Three-dimensional Heat Conduction Research Articles

Vertical particle alignment of boron nitride and silicon carbide binary filler system for thermal conductivity enhancement

Thermally conductive BN/SiC binary filler and epoxy composite materials were fabricated via magnetic alignment. The magnetic iron oxide particles on the surface of the filler allowed particle re-orientation under the external magnetic field. Owing to its anisotropy, the vertically aligned BN composite had a high thermal conductivity and generated a vertical heat flow path. When the SiC nanoparticles were added to the binary filler, they hindered BN-particle aggregation and led to the formation of a three-dimensional heat conduction path, thereby resulting in increased thermal conductivity. The maximum thermal conductivity (5.77 W/mK) was obtained with an addition of SiC filler, and was 3.08-fold and 1.1-fold higher than that of randomly mixed BN and vertically aligned BN composites, respectively. The additional SiC–Fe3O4 particles resulted in significant aggregation of the filler, which in turn led to a decrease in the thermal conductivity. The measured storage modulus of the BN–Fe3O4/SiC binary filler composite was also higher than those of the BN–Fe3O4 and BN–Fe3O4/SiC–Fe3O4 composites, owing to the aggregation of particles.

Transient response of a thermoelectric generator subjected to spatially non-uniform heating: Implications for heat and IR sensing applications

We present a combined experimental and computational investigation of the transient behavior of a thermoelectric generator (TEG) subjected to temperature gradients of less than 0.5K across its thickness. Such conditions can exist when TEGs are used as heat sensors or IR detectors. Spatially non-uniform heating was initiated by allowing light to strike the central portion of one side of the TEG or by placing a small heated probe in contact with that surface. The time-dependent, open circuit voltage output of the TEG was predicted using temperature results from a three dimensional transient heat conduction finite element model. It is shown that the transient voltage output is influenced by the configuration of the mounting hardware, by the thermal properties of the TEG’s materials of construction, and by convection. Three-dimensional heat conduction in the TEG determines the nature of the transient voltage output, which, in some cases, exhibits an overshoot.

A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction

This study documents the first attempt to apply a nonsingular indirect boundary element method (BEM) for the solution of three-dimensional (3D) inverse heat conduction problems. The present BEM formulation avoids the calculation of hyper-singular integrals. Furthermore, the exact geometrical representation of computational domain is adopted by parametric equations to eliminate the errors in traditional approaches of polynomial shape functions. Due to its boundary-only discretizations and semi-analytical nature, the proposed method can be viewed as a competitive candidate for the solution of inverse problems. Four benchmark numerical examples indicate that the proposed method, in conjunction with proper regularization techniques, is accurate, computationally efficient and numerically stable for the solution of 3D inverse problems subjected to various levels of noise in input data.

Thermal–hydraulic modeling and transient analysis of helium-cooled tungsten target coupled with ADS core

The Accelerator Driven Subcritical Reactor System (ADS) is a kind of nuclear reactor which can burn minor actinide waste produced from conventional reactors with inherent safety features. This paper presents a concept design of helium gas-cooled tungsten target for 10MW helium-cooled experimental ADS.In the design scheme, the tungsten spallation target was modeled into the honeycomb structure. The thermal–hydraulic model of the target coupling with core was built, in which the solid domain was simulated with three-dimensional heat conduction model and the fluid domain was simulated with one-dimensional quasi-static model. The target was modeled with fine meshes. The core was modeled roughly as the boundary condition of the target. In order to analyze the transient characteristics of the target with cooling system, a RELAP5–TRCAP coupling model for cooling system was established, in which the decay heat of the target and core was considered. The simulated results indicate that the peak temperature in the target is lower than the limiting value under the rated operation state and during the Loss of Flow Accident (LOFA) transient with actuation of the safety system.

