Transient Heat Conduction Analysis Research Articles

Nonlinear Transient Heat Conduction Analysis for a Thick Hollow 2D-FGM Cylinder with Finite Length

In this study, the nonlinear transient heat conduction analysis has been developed for a hollow thick temperature-dependent two-dimensional functionally graded material (2D-FGM) cylinder subjected to the transient non-uniform axisymmetric thermal loads. In order to do this, the graded finite element method and quadratic Lagrange shape function together have been considered to improve the accuracy of the temperature distribution in two dimensions. Moreover, two new material models for 2D-FGM have been developed and compared with each other. Accordingly, it is demonstrated that the temperature-dependent material properties in 2D-FGM structure would lead to high nonlinear governing equations in addition to bringing about the material properties variation. The new material model and FE analysis have been validated by experimental results. Subsequently, time history of the temperatures and the effects of material properties distribution along two radial and axial directions as well as the effect of two material models on the temperature distribution have been taken into account. It is therefore presented that the variation of material properties in axial direction has significant effect on the temperature distribution, and thus, this would be important for the designers to take into consideration the new material model and 2D-FGM for thermal barrier components purposes.

Nonlinear transient heat conduction analysis of hollow thick temperature-dependent 2D-FGM cylinders with finite length using numerical method

Nonlinear transient heat conduction analysis is developed for hollow thick temperature-dependent 2D-FGM cylinders subjected to transient non-uniform axisymmetric thermal loads. It is demonstrated here that the temperature-dependency in addition to the material properties variation in the 2D- FGM would lead to highly nonlinear governing equations. To do this, the graded finite element method is employed to model the structures and a quadratic Lagrange shape function has been used to improve the accuracy of the temperature distribution for the two-dimensional heat conduction analysis. Furthermore, time variation of the temperatures and the effects of material distribution variability in two radial and axial directions and the temperature-dependency of the material properties on the temperature are discussed in detail. It is assumed that the material, geometry and volume fraction distribution are axisymmetric but not uniform along the axial direction. According to the results, the variation of the material properties in two dimensions has significant effect on temperature distribution; therefore, it gives more designing flexibility benefits to the designers to implement this kind of material for the thermal barriers purposes.

Formulation of Kansa's method in the frequency domain for the analysis of transient heat conduction

Purpose – A number of works have been published in the scientific literature proposing the solution of heat diffusion problems by first transforming the relevant partial differential equation to the frequency domain. The purpose of this paper is to present a mesh-free strategy to assess transient heat propagation in the frequency domain, also allowing incorporating initial non-zero conditions. Design/methodology/approach – The strategy followed here is based in Kansa's method, using the MQ RBF as a basis function. The resulting method is truly mesh-free, and does not require any domain or boundary integrals to be evaluated. The definition of good values for the free parameter of the MQ RBF is also addressed. Findings – The strategy was found to be accurate in the calculation of both frequency and time-domain responses. The time evolution of the temperature considering an initial non-uniform distribution of temperatures compared well with a standard time-marching algorithm, based on an implicit Crank-Nicholson implementation. It was possible to calculate frequency-dependent values for the free parameter of the radial basis function. Originality/value – As far as the authors are aware, previous implementations of the frequency domain heat transfer approach required domain integrals to be evaluated in order to implement non-zero initial conditions. This is totally avoided with the present formulation. Additionally, the method is truly mesh-free, accurate and does not require any element or background mesh to be defined.

Inverse analysis for transient thermal load identification and application to aerodynamic heating on atmospheric reentry capsule

A transient inverse heat conduction analysis enables the identification of the unknown boundary heat flux from finite number of temperature data obtained, e.g., in the high temperature structural tests or in the actual operation. Since the prediction of thermal load (heat flux) is difficult, the inverse analysis is expected to improve structural design of high temperature components. The present study develops a computational method of transient inverse heat conduction analysis. The developed code is applied to problems of a simple two-dimensional plate and of an atmospheric reentry capsule. Sequential Function Specification (SFS) method and Truncated Singular Value Decomposition (TSVD) are employed to improve the stability of the inverse analysis. Effects of these regularization methods are numerically discussed.

Parametric integral equations systems in 2D transient heat conduction analysis

Currently the most popular numerical methods used for solving transient heat conduction problems, finite element method (FEM) and boundary element method (BEM), have one fundamental defect – the necessity of discretizing the boundary or the domain. This problem escalates even more, when using an iterative process. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES), which do not require classical discretization of the boundary and the domain while being numerically solved. PIES method was previously used with success to solve steady-state problems. The purpose of this paper is to present PIES method for 2D transient heat conduction problems and present results obtained by solving few numerical examples. Accuracy and effectiveness of the method are shown in comparison with analytical solutions and FEM.

