic heat source, nonuniformities may propagate through the heat sink base to the coolant. Available transient models predict the effective heat spreading resistance to calculate chip temperature rise, or simplify to a representative axisymmetric geometry. The coolant-side temperature response is seldom considered, despite the potential influence on flow distribution and stability in two-phase microchannel heat sinks. This study solves three-dimensional transient heat conduction in a Cartesian chip-on-substrate geometry to predict spatial and temporal variations of temperature on the coolant side. The solution for the unit step response of the three-dimensional system is extended to any arbitrary temporal heat input using Duhamel's method. For time-periodic heat inputs, the steady-periodic solution is calculated using the method of complex temperature. As an example case, the solution of the coolant-side temperature response in the presence of different transient heat inputs from multiple heat sources is demonstrated. To represent a case where the thermal spreading from a heat source is localized, the problem is simplified to a single heat source at the center of the domain. Metrics are developed to quantify the degree of spatial and temporal nonuniformity in the coolant-side temperature profiles. These nonuniformities are mapped as a function of nondimensional geometric parameters and boundary conditions. Several case studies are presented to demonstrate the utility of such maps.

An alternative approach to thermal analysis using inverse problems in aluminum alloy welding

PurposeThe purpose of this article is the determination of the temperature fields in a weld region has always been an obstacle to the improvement of welding processes. As an alternative, the use of inverse problems to determine the heat flux during the welding process allows an analysis of these processes.Design/methodology/approachThis paper studies an alternative for the thermal analysis of the tungsten inert gas welding process on a 6,060 T5 aluminum alloy. For this purpose, a C++ code was developed, based on a transient three-dimensional heat transfer model. To estimate the amount of heat delivered to the plate, the specification function technique was used. Lab experiments were carried out to validate the methodology. A different experimental methodology is proposed to estimate the emissivity (radiation coefficient).FindingsThe maximum difference between experimental and numerical temperatures is lower than 5 per cent. The determined emissivity value for the aluminum 6,060 T5 presented a good agreement with literature values. The thermal fields were analyzed as function of the positive polarity. The specification function method proved to be an adequate tool for heat input estimation in welding analysis.Originality/valueThe proposed methodology proves to be a cheaper way to estimate the heat flux on the sample. The estimated power curves for the welding process are presented. The methodology to calculate the emissivity (radiation coefficient) was validated.

Dimensionless numbers in additive manufacturing

The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.

Simulation of three-dimensional transient heat conduction problem with variable coefficients based on the improved parallel smoothed particle hydrodynamics method

In this work, an improved parallel SPH method is proposed to accurately solve the three-dimensional (3D) transient heat conduction equation with variable coefficients. The improvements are described as follows. Firstly, the first-order symmetric smoothed particle hydrodynamics (SPH) method is extended to the simulating of the 3D problem based on Taylor expansion. Secondly, the concept of stabilized up-wind technique is introduced into the convection term. Thirdly, the MPI parallel technique based on the neighboring particle mark method is introduced into the above improved SPH method, and named the corrected parallel SPH method for 3D problems (CPSPH-3D). Subsequently, the accuracy, convergence and the computational efficiency of the proposed CPSPH-3D method are tested by simulating the 3D transient heat conduction problems with constant/variable coefficient, and compared with the analytical solution. Meanwhile, the capacity of the proposed CPSPH-3D for solving the 3D heat conduction problems with the Dirichlet and Newmann boundaries is illustrated, in which the change of temperature with time under the complex cylindrical area is also considered. The numerical results show that:1) the proposed CPSPH-3D method has the better stability, higher accuracy and computational efficiency than the conventional SPH method no matter whether the particle distribution is uniform; 2) the calculating time can be well reduced by increasing the number of CPUs when the particle number is refined in the simulations of CPSPH-3D. Finally, the temperature variation in the 3D functionally gradient material is predicted by the corrected parallel SPH method, and compared with the other numerical results. The process of temperature variation in the functionally gradient material can be shown accurately.