Conjugate heat transfer analysis for in-vessel retention with external reactor vessel cooling

A conjugate heat transfer analysis method for the thermal integrity of a reactor vessel under external reactor vessel cooling conditions is developed to resolve light metal layer focusing effect issue for in-vessel retention. The method calculates steady-state three-dimensional temperature distribution of a reactor vessel using coupled conjugate heat transfer between in-vessel three-layered stratified corium (metallic pool, oxide pool and heavy metal and polar-angle dependent boiling heat transfer at the outer surface of a reactor vessel). The three-layer corium heat transfer model is utilizing lumped-parameter thermal-resistance circuit method. For the ex-vessel boiling boundary conditions, nucleate, transition and film boiling are considered. The thermal integrity of a reactor vessel is addressed in terms of heat flux at the outer-most nodes of the vessel and remaining thickness profile. The vessel three-dimensional heat conduction is validated against a commercial code. It is found that even though the internal heat flux from the metal layer goes far beyond critical heat flux (CHF) the heat flux from the outermost nodes of the vessel may be maintained below CHF due to massive vessel heat diffusion. The heat diffusion throughout the vessel is more pronounced for relatively low heat generation rate in an oxide pool. Parametric calculations are performed considering thermal conditions such as peak heat flux from a light metal layer, heat generation in an oxide pool and external boiling conditions. The major finding is that the most crucial factor for success of in-vessel retention is not the mass of the molten light metal above the oxide pool but the heat generation rate inside an oxide pool and the three-dimensional vessel heat transfer provides much larger minimum vessel thickness.

Steady and Transient Thermal Analyses on a Segmented High-Temperature Superconducting Magnet with Porous Media-Inserted Cryogenic Cooling

This paper discusses thermal design of a segmented high-temperature superconducting (HTS) magnet depending on geometry of HTS conductors, cooling system (indirect cooling or partial forced flow cooling), cooling techniques and joint resistance. For the purpose, three-dimensional heat conduction analysis was carried out with a finite element code, modeling geometry and operating condition of helical coils in a helical fusion reactor, FFHR as an example. In this analysis, liquid neon was assumed to be used as a coolant at an operating temperature of 25 K. As a heat removal technique for the joint, cooling system of a cryogenic liquid coolant with metal porous media has been proposed and it was also modeled in the heat conduction analysis. The numerical results showed that stainless steel jacket and a low thermal conductivity insulator determine temperature distribution and any cooling techniques cannot contribute to prevent the temperature rise when joint resistance increases in the case of the indirect cooling system. On the other hand, a high performance cooling technique such as metal porous media-inserted channel is effective to reduce temperature rise in the partial force cooling system.

Numerical simulation of continuous casting of steel alloy for different cooling ambiences and casting speeds using immersed boundary method

This article demonstrates implementation of immersed boundary method in continuous casting simulation involving boundary movement. In this methodology, the immersed boundary method is coupled with the second-order accurate finite difference solution of unsteady three-dimensional heat conduction equation. The moving molten metal front is modelled using the immersed boundary method in a Cartesian mesh framework that provides simplicity in its implementation and reduces the computational time as compared to the adaptive mesh solutions. A parallel programming paradigm using message passing interface has been implemented to obtain enhanced computational efficiency. This study has focused on capturing moving boundary during continuous casting and predicts the temperature distribution and shell thickness under different cooling ambiences and casting function. Good agreements with published data and correlations are obtained through numerical analysis. Mould-region shell thickness agrees well with Chipman–Fondersmith correlations. A new correlation has been further proposed for the delay constant at different heat extraction rates. The effects of key parameters like casting speed, convection and radiation from the continuous casting are also quantified in attempt to avail the data for optimal design of continuous caster.

