Boundary Conditions In Heat Conduction Research Articles

Experimental Evaluation of Thermoelectric Generator Performance under Different Heat Conduction Boundary Conditions

Heat conduction boundary conditions play a crucial role in the performance of thermoelectric generators (TEG). The TEG output voltage and power were measured under constant temperature boundary and heat flux conditions to evaluate the TEG performance under different heat conduction boundary conditions. External loading pressure and thermal interface material (TIM) were applied to reduce the interfacial thermal contact resistance. In our measurement setup, a fast-response electronic load was used for the rapid current-voltage scan, which can eliminate the thermal drift caused by the Peltier effect. A guard heater arrangement is used to minimize heat loss. In constant temperature boundary conditions, reducing the thermal contact resistance can increase the effective temperature drop across the TEG module and significantly improve the output voltage and power. But in the constant heat flux conditions, since the heat flux flow through the TEG is unchanged, the temperature drop across the TEG was unaffected by the thermal contact resistance. As a result, the TEG performance was lightly influenced by the thermal contact resistance.

Nonlocal heat conduction in silicon nanowires and carbon nanotubes

Experimental results showed that the effective thermal conductivity of silicon nanowire is smaller than the bulk thermal conductivity, while that of carbon nanotube (CNT) is usually much larger than its bulk counterpart. In order to resolve this paradox, a nonlocal heat conduction model for one-dimensional materials is proposed. This nonlocal model indicates that the different heat conduction boundary conditions of silicon nanowire and CNT lead to the different behaviour of their thermal conductivities in comparison with their bulk counterparts. Furthermore, the nonlocal effect of heat flux on the surfaces of the CNT makes the thermal conductivity of the single-wall CNT more than seven orders of magnitude higher than its bulk thermal conductivity. The thermal conductivities of the single-wall and multi-wall CNTs obtained by using the nonlocal model show an agreement with the experimental ones.

Analysis of transient heat source and coupling temperature field during cold strip rolling

In the process of cold thin strip rolling, the effect of the roll gap heat source on the transient temperature of cold rolled strip is very significant, and especially for the lateral temperature difference fluctuation which easily leads to the additional shape deviation of the rolled strip. In this study, according to the new heat resource model, the coupled temperature field model with high precision can be established, and the influence of the heat resource on the transient temperature of the cold rolled strip can be obtained by comprehensively considering the emulsion heat transfer coefficient, the air cooling, and the heat conduction boundary conditions. Based on the above models and the actual working parameters, several cases were performed to show the detailed analyses of the transient temperature distributions under various rolling conditions. The results at different strip positions show that the lateral distributions of the roll gap heat source and the strip transient temperature at every stand or pass can be simulated well. This study can improve the calculation precision of the transient lateral temperature difference for the complex online shape deviations during cold thin strip rolling.

A numerical method for two-dimensional inverse heat conduction problems

Purpose – The purpose of this paper is to introduce an effective method for two-dimensional inverse heat conduction problems. Design/methodology/approach – The variational iteration method (VIM) is used to solve two-dimensional inverse heat conduction problems and restore boundary conditions in heat conduction. Findings – Numerical results compared with other methods show that the present method is remarkably effective for solving two-dimensional inverse heat conduction problems. This method is a very promoting method, which will be certainly found wide applications. Originality/value – The VIM is applied to two-dimensional inverse heat conduction problems for the first time.

Restoring boundary conditions in heat conduction

The restoration of boundary conditions in one-dimensional transient inverse heat-conduction problems (IHCP) is described. In the formulation, the boundary conditions are represented by linear relations between the temperature and the heat flux, together with an initial condition as a function of space. The temperature inside the solution domain, together with the space or time-dependent ambient temperature of the environment surrounding the heat conductor, are found from additional boundary-temperature or average boundary-temperature measurements. Numerical results obtained using the boundary-element method are presented and discussed.

Determination of Temperatures and Heat Fluxes on Surfaces and Interfaces of Multidomain Three-Dimensional Electronic Components

A finite element method (FEM) formulation for the prediction of unknown steady boundary conditions in heat conduction for multidomain three-dimensional (3D) solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently overspecified on other boundaries. An inverse finite element program has been previously developed and successfully tested on 3D simple geometries. The finite element code uses an efficient sparse matrix storage scheme that allows treatment of realistic 3D problems on personal computer. The finite element formulation also allows for very straightforward treatment of geometries composed of many different materials. The inverse FEM formulation was applied to the prediction of die-junction temperature distribution in a simple ball grid array electronic package. Examples are presented with simulated measurements, which include random measurement errors. Regularization was applied to control numerical error when large measurement errors were added to the overspecified boundary conditions.

Thermophysical property measurements using time-resolved photothermal deflection spectrometry with step optical excitation

This letter reports the theoretical and experimental results of thermophysical property measurements using our recently developed time-resolved photothermal deflection spectrometry (PDS) with step optical excitation. One-dimensional heat conduction boundary conditions of the third kind were derived, and a theoretical model with the boundary conditions was proposed. Both thermal diffusivity and effusivity of two well-known samples were precisely measured simultaneously by fitting experimental data to the theory. Thermal conductivity and unit volume specific heat then can be deduced. Moreover, time-resolved PDS with step optical excitation has the advantages of simpler experimental apparatus and less time consuming measurement, compared with the traditional periodically modulated PDS.