Empirical Validation of Heat Transfer Performance Simulation of Graphite/PCM Concrete Materials for Thermally Activated Building System

To increase the heat capacity in lightweight construction materials, a phase change material (PCM) can be introduced to building elements. A thermally activated building system (TABS) with graphite/PCM concrete hollow core slab is suggested as an energy-efficient technology to shift and reduce the peak thermal load in buildings. An evaluation of heat storage and dissipation characteristics of TABS in graphite/PCM concrete has been conducted using dynamic simulations, but empirical validation is necessary to acceptably predict the thermal behavior of graphite/PCM concrete. This study aimed to validate the thermal behavior of graphite/PCM concrete through a three-dimensional transient heat transfer simulation. The simulation results were compared to experimental results from previous studies of concrete and graphite/PCM concrete. The overall thermal behavior for both materials was found to be similar to experiment results. Limitations in the simulation modeling, which included determination of the indoor heat transfer coefficient, assumption of constant thermal conductivity with temperature, and assumption of specimen homogeneity, led to slight differences between the measured and simulated results.

3D transient heat transfer numerical analysis of multiple energy piles

This paper presents a three-dimensional (3D) transient heat transfer numerical model for multiple energy piles based on the finite volume method (FVM). The initial and boundary conditions are established and the effects of “thermal short-circulating” between two pipes of a U-tube in energy pile are investigated. Thermal partial differential equations are discretized at the spatial nodal points and solved by linear approximation method. Temperature variations of working fluid, energy pile and its surrounding soil from simulation program are compared with experimental data to validate the developed model. In addition, the influences of fluid flow rate and U-tube shank spacing are analysed. It is established that the shank spacing should be set in a range of 0.06m to 0.10m to reduce heat transfer between the two pipes and meet the structural requirement. Meanwhile, the flow rate should be controlled in a range of 0.5m3/h to 0.7m3/h to avoid the low outlet fluid temperature and decrease the influence of “thermal short-circuiting”.

Analytically-integrated radial integration BEM for solving three-dimensional transient heat conduction problems

This paper presents a new strategy using radial integration boundary element method (RIBEM) to solve three-dimensional transient heat conduction problems. In this method, the radial integral, which is used to transform the domain integrals into equivalent boundary integrals, is analytically integrated by using some newly proposed analytical expressions. This analytical approach can improve the computational efficiency and computational accuracy considerably compared with traditional RIBEM in evaluating the domain integrals through using the radial integration method (RIM). The Green's function for the Laplace equation is utilized as the fundamental solution to derive the boundary-domain integral equation for transient heat conduction. RIM is used to convert the domain integrals associated with the time derivative of temperature into equivalent boundary integrals. The derivation process about the analytical radial integral expressions published before is further investigated, the adequate and simple expression for settling the special circumstances in which the newly derived analytical expressions become invalid, is deduced in this paper. Numerical examples are given to demonstrate the efficiency of the presented method.

Estimation of temperature-dependent thermal conductivity using proper generalised decomposition for building energy management

A proper generalised decomposition for solving inverse heat conduction problems is proposed in this article as an innovative method offering important numerical savings. It is based on the solution of a parametric problem, considering the unknown parameter as a coordinate of the problem. Then, considering this solution, all sets of cost function can be computed as a function of the unknown parameter of the defined domain, identifying the argument that minimises the cost function. In order to illustrate the applicability, the method is used to solve a non-linear inverse heat conduction problem to determine a temperature-dependent thermal conductivity. Then, a comparison is carried out with the local sensitivity and the genetic algorithm methods. It is shown that the proper generalised decomposition method estimates the unknown parameter with the same accuracy as the other two methods. Due to its advantage in terms of reducing the complexity, the method was then used to solve a transient three-dimensional non-linear heat transfer inverse problem. The results have shown that the method is appropriate to determine the unknown parameter with a low computational cost. Furthermore, the main advantage of the technique is its low capacity for storage, which can be used, as an inverse method, for building energy management and extended to evaluate thermal bridges from on-site measurements.

Analysis of Heat Transfer in Laser Assisted Machining of Slip Cast Fused Silica Ceramics

Machining of ceramics often involves many challenges due to their high hardness, brittleness, and low thermal properties. Laser assisted machining (LAM) is a promising technology for improving the machinability of hard-to-cut materials. In this work, laser assisted machining of slip cast fused silica (SCFS) ceramics is investigated by presenting a numerical thermal analysis of laser effects on material behaviour. A transient three-dimensional heat transfer analysis for laser assisted turning of SCFS is performed using finite element method. Temperature distributions in SCFS cylindrical specimens are obtained. Experimental results are provided to validate the numerical results.