Improved variational bounds for conductive periodic composites with 3D microstructures and nonuniform thermal resistance

Improved variational bounds for the effective conductivity of a matrix-inclusion conductive periodic composite are obtained. The studied composite is macroscopically anisotropic with nonuniform interfacial thermal resistance between isotropic phases. The homogenization theory is applied to a three-dimensional heat conduction problem which is stated in terms of nondimensional parameters. The Biot number is explicitly given in the variational formulation of the local problems and in the related minimization problems. The approach is based on the Lipton–Vernescu variational principles which allow to derive narrower bounds by incorporating more detailed morphological information. The bounds depend on the concentration and the conductivity of each phase, the periodic distribution and the shape of the inclusions, the Biot number and the nonuniform interfacial resistance.

Estimation of a Location- and Time-Dependent High-Magnitude Heat Flux in a Heat Conduction Problem Using the Kalman Filter and the Approximation Error Model

This paper aims to estimate a location- and time-dependent high-magnitude heat flux in a heat conduction problem. The heat flux is applied on a small region of a surface of a flat plate, while transient temperature measurements are taken on the opposite surface. This inverse problem is solved using the Kalman filter and a reduced forward model, obtained by simplifications of a three-dimensional and nonlinear heat conduction problem. To deal with the modeling errors of this reduced model, the Approximation Error Model is used. The results show that excellent estimates can be obtained at feasible computational times.

Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

In this paper, analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source are presented, the double-layer structure includes a coating layer and FGM layer. The Poisson method and layer wise (LW) approach are applied to solve the three-dimensional steady heat conduction problem. Meanwhile, to solve the three-dimensional transient heat conduction problem of the double-layer plate, the method of separation of variables (SOV) and LW approach are together applied. The aim of this research is to understand the influences of selected coating material, local heat source and structural parameters on temperature distribution of the double-layer plate, and to guide engineers designing the double-layer structures in thermal environment.

Dynamic simulation of three-dimensional heat conduction through cylindrical inclusions using a BEM model formulated in the frequency domain

The analysis of surface temperatures in constructive elements using infrared thermography can be a useful tool for the in situ identification of constructive details and materials and for the evaluation of their thermal behaviour. It is therefore very important to be able to predict the effect of the materials’ thermophysical properties on heat diffusion.We present a numerical simulation model for the study of three-dimensional heat diffusion through cylindrical inclusions. This model is based on the boundary elements method (BEM), formulated in the frequency domain, and it was verified against two-dimensional analytical solutions that are known for cylindrical geometries. The proposed model was used to simulate heat conduction through a concrete column with a cylindrical inclusion embedded within it, subjected to a three-dimensional external heat point source. The effect of the inclusion properties and inclination on the temperature distribution inside the column and on its outer surface was analysed. The different heat wave phases of the physical models were compared.

Unsteady Conjugate Natural Convection in a Three-Dimensional Porous Enclosure

Transient-free convection in a porous enclosure having heat-conducting solid walls of finite thickness under conditions of convective heat exchange with an environment was studied numerically. A heat source of constant temperature was located at the bottom of the cavity. The governing equations in porous volume formulated in dimensionless variables such as the temperature and vector potential functions within the Darcy–Boussinesq approach and the transient three-dimensional heat conduction equation based on the Fourier hypothesis for solid walls with corresponding initial and boundary conditions were solved using an iterative implicit finite-difference method. The main objective was to investigate the influence of the Rayleigh number 103 ≤ Ra ≤ 106, the Darcy number 10−5 ≤ Da ≤ 10−3, the thermal conductivity ratio 1 ≤ k1,2 ≤ 20, the solid wall thickness ratio 0.1 ≤ l/L ≤ 0.3, and the dimensionless time 0 ≤ τ ≤ 200 on the fluid flow and heat transfer. Comprehensive analysis of the effects of these key parameters on the average Nusselt number at the heat source surface was conducted.