Coupled thermo‐mechanical analysis for plastic thermoforming

AbstractAn FEM software ARVIP‐3D was developed to simulate the process of 3‐D plastic thermoforming. The coupled thermo‐mechanical analysis, thermal stress and warpage analysis for plastic thermoforming was carried out by means of this software. Rigid visco‐plastic formula was adopted to simulate the deforming process. During this process, the method of comparing velocity, time and area was adopted as the contact algorithm at different nodes and triangular elements. Sticking contact was assumed when the nodes become in contact with tool surface. The Arrhenius equation and the Williams equation were employed to ascertain the temperature dependence of material properties. In order to analyze the temperature field of plastic thermoforming, the Galerkin FEM code and the dynamic heat conduction boundary condition were adopted; latent heat and deformation heat were treated as dynamic internal heat sources. Based on the above, the model of coupled thermomechanical analysis was established. Assuming that the thermal deformation occurs under elastic conditions, the thermal stress and the warpage following the cooling stage were estimated. Experiments of plastic thermoforming were made for high‐density polyethylene (HDPE). An infrared thermometer was used to record the temperature field and a spiral micrometer was used to measure the thickness of the part. Results of numerical calculation for thickness distribution, temperature field and warpage were in good agreement with experimental results.

3-D FEM analysis of the temperature field and the thermal stress for plastics thermalforming

The FEM software ARVIP-3D is developed to simulate the deformation, temperature field, thermal stress and warpage of 3-D plastics thermalforming and blow molding. Temperature has a great effect on plastics forming behavior by influencing the material performance parameters, the fluid viscosity and the fluid behavior exponent. Combined with the rigid–visco-plastic FEM equation for forming computation, the Arrhenius and Williams equation for viscosity computation, the Calerkin FEM equation for the temperature field, the FEM software is developed. Whilst simulating the 3-D temperature field, the dynamic heat-conduction boundary condition is adopted, latent heat and deformation heat being treated as dynamic internal heat source in FEM equation. The computational results of adopting the analytical method and the FEM program developed by the authors indicate that the program of analyzing the temperature field is accurate. The simulation result of the temperature distribution corresponding to the thickness distribution agrees well with the experimental results of other researchers. This provides the theoretical basis and a guide for acquiring the thickness distribution of a part by a simple, convenient and non-destructive temperature measurement in practical production, and provides a useful tool to optimize the technique to secure an even distribution of thickness in the part. The warpage and thermal-stress analysis can predict defects and optimize the cooling system to secure an even temperature distribution within the part to assure the part's final shape, practical performance and strength.

Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries

A finite element method formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and combined thermoelasticity continuum problems is presented. The present finite element method formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently overspecified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for two-dimensional problems are presented.

Rolling process analysis of aluminum strip by a coupled thermo-elastic-plastic model

The phenomenon of longitudinal curvature on an aluminum strip caused by different heat conduction boundary conditions on the top and bottom surfaces of the strip while it undergoes a rolling process is studied. This research adopts large deformation-large strain theory to develop rolling process analysis of an aluminum strip by a coupled thentto-elastic-plastic model using the updated Lagrangian formulation (ULF) and incremental method. The flow stress of the materials is considered as a function of strain, strain rate and temperature, and the finite difference method is used simultaneously to solve equations of transient heat transfer. Finally, the numerical analysis method developed from this study is used to determine the temperature change and deformation of an aluminum strip when it undergoes hot rolling. At the same time, the simulation results on normal stress and contact angle are compared with the results of experiments and other published references; the comparison results verify that the present model is reasonable. In addition, the average rolling force during hot rolling is simulated and comparison is also made with the results of experiments provided by the China Steel Corporation. The simulated results in this article are generally considered to be reasonable.

Solution methods for problems with discontinuous boundary conditions in heat conduction and diffusion with reaction

Comparaison de trois methodes de resolution des problemes de valeurs limites: la methode des residus ponderes, la methode d'equation integrale et la methode des elements finis. Exemples d'application concernant: le facteur d'efficacite d'un catalyseur discretement distribue sur un support non adsorbant; le facteur de correction necessaire aux coefficients de transfert de matiere pour le transfert a des surfaces non uniformes; le facteur d'efficacite corrige pour les pores non spheriques tels que ceux que l'on rencontre dans les zeolites

The equivalence of transient heat generation and transient surface temperature boundary conditions in heat conduction

Two common classes of transient heat conduction problems are those with no heat generation and the surface or surrounding medium temperature a prescribed function of time, and those with prescribed uniform heat generation and constant surface or surrounding medium temperature. It is pointed out that the solution to any problem in one of these classes is also a solution to a problem in the other class. At any time t, the difference between the temperature at any location and the surface temperature in a body with no heat generation and surface temperature ƒ 4(t) is the same as that in the given body with constant surface temperature and volumetric heat generation Q = − C ϱ ∂ƒ 4 ∂t .