Transient Heat Conduction Process Research Articles

Investigation into the mechanism of ignition of magnesium alloy plates by high-temperature molten droplet

The ignition and spread of magnesium alloy fires are mainly attributed to the ignition of high-temperature molten metal droplets, but the underlying ignition mechanism remains unclear. This study addresses this knowledge gap by employing metallic aluminum and copper particles heated to temperatures over 1200 °C. Systematically, these heated particles were released at a fixed rate onto a magnesium alloy plate located inside a controlled heating furnace that maintained a constant temperature of 500 °C. Experimental results show that whether there are irregular pores and cracks in the resulting molten product can be used as a criterion for judging whether the magnesium alloy sample ignites. Furthermore, it is worth noting that molten copper droplets of the same size exhibit a higher heat-carrying capacity than their aluminum counterparts when both are heated to the same temperature. In addition, this study expanded the research scope through numerical simulation and analysis, using the PATO (Porous-Material Analysis Toolbox) solver to clarify the transient heat conduction process between the high-temperature droplet and the magnesium alloy plate. Simulations show that heat transfer upon droplet impact is primarily longitudinal, directed toward the base of the material. This results in a significantly higher temperature in the center of the affected magnesium alloy plate than at its periphery. In summary, this study helps to improve the understanding of the dangers of high-temperature molten droplets, and it is of great significance to investigate fire accidents caused by high-temperature molten droplets.

T-phPINN: Physics-informed neural networks for solving 2D non-Fourier heat conduction equations

Non-Fourier heat conduction plays a dominant role in many extreme transient heat conduction processes, such as laser pulses and heat transfer in biological systems, but the heat wave effect makes it difficult to solve the temperature field accurately and quickly. In order to solve this problem, the first order time derivative enhanced parallel hard constraints physics-informed neural networks (T-phPINN) is proposed. T-phPINN comprises two subnetworks and incorporates a first order time derivative to capture sharp temperature changes. Two numerical cases show that the minimum relative error of T-phPINN is 0.001 % and 0.015 %, which is 1.04 % and 12.30 % of the error of conventional PINN respectively, proving the accuracy of our architecture. A transfer learning framework is established for scenarios of different parameters, the training only requires 1/6 iterations of the basic model, and close accuracy is obtained. The computational cost of T-phPINN is evaluated using the finite element method as the baseline. For the two cases, the single calculation time is 33.43 % and 51.50 % of the baseline, while the multiple calculation time under the acceleration of transfer learning is 11.59 % and 17.75 % of the baseline. This study will be helpful for solving large-scale non-Fourier heat conduction equations precisely and expeditiously.

Design via topology optimisation and experimental assessment of thermal metadevices for conductive heat flux shielding in transient regime

The design via density-based topology optimisation (TO) of thermal metadevices for conductive heat flux manipulation in transient regime is introduced in this work. Such approach consists in the solution of a TO problem conceived to achieve simple devices of feasible manufacture, which are made of two macroscopically distinguishable isotropic materials of highly contrasting thermal properties. The objective function to be minimised during the solution of such TO problem is defined as the error in achieving a prescribed behaviour of the conductive heat flux in the region intended for its manipulation, and the well-known solid isotropic material with penalisation (SIMP) technique is used to define the material distribution as a continuous function. The finite element method is used for the numerical analysis of the metadevices performance, and for each finite element there is a single microparameter (artificial density) determining the material from which it is made. The proposed approach has been particularly applied to the design of metadevices to shield the conductive heat flux in a given region during a transient heat conduction process. Although the so-designed metadevices are made of standard isotropic materials, they actually behave as metamaterials allowing the desired manipulation of the heat flux. Such approach has been implemented in the design of an easy-to-manufacture metadevice capable of fulfilling the assigned task better than other design merely based on intuition, whose material distribution was conceived to at least roughly emulate the heterogeneous effective properties dictated by the method of transformation thermodynamics. Since the microparameters directly define the distribution of both isotropic materials, it has also been possible to manufacture a metadevice designed under the proposed approach and to experimentally evaluate its performance.