Temperature rise characteristic of MR fluid in a multi-disc MR clutch under slip condition

Purpose – This study aims to reveal the temperature rise characteristic of magnetorheological (MR) fluid in a multi-disc MR clutch under slip condition, including the temperature distribution regularity and the impact factors. Design/methodology/approach – Three-dimensional transient heat conduction equation for the MR fluid in the working gap was derived based on the heat transfer theory. Then, numerical simulation was conducted to analyze the temperature field of MR fluid. Furthermore, an experimental study was performed to explore the temperature distribution of the MR fluid in radial and circumferential directions, as well as the effects of disc groove, slip power and gap size on temperature rise characteristic of the MR fluid. Findings – The results show that temperature appears to be largest in the center of the working gap and the temperature difference increases with the slip time. However, the temperature field in a circumferential direction is basically the same, but it presents slightly lower in the groove area. The temperature of the MR fluid increases linearly with the slip time and the rise rate increases with the slip power. Moreover, the temperature rise value decreases with the increase of gap size. Originality/value – In this paper, the temperature gradients, both in radial and circumferential directions, are experimentally measured going beyond the estimation by computer simulations. In addition, the factors that influence the temperature rise characteristic of MR fluid were fully analyzed. The results could provide a reliable basis for the development of cooling technology for high-power MR devices.

A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media

The singular boundary method (SBM) is a relatively new meshless boundary collocation method for the numerical solution of certain elliptic boundary value problems. The method, based on the notion of the boundary element method (BEM) and method of fundamental solutions (MFS), fully inherits the merits of both and in the meantime possessing its unique advantages. Due to the boundary-only discretizations and its semi-analytical nature, the method can be viewed as an ideal candidate for the solution of inverse problems. In this study, we document the first attempt to apply the SBM, together with several regularization techniques, for the solution of inverse heat conduction problems in three-dimensional (3D) anisotropic media. Four benchmark numerical examples are well-studied which indicate that the proposed scheme is accurate, computationally efficient and numerically stable for the solution of 3D inverse problems with various levels of noisy input data.

IMPACT OF ANISOTROPY ON GEOMETRICAL AND THERMAL CONDUCTIVITY OF METALLIC FOAM STRUCTURES

The thermo-physical properties of open cell metal foams depend on their microscopic structure. Various virtual ideal periodic isotropic foam samples having circular, square, hexagon, diamond, and star strut cross sections with various orientations are realized in the porosity range from 60 to 95%. The anisotropy of the original foam sample is then realized by elongating in one direction by a factor Ω, while a factor of 1/√Ω is applied along the two perpendicular directions to conserve the porosity of the original sample. A generalized analytical model of geometrical parameters has been proposed and all results are fully compared with the original measured data. Three-dimensional heat conduction numerical simulations at the pore scale have been performed, which allow determining the macroscale physical properties, such as the effective thermal conductivity, using the volume averaging technique. Two analytical models are derived simultaneously in order to predict the intrinsic solid phase conductivity (λs) and effective thermal conductivity (λeff). A modified correlation term (F) is introduced in the analytical resistor model to take into account the thermal conductivities of constituent phases and a modified Lemlich model is derived. The analytical results of the effective thermal conductivity are compared with the numerical data and excellent agreement is observed.

Решение трехмерных уравнений теплопроводности с помощью разрывного метода Галeркина на неструктурированных сетках

Для решения уравнений диффузионного типа в настоящее время широко применяется конечно-элементный метод Галeркина с разрывными базисными функциями (РМГ), который характеризуется высоким порядком точности получаемого решения. Для применения РМГ исходное уравнение второго порядка преобразуется к системе дифференциальных уравнений в частных производных первого порядка. Для этого вводятся вспомогательные потоковые переменные. В соответствии с традиционным подходом в РМГ решение в каждой ячейке основной сетки представляется в виде линейной комбинации базисных функций. Тепловой поток ищется в виде линейной комбинации базисных функций на ячейках двойственной сетки. Двойственная сетка состоит из медианных контрольных объемов, построенных относительно вершин основной сетки. Интегрирование по объемам и граням ячеек базируется на использовании квадратурных формул Гаусса. Численный алгоритм рассматривается на примере решения начально-краевой задачи для трехмерного уравнения теплопроводности. Численная методика реализована в виде программного продукта и ориентирована на решение трехмерных задач теплопроводности на неструктурированных тетраэдральных сетках. В работе представлены результаты расчетов ряда тестовых задач, демонстрирующие возможности и точность методики.

