Numerical experiments using hierarchical finite element method for nonlinear heat conduction in plates

Heat conduction [1] is usually modeled as a diffusion process embodied in heat conduction equation. The traditional numerical methods [2, 3] for heat conduction problems such as the finite difference or finite element are well developed. However, these methods are based on discretized mesh systems, thus they are inherently limited in the geometry treatment. This chapter describes the Monte Carlo method that is based on particle transport simulation to solve heat conduction problems. The Monte Carlo method is “meshless” and thus can treat problems with very complicated geometries. The method is applied to a pebble fuel to be used in very high temperature gas-cooled reactors (VHTGRs) [4], which is a next-generation nuclear reactor being developed. Typically, a single pebble contains ~10,000 particle fuels randomly dispersed in graphite– matrix. Each particle fuel is in turn comprised of a fuel kernel and four layers of coatings. Furthermore, a typical reactor would house several tens of thousands of pebbles in the core depending on the power rating of the reactor. See Fig. 1. Such a level of geometric complexity and material heterogeneity defies the conventional mesh–based computational methods for heat conduction analysis. Among transport methods, the Monte Carlo method, that is based on stochastic particle simulation, is widely used in neutron and radiation particle transport problems such as nuclear reactor design. The Monte Carlo method described in this chapter is based on the observation that heat conduction is a diffusion process whose governing equation is analogous to the neutron diffusion equation [5] under no absorption, no fission and one speed condition, which is a special form of the particle transport equation. While neutron diffusion approximates the neutron transport phenomena, conversely it is applicable to solve diffusion problems by transport methods under certain conditions. Based on this idea, a new Monte Carlo method has been recently developed [6-8] to solve heat conduction problems. The method employs the MCNP code [9] as a major computational engine. MCNP is a widely used Monte Carlo particle transport code with versatile geometrical capabilities. Monte Carlo techniques for heat conduction have been reported [10-13] in the past. But most of the earlier Monte Carlo methods for heat conduction are based on discretized mesh systems, thus they are limited in the capabilities of geometry treatment. Fraley et al[13] uses a “meshless” system like the method in this chapter but does not give proper treatment to the boundary conditions, nor considers the “diffusion-transport theory correspondence” to be described in Section 2.2 in this chapter. Thus, the method in this chapter is a transport theory treatment of the heat conduction equation with a methodical boundary correction. The

High-order three-scale computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales

Boundary knot method for heat conduction in nonlinear functionally graded material

Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

Initial configuration effect is investigated for a both highly accurate and highly diverse biased heat conduction method. According to the individual object degree, we assign a heterogeneous initial resource for each object. Experimental results obtained from the MovieLens dataset show that, the proposed method outperforms the standard heat conduction method by 47.33%, and also outperforms an accurate mass diffusion method by 24.04% in recommendation accuracy. Especially, even compared with an excellent hybrid method of heat conduction and mass diffusion, and the original biased heat conduction method, the manifested method further enhances both the recommendation accuracy and the diversity.

The DC steady E-field is a state of composite insulation in the converter transformer outlet barrier system. The electrical properties of insulating material are both function of electric stress and temperature, thus, changes of electrical parameters due to temperature gradient will affect the DC steady E-field distribution of composite insulation structure. Based on this, to accurately simulate DC steady E-field of composite insulation structure with temperature gradient, this paper applied nonlinear finite element method to the coupling analysis of these two affecting factors. Firstly, relationship between electrical parameters of insulation materials and temperature, electrical stress was investigated. Then, the DC steady E-field calculation method with nonlinear finite element was proposed and verified by the simple coaxial insulation structure model. Finally, 2D simulation model of barrier system was established to simulate and analyze the DC steady E-field considering nonlinear characteristics of materials. The results show that the results of traditional simulation are quite different from those when considering material nonlinearity. The nonlinear finite element method proposed in this paper and the calculation results provide references for the design of converter transformer outlet barrier system.