Fluorescent paint for determination on the effective thermal conductivity of YBCO coated conductor

Recently, YBa2Cu3O7−x coated conductor (YBCO CC) has been developed intensively for different applications including power cables and high-filed magnets. Of all its physical properties, the thermal conductivity of the YBCO CC is considered as one of the most important parameters in guiding the temperature distribution, heat flux, and prediction of quench propagation. To accurately predict this property, a thermometry technique of high-speed fluorescent thermal imaging is introduced to monitor heat diffusion of commercial YBCO CCs in real time based on the Europium tris[3-(trifluoromethylhydroxymethylene)-(+)-camphorate] (EuTFC) in this study. We propose a new imaging process to eliminate the influences of background intensity and non-uniform illumination on the calibration results accompanying with good accuracy of measurement. And the fluorescence performances are evaluated by static and dynamic calibration experiments. The experimental results show that the photoluminescence of EuTFC has excellent photostability and temperature dependence, and there is no hysteresis in the temperature response when comparing with the PT100 measurements. Subsequently, four kinds of commonly used theoretical models of thermal conductivity and the corresponding calculation curves of the YBCO CC are presented. Finally, the numerical simulation based on the theoretical models has been conducted to reproduce the transient heat conduction process. The simulation results show that the transient heat conduction predicted by the Maxwell’s equivalent model show the best agreement compared with experimental results.

Nonlinear Constitutive Models for Nano-Scale Heat Conduction

We present a first-principle based approach that leads from a many-particle description to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at t...

Inverse Filtering Method of Bare Thermocouple for Transient High-Temperature Test With Improved Deep Belief Network

In this paper, we focus on the inverse filtering method for restoring transient heat conduction processes. First, we address the defects of contact temperature sensor used in transient high temperature test, further we expand the distortion of transient calibration result caused by the lack of dynamic characteristics of bare thermocouple, then the inverse filtering idea is proposed. Second, we propose an improved deep belief network (DBN) to extract the characteristic of thermocouple dynamic nonlinearity on dynamic response signal. The continuous restricted Boltzmann machine (CRBM) is adopted to improve the input layer structure which the input samples can be continuous, and the back propagation (BP) neural network is adopted to realize input-output approximation at output layer. Additionally, dynamic response signal of the thermocouple is obtained through the constructed laser narrow pulse calibration system, and dynamic inverse filtering of thermocouple is realized by using the standard source as the approximation target. The performance of the inverse filtering is analyzed by comparing with the traditional linear least square(LS) method, and it is verified that this method can more accurately approximate the transient high temperature physical process in the calibration environment.

A DEM-embedded finite element method for simulation of the transient heat conduction process in the pebble bed

A DEM-embedded-finite-element-method (DEFEM) with a 2D-asymmetric circular particle heat conduction model is proposed. DEFEM combines the discrete-element (DE) and finite-element model (FEM) with heat conduction. With embedded discrete elements (EDE), DEFEM solves heat conduction between particles and temperature field inside particles. EDE solves heat conduction in asymmetric circular element, and FEM simulates transient heat conduction after the heat flux at boundaries is known. Verified by experiments, results show that DEFEM can accurately simulate transient heat conduction of pebble beds. Discrete-model (DM) and continuum-model (CM) are comparatively analyzed under the same thermal responses and temperature distributions. In CM, the standard function of thermal conductivity is fitted with an attenuation part, an increment part and a constant part. The constant part is defined as effective thermal conductivity (ETC) of CM, which is directly proportional to that of DM, and independent of heat capacity. Herein, ETC of the CM is a key parameter, which could be used to measure the overall heat transfer capability of the bed

Computational design of metadevices for heat flux manipulation considering the transient regime

The present work introduces the optimization-based approach for the design of metadevices to manipulate the heat flux in transient regime. It consists of solving a continuous, nonlinear, constrained, large-scale optimization problem where the objective function (to be minimized) is the error in accomplishing a given heat flux manipulation task along a transient heat conduction process. The response of the metadevice is modeled by using the finite element method, and its design is characterized by a set of parameters defining the material at all the finite elements in the device. These parameters are the design variables of the optimization problem, being chosen from an admissible design set in order to guarantee the feasibility of the optimal solution. As an example, this optimization-based approach is applied to the design of a heat flux shielding metadevice. Compared to a metadevice designed under the classical thermodynamics transformation approach and intuition, the current device performs the shielding task with considerably higher success. In order to highlight the versatility of the proposed optimization-based design method, this approach is also applied to the design of metadevices to satisfy multiple different simultaneous tasks, particularly shielding and cloaking.