Study on the relationship between the heat transfer characteristics of preheating gas and cutting performance of oxyfuel gas cutting

Plate temperature and heat input in an oxyfuel gas cutting process with H2/LP gas and LPG flame are calculated by three-dimensional FE heat conduction analyses. FE analyses are performed by using moving coordinates, and cutting groove temperature is determined by iterative calculation. The two-dimensional groove temperature distribution determined by Matsuyama's theory is chosen as the initial values in this iterative calculation. The heat transfer properties of the preheating flame are determined by using the genetic algorithm-based heat transfer estimation technique proposed in the previous report. The validity of the proposed numerical procedure and the accuracy of the determined groove temperature are examined by comparing the calculated and measured plate temperature and heat-affected zone sizes. Heat input due to preheating, qG, and that due to self-burning of steel, qB, are estimated in these analyses, and they are compared with the heat inputs estimated by Wells' and modified Wells' equations. The relation between the heat transfer characteristics of the preheating gas flame and plate temperature distribution is examined, and the cutting performance improvement mechanisms of hydrogen preheating are discussed. As a result, the followings are found: (1) the three-dimensional groove temperature distribution can be calculated by performing the iterative analyses procedure proposed in this study; (2) the critical cutting speed can be estimated once the gas heat transfer parameters are known; (3) it is not appropriate to evaluate the magnitude of cutting thermal deformation only from the preheating gas's total calorific value; (4) under the conditions chosen, the heat generated by self-burning is inadequate to maintain the cutting process, and it is essential to supplement heat by preheating; (5) the faster cutting speed and smaller total heat input of H2/LP gas are results of the larger local heat transfer coefficient below the gas ejection hole. It is supposed that the improvement in oxyfuel gas cutting performance can be achieved by modifying the heating apparatus so that the local heat transfer coefficient becomes larger.

Three-dimensional heat conduction analysis of inhomogeneous materials by triple-reciprocity boundary element method

Homogeneous heat conduction can be easily analyzed by the boundary element method. However, domain integrals are generally necessary to solve the heat conduction problem in non-homogeneous and functionally gradient materials. This paper shows that the three-dimensional heat conduction problem in non-homogeneous and functionally gradient materials can be solved approximately without the use of a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of domain effects is interpolated using integral equations. A new computer program is developed and applied to several problems.

Exact Analytical Solution for 3D Time-Dependent Heat Conduction in a Multilayer Sphere with Heat Sources Using Eigenfunction Expansion Method.

An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed.

DEVELOPMENT OF A CORE THERMO-FLUID ANALYSIS CODE FOR PRISMATIC GAS COOLED REACTORS

A new computer code, named CORONA (Core Reliable Optimization and thermo-fluid Network Analysis), was developed for the core thermo-fluid analysis of a prismatic gas cooled reactor. The CORONA code is targeted for whole-core thermo-fluid analysis of a prismatic gas cooled reactor, with fast computation and reasonable accuracy. In order to achieve this target, the development of CORONA focused on (1) an efficient numerical method, (2) efficient grid generation, and (3) parallel computation. The key idea for the efficient numerical method of CORONA is to solve a three-dimensional solid heat conduction equation combined with one-dimensional fluid flow network equations. The typical difficulties in generating computational grids for a whole core analysis were overcome by using a basic unit cell concept. A fast calculation was finally achieved by a block-wise parallel computation method. The objective of the present paper is to summarize the motivation and strategy, numerical approaches, verification and validation, parallel computation, and perspective of the CORONA code.