In this paper, a new explicit time integration method for transient heat conduction analysis is proposed based on the uniform trigonometric B-spline function. The algorithmic calculation procedure for solving the heat conduction problem is given. The influence of algorithm parameters on accuracy and stability is determined by theoretical analysis and numerical experiments. With adjustable parameters, the proposed method can obtain high-order calculation accuracy and a large stability region. The local truncation error analysis of transient heat conduction shows that the proposed method has at least second-order accuracy. The numerical examples verify the effectiveness of the proposed method for linear and nonlinear heat conduction problems.

Transient heat-conduction solutions are used to determine the thermal characteristics of fluid flowing in circular conduits, annuli, and between parallel plates. Jaeger’s method of deriving the time lag for heat conduction in composite slabs (herewith extended to include composite cylinders) reduces the problem to a series of arithmetical calculations. Numerical results are presented for flow between parallel plates with the following boundary conditions: Constant heat rate, linear wall-temperature variation, and constant wall temperature at one of the external surfaces with constant heat rate, no heat transfer, or zero temperature at the other surface. Some solutions are extended to account for external wall resistance, and thermal entry lengths are evaluated for fluids with high or low Prandtl numbers.

This paper proposes an efficient numerical method for transient heat conduction in a quasi-periodic structure with nonlinear defects. According to the physical features of transient heat conduction, a quasi-superposition principle for transient heat conduction in a quasi-periodic structure with nonlinear defects is presented, and then a new method is developed to separate the above nonlinear problem to be solved into a linear problem of a perfect periodic structure and nonlinear problems of some small-scale structures with defects. As the scale of nonlinear problem to be solved is significantly reduced and low computational resource is required, outstanding efficiency is achieved. Finally, a numerical example shows that the proposed method is effective and accurate.

A method for static aeroelastic trim analysis of a flexible aircraft with large deformations has been presented in this paper, which considers the geometric nonlinearity of the structure and the nonplanar effects of aerodynamics. A nonplanar vortex lattice method is used to compute the nonplanar aerodynamics. The nonlinear finite element method is introduced to consider the structural geometric nonlinearity. Moreover, the surface spline method is used for structure/aerodynamics coupling. Finally, by combining the equilibrium equations of rigid motions of the deformed aircraft, the nonlinear trim problem of the flexible aircraft is solved by iterative solution method. For instance, the longitudinal trim analysis of a flexible aircraft with large-aspect-ratio wings is carried out by both the nonlinear method presented and the linear method of MSC Flightloads. Results obtained by these two methods are compared, and it is indicated that the results agree with each other when the deformation is small. However, because the linear method of static aeroelastic analysis does not consider the nonplanar aerodynamic effects or structural geometric nonlinearity, it is not applicable as the deformations increase. Whereas the nonlinear method presented could solve the trim problem accurately, even the deformations are large, which makes the nonlinear method suitable for rapid and efficient analysis in engineering practice..

The fully ceramic microencapsulated (FCM) fuel, one of the accident tolerant fuel (ATF) concepts, consists of TRISO particles randomly dispersed in SiC matrix. This high heterogeneity in compositions leads to difficulty in explicit thermal calculation of such a fuel. For thermal analysis of a fuel element in very high temperature reactors (VHTRs) which has a similar configuration to the FCM fuel, a two-temperature homogenized model was proposed by the authors. The model was developed using particle transport Monte Carlo method for heat conduction problems. It gives more realistic temperature profiles and provides the fuel-kernel and graphite temperatures separately. In this paper, we apply the two-temperature homogenized model to single-channel thermal analysis of the FCM fuel element for steady- and transient-states using 2-D FEM/1-D FDM hybrid method. The results of analyses are compared to those of conventional UO2 fuel having the same geometric dimension and operating conditions.

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

A singular integral method of numerical analysis for two-dimensional steady-state heat conduction problems with any combination of temperature, gradient, or convection boundary conditions is presented. Excellent agreement with the exact solution is illustrated for an example problem. The method is used to determine the solution for a fin bank with convection.

Data-Driven M-Vcut Topology Optimization Method for Heat Conduction Problem of Cellular Structure with Multiple Microstructure Prototypes

Homotopy method of fundamental solutions for solving nonlinear heat conduction problems