Finite block method for transient heat conduction analysis in functionally graded media

SUMMARYBased on the one‐dimensional differential matrix derived from the Lagrange series interpolation, the finite block method is proposed first time to solve both stationary and transient heat conduction problems of anisotropic and functionally graded materials. The main idea is to establish the first order one‐dimensional differential matrix constructed by using Lagrange series with uniformly distributed nodes. Then the higher order of derivative matrix for one‐dimensional problem is obtained. By introducing the mapping technique, a block of quadratic type is transformed from Cartesian coordinate (xyz) to normalised coordinate (ξης) with 8 seeds or 20 seeds for two or three dimensions. Then the differential matrices in physical domain are determined from that in normalised transformed coordinate system. In addition, the time dependent partial differential equations are analysed in the Laplace transformed domain, and the Durbin inversion method is used to determine the values in time domain. Illustrative two‐dimensional and three‐dimensional numerical examples are given, and comparisons have been made with analytical solutions. Copyright © 2014 John Wiley & Sons, Ltd.

A stochastic analysis of steady and transient heat conduction in random media using a homogenization approach

We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total number N. Both steady and transient solutions T are expressed in terms of the homogenized solution T∼ and its spatial derivatives T(x,t)=T∼+∑n=1∞Ln(x)∂nT∼/∂xn, where homogenized solution T∼ is obtained by solving the homogenized equation with effective thermal conductivity. Both mean and variance of stochastic solutions can be obtained analytically for K field consisting of independent identically distributed (i.i.d) random variables. The mean and variance of T are shown to be dependent only on the mean and variance of these i.i.d variables, not the particular form of probability distribution function of i.i.d variables. Variance of temperature field T can be separated into two contributions: the ensemble contribution (through the homogenized temperature T∼); and the configurational contribution (through the random variable Ln(x)). The configurational contribution is shown to be proportional to the local gradient of T∼. Large uncertainty of T field was found at locations with large gradient of T∼ due to the significant configurational contributions at these locations. Numerical simulations were implemented based on a direct Monte Carlo method and good agreement is obtained between numerical Monte Carlo results and the proposed stochastic analysis.

Transient heat conduction analysis of a cracked half-plane using dual-phase-lag theory

In this paper, the transient temperature field around a partially insulated crack in a half-plane is obtained by applying the dual-phase-lag heat conduction model. Fourier and Laplace transforms are applied and the heat conduction problem is reduced to solving a singular integral equation. The asymptotic fields near the crack tip are obtained in an explicit form and the intensity factors of temperature gradients are determined. Numerical results show that temperature overshooting phenomenon may occur due to the thermal disturbance of crack based on the dual-phase-lag model. The dual-phase-lag model parameters, the heat conductivity of the crack surfaces and the geometric size of the half-plane have significant influence on the dynamic temperature fields.

Multiphysics model of thermomechanical and helium-induced damage of tungsten during plasma heat transients

A combination of transient heating and bombardment by helium and hydrogen atoms has been experimentally proven to lead to severe surface and sub-surface damage. We developed a computational model to determine the relationship between the thermomechanical loading conditions and the onset of damage and failure of tungsten surfaces. The model is based on a thermoelasticity fracture damage approach that was developed using the phase field method. The model simulates the distribution of helium bubbles inside the grains and on grain boundaries using space-dependent rate theory. In addition, the model is coupled with a transient heat conduction analysis for temperature distributions inside the material. The results show the effects of helium bubbles on reducing tungsten surface energy. Further, a temperature gradient in the material equals to 10K/μm, resulted in deep cracks propagating from the tungsten surface.

An Unstructured Finite-Volume Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

An unstructured finite-volume time-domain method (UFVTDM) is developed to solve two-dimensional transient heat conduction in multilayer functionally graded materials (FGMs). A four-node quadrilateral grid and a three-node triangular grid are employed to deal with mixed-grid problems. The accuracy of the method is improved by treating the quadrilateral grid as a bilinear element with consideration of both the linear term and the constant term. The improvement is validated to be vital to avoid violent numerical oscillation when applying the method to heat point-source problems. The accuracy and capability of the UFVTDM are validated by numerical tests.