Thermal Insulation Performance of Metal-exterior Curtain Wall Panel Systems with Thermal Bridges in Winter

To reduce energy consumption in buildings, it is essential to enhance the thermal insulation performance of building envelopes. For metal-exterior curtain wall panel systems, thermal insulation performance cannot be ensured because of the additional heat loss through thermal bridges, such as joints between panels, metal screws, and brackets. This study examined thermally improved metal-exterior curtain wall panel systems with bracket fixings. The thermal insulation performance of a conventional panel and three alternatives were evaluated by conducting three-dimensional transient heat transfer simulations during winter. The results showed that the total heat loss from the Base, alternative 1 (Alt1), alternative 2 (Alt2), and alternative 3 (Alt3) systems were 120.4, 62.0, 34.2, and 20.3MJ per unit wall area, respectively. Alt3 reduced the heat loss by 83.2% compared with the Base. Alt3 had a thermally insulated bracket with Azon and a modified aluminum mold with joints between the panels for reducing thermal bridges.

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.

Three-dimensional transient heat transfer and airflow in an indoor ice rink with radiant heat sources

Three-dimensional mixed convection in an ice rink heated by thermostatically controlled radiant heaters was simulated numerically using the standard k–e model with wall functions. This large building was modelled under transient conditions by considering the real outdoors atmospheric conditions for a typical spring day in Montreal, Canada. Results indicate the usefulness of the CFD technique as a powerful tool which provides a detailed description of the flow and temperature fields as well as the heat fluxes into the ice. The most important results are: Heating is needed only during the night (from 22 h to 7 h) when the outdoors temperature is relatively low. The On/Off switching of the radiant panels influences the temperature profiles throughout the ice rink; even the ice surface temperature is affected although the view factor between these two surfaces is zero. The radiation heat flux towards the ice increases significantly when the radiant panels are turned On; this can influence ice quality. The resurfacing operation increases the ice temperature and, by convection, the temperature of the air immediately above the stands. The air near the ice surface (1 meter over the ice) is essentially stagnant and significant air velocities can only be found above the stands and near the ceiling above the ice. The volumetric flow rate and temperature of the air evacuated from the building vary significantly between the different outlets.

Thermal protective performance evaluation of fire proof garment eliminating air gaps effect based on computational fluid dynamics simulation

To evaluate thermal protective performance of fire proof garment under flash fire exposures, it is important to discuss garment heat transfer characteristics eliminating the effect of air gaps between garment and body. In this study, a test of flame manikin clothed with close-fitting garment was designed. And a three-dimensional transient heat transfer computational fluid dynamics simulation of the test was achieved to gain the garment surface temperature. By means of three-dimensional body scanner, Geomagic and Gambit software, we developed a method of three-dimensional geometrical modeling of the full-scale close-fitting clothed manikin. The accuracy of the computational fluid dynamics simulation was validated by actual experiments. It was found that the average incident heat flux to the exterior of the Nomex® IIIA garment is not 84 kW/m2, the value measured in nude manikin tests, but the value is 11% lower than it. This will help to set more accurate boundary conditions on garment surface in further simulations.

Three-Dimensional Transient Heat, Mass, and Momentum Transfer Model to Predict Conditions of Canola Stored inside Silo Bags under Canadian Prairie Conditions: Part II. Model of Canola Bulk Temperature and Moisture Content

A three-dimensional transient heat, mass, and momentum transfer model was developed to predict temperatures and moisture contents of canola stored inside silo bags under Canadian Prairie conditions. The developed model calculated the condensation and production of water and heat generated by the respiration of microorganisms inside silo bags. This model was coupled with the soil temperature model developed in part I. These developed models were validated using weather data as input and measured temperatures and moisture contents inside silo bags filled with canola at 9.1%, 10.5%, or 14.4% initial moisture content (MC). The developed models had a poor prediction of the temperature and moisture content of the 14.4% MC canola because the canola seeds spoiled and clumped together in less than four months. The developed models could explain more than 90% of the measured temperatures inside the silo bags filled with 10.5% MC canola without underestimation or overestimation. The average absolute difference was less than 1.9°C ±0.1°C and 0.7°C ±0.0°C inside silo bags with 9.1% and 10.5% initial MC, respectively. The developed models could explain more than 94% of the measured moisture contents of canola stored inside the silo bags with ≤10.5% initial MC. The average absolute difference between measured and predicted moisture contents of canola was ≤0.4% ±0.0% inside the silo bags filled with 9.1% and 10.5% MC canola. Simulation results showed that condensation on the canola seeds mostly occurred at the boundary of silo bags, and canola inside hot spots might produce ≥2.5 fold of heat production, which was measured under small-scale laboratory conditions.