Measurement of transient heat transfer in vicinity of gas–liquid interface using high-speed phase-shifting interferometer

The heat transfer process and initial stage of coupled convection at a gas–liquid interface are observed with high temporal and spatial resolutions in view of understanding phase transition dynamics such as evaporation or condensation for energy technologies. A high-speed phase-shifting interferometer is used to precisely measure the transient heat conduction and convection processes near the gas–liquid interface of a small water droplet. In the present study, the transient heat conduction around a water droplet interface during the adiabatic expansion process before the appearance of convection is visualized and examined. In the visualization experiment, transient density variations due to heat conduction in the vicinity of the gas–liquid interface are observed with temporal and spatial resolutions of 1ms and 8.83μm/pixel, respectively. It is determined that convection appears at approximately t=0.25s in a fast depressurization process, while transitions in both temperature and pressure are observed. In addition, the transient density variations and distributions of the gas phase before convection are compared with numerical simulations as an optical path length difference, and there is good agreement between the simulations and experimental results. The measurement methods developed in this study can be applied in the measurement of interfacial heat and mass transfers with high temporal and spatial resolutions.

Optimization of the one-dimensional transient heat conduction problems using extended entransy analyses

Heat transfer optimization principle is critically important for further explaining the underlying mechanisms and guiding practical designs of heat transfer processes. Recently, the entransy theory has been successfully used to optimize various steady-state heat transfer processes. Nevertheless, it is still an open question whether this theory can be utilized in transient cases. Here, we examined the applicability of the entransy analyses on the one-dimensional transient heat conduction process. It was found that the entransy dissipation rate can neither derive the transient governing equation nor correspond to the optimal result in the transient optimization problem. Therefore, an extended entransy dissipation rate was defined as the convolution integral of heat flux and negative temperature gradient. The total extended entransy dissipation rate over the time and space domain can correspond to the optimal result of the transient optimization problem. Additionally, Fourier transform was used to convert the transient problem from the time domain into the frequency domain, and the total entransy dissipation rate in the frequency domain will give a convenient optimization criterion that the temperature gradient field should be spatially uniform to reach the shortest characteristic time. Also, the inverse Fourier transform of the entransy dissipation rate in the frequency will be the extended entransy dissipation rate in the time domain. Finally, these findings were used to optimize a practical transient heat conduction problem for a solid thermal energy storage unit.

Entropy generation minimization in steady-state and transient diffusional heat conduction processes Part I – Steady-state boundary value problem

Abstract An application of the Entropy Generation Minimization principle allows new formulation of the boundary and initial boundaryvalue problems. Applying Euler-Lagrange variational formalism new mathematical form of heat conduction equation describing steady-state processes have been derived. Mathematical method presented in the paper can also be used for any diffusion heat and mass transfer process. Linear and non-linear problems with internal heat sources have been analyzed.

Entropy generation minimization in transient heat conduction processes PART II – Transient heat conduction in solids

Abstract Formulation and solution of the initial boundary-value problem of heat conduction in solids have been presented when an entropy generation minimization principle is imposed as the arbitrary constraint. Using an entropy balance equation and the Euler-Lagrange variational approach a new form of the heat conduction equation (non-linear partial difference equation) is derived.

Thermomechanical Effects Induced by Energy Piles Operation in a Small Piled Raft

AbstractIn this work, a series of fully coupled three-dimensional thermomechanical finite-element analyses has been carried out to investigate the mechanical and thermal interaction effects induced in a small piled raft equipped with energy piles during the operation of an air-conditioning system based on ground source heat pumps (GSHPs). In particular, attention has focused on (1) the axial-load redistribution among the various piles of the raft as a result of differential thermal dilations occurring in the pile and the soil during the transient heat conduction process and (2) the thermal interaction effects that may affect the heat exchange process when multiple energy piles are placed at short distances within the same piled raft. The results of the numerical simulations, which are in qualitative agreement with the limited experimental observations from full-scale tests on energy piles currently available in the literature, show that significant (positive and negative) axial-load changes can be experie...

Development and testing of a simple heat gauge for the measurement of high-intensity thermal radiation

A simple and inexpensive radiation heat gauge was developed and tested for high-intensity thermal radiation measurements. The gauge used a thermal image camera to record the temperature variation of a metallic bar painted in black and heated at one end by thermal radiation. The average flux of the irradiation was determined from the rate of temperature change at a selected point on the bar. The aperture of the gauge can be easily varied by changing the diameter of the washer in front of the metallic bar. Numerical solutions were obtained for the transient heat conduction process in the metallic bar, and casted into dimensionless forms which can be conveniently used for bars of different sizes and materials, and/or subjected to different radiation fluxes. The gauge was employed to measure the radiation beams produced by a commercial IR (Infrared) heater and the results were in good agreement with the heater manufacturer's data.