Transient heat conduction analysis of solids with small open-ended tubular cavities by boundary face method

Abstract This paper applies the boundary face method (BFM) to solve transient heat conduction problems for the first time. Rather than using a transformation scheme, a direct solution of the boundary integral equation (BIE) with time domain fundamental solution is performed in this application. To avoid the domain integrals, the boundary integral equation is solved by the time stepping convolution method. For problems on structures that contain a large number of open-ended tubular shaped cavities in small diameters, a curvilinear tube element is employed to approximate the variables on the cavity surface. Furthermore, to perform integration and boundary variable approximation on the end faces that are intersected by the tubular cavity, a triangular element with negative part is adopted. With the two types of specified elements, the BFM is implemented to solve transient heat conduction problems on structures with open-ended tubular shaped cavities of small size which are usually inconvenience in finite element implementations. Three numerical examples on different structures are presented to illustrate the validity and efficiency of the method.

Analysis of Transient Heat Conduction in a Hollow Cylinder Using Duhamel Theorem

The objective of this paper is to derive the mathematical model of two-dimensional heat conduction at the inner and outer surfaces of a hollow cylinder which are subjected to a time-dependent periodic boundary condition. The substance is assumed to be homogenous and isotropic with time-independent thermal properties. Duhamel’s theorem is used to solve the problem for the periodic boundary condition which is decomposed by Fourier series. In this paper, the effects of the temperature oscillation frequency on the boundaries, the variation of the hollow cylinder thickness, the length of the cylinder, the thermophysical properties at ambient conditions, and the cylinder involved in some dimensionless numbers are studied. The obtained temperature distribution has two main characteristics: the dimensionless amplitude (\(A\)) and the dimensionless phase difference (\(\varphi \)). These results are shown with respect to Biot and Fourier and some other important dimensionless numbers.

Taylor Series Numerical Method in Transient Heat Conduction Analysis

Taylor series numerical method (TSNM) is extended to the field of transient heat conduction. Theoretical description of TSNM for transient heat conduction problems is presented. Furthermore, the algorithm is realized and embedded in commercial software ANSYS®. If a lumped mass heat capacity matrix provided, the governing equation of transient heat conduction problems, which is a differential equation, will be solved by a series of recursion calculation of Taylor expanding coefficients. A typical transient heat conduction problem with analytical solution was discussed to verify the TSNM. At last, the TSNM is applied in the transient heat analysis of an all-solid fiber optic gyro (FOG).

10807 沸騰におけるミクロ液膜の形成機構と蒸発特性(OS6-1【熱流体工学のフロンティア(1)】)

The wall temperature under a boiling bubble in the mini-channel was measured at high speed with the MEMS thermal sensor. The surface heat flux was evaluated by a one-dimensional transient heat conduction analysis in the sensor substrate with the measured data as a surface boundary condition. The initial microlayer thickness was calculated from amount of heat transferred until the dryout of the heating wall. The calculated initial microlayer thickness was a few μm and was found to become thicker with a bubble forefront velocity. The non-dimensional initial microlayer thickness showed a correlation to Capillary number corresponding to the ratio of the viscous force and surface tension. Superheat of liquid-vapor interface was observed during the evaporation of the microlayer by the transient heat conduction analysis in the microlayer.

Non-Linear Large Deformation Kinetics of Polymeric Gel

The transient swelling process of polymeric gels is studied and a finite element model is introduced to simulate the phenomena based on existing hyperelastic theory for inhomogeneous swelling of gels and analogies made to transient heat conduction analysis. Examples of free swelling of a cube and a fixed cylinder were investigated, showing the highly non-linear deformation present during transition from the initial state to equilibrium.

Three-dimensional transient heat conduction analysis by Laplace transformation and multiple reciprocity boundary face method

In this paper, a new multiple reciprocity formulation is developed to solve the transient heat conduction problem. The time dependence of the problem is removed temporarily from the equations by the Laplace transform. The new formulation is derived from the modified Helmholtz equation in Laplace space (LS), in which the higher order fundamental solutions of this equation are firstly derived and used in multiple reciprocity method (MRM). Using the new formulation, the domain integrals can be converted into boundary integrals and several non-integral terms. Thus the main advantage of the boundary integral equations (BIE) method, avoiding the domain discretization, is fully preserved. The convergence speed of these higher order fundamental solutions is high, thus the infinite series of boundary integrals can be truncated by a small number of terms. To get accurate results in the real space with better efficiency, the Gaver-Wynn-Rho method is employed. And to integrate the geometrical modeling and the thermal analysis into a uniform platform, our method is implemented based on the framework of the boundary face method (BFM). Numerical examples show that our method is very efficient for transient heat conduction computation. The obtained results are accurate at both internal and boundary points. Our method outperforms most existing methods, especially concerning the results at