Mathematical modeling and investigations of the processes of heat conduction of ammonium perchlorate with phase transitions in thermal decomposition and gasification

Transient heat-conduction processes occurring in the period of thermal decomposition and gasification of a crystalline oxidant — ammonium perchlorate — have been investigated and analyzed on the basis of the developed mathematical model.

Initial surface fluxes in transient heat conduction

In the heat transfer literature, it appears that numerical analyses focusing on surface heat fluxes in the initial phase for transient heat-conduction systems, i.e., qx at x=0 and t=Δt, have not been sufficiently reported. Due to this scarcity, some results may need to be re-examined for their accuracies or even their validities. The objective of the present study is twofold. First, we have identified two specific cases that may call for the awareness of the heat transfer community. Second, after such identification, we have further developed and proposed a technique, called the surface cubic-spline method, to help improve accuracies of heat-flux solutions. An effort is made to render the implementation of this method easy for interested readers, along with a MATLAB code offered in the appendix for them to directly cut and paste. Finally, some discussions of the second law of thermodynamics are presented, as they are related to transient heat conduction processes, and none of these essential ideas has been adequately reported in the literature.

Solving two-dimensional Cartesian unsteady heat conduction problems for small values of the time

This paper is intended to provide very accurate analytical solutions modeling transient heat conduction processes in 2D Cartesian finite bodies for small values of the time. Analysis of diffusion of thermal deviation effects indicates that, when the space and time coordinates satisfy a criterion developed in the paper, the simple transient 1D semi-infinite solutions may be “used” for generating extremely accurate values for temperature and heat flux at any point of a finite rectangle. Also, they may be “used” with excellent accuracy as short-time solutions when the time-partitioning method is applied (so avoiding the usually difficult integration of the short-cotime Green's functions). A complex 2D semi-infinite problem is solved explicitly and evaluated numerically as part of the analysis. The proposed criterion is based on an accuracy of one part in 10n (n = 1,2,...,10,...), where n = 2 is for engineering insight and visual comparison while n = 10 is for verification purposes of large numerical codes.

A simplified method to predict the outdoor thermal environment in residential district

The outdoor thermal environment is very important to pedestrian’s comfort and safety. Under the fast development of urbanization it is essential to develop a quick assessment method to assist design. The present paper introduces a simplified simulation system consisting of convection, conduction and radiation to predict the outdoor thermal environment. A double mesh system for radiation simulation is used to reduce the amount of calculation and storage, meanwhile a thermal response factor method is introduced to calculate the transient heat conduction process. By taking advantage of the thermal response factor method, two kinds of simplified coupling methods are proposed. To validate the simulation system, a filed measurement was carried out and the simulation results are in compliance with the experiment. The simulation results show that the error caused by simplification is acceptable in most conditions, and a lot of coupling calculation amount could be saved.

Investigation on the three-dimensional multiphase conjugate conduction problem inside porous wick with the lattice Boltzmann method

A lattice Boltzmann model is developed for investigating the heat conduction process inside the three-dimensional random porous media. Combined with the algorithm for the reconstruction of the three-dimensional porous media, this model is used to investigate the transient heat conduction process inside the porous wick of CPLs/LHPs, which is vital for analyzing the startup stability of a CPL/LHP. The temperature distribution inside the porous wick is obtained and the influence of the porosity and the heat load on the conduction process also is investigated using the present model. The present model is applicable to predicting the effective conductivity of such a complex structure.

Modeling of Mass Dynamics in Arterial Drug-Eluting Stents

A mathematical model describing the advection-diffusion reaction of a substance between two porous homogeneous media of different properties and dimensions is presented. A strong analogy with the one-dimensional transient heat conduction process across two layered slabs is evidenced and a similar methodology is proposed. The model incorporates not only drug diffusive effects, but also convection phenomena and metabolic processes in the wall. Transformation and separation of variables leads to a Sturm-Liouville problem with discontinuous coefficients and an exact analytical solution is given in the form of an infinite series expansion. The model points out the role of the nondimensional parameters, which control the complex transfer mechanism across the two layers. In particular, the drug diffusivity in the wall is shown to greatly influence the residence time. Drug concentration profiles at various times are given and discussed. Received September 19, 2007; Accepted February 14, 2008 Copyright c © 2009 Begell House, Inc. 19 20 Pontrelli and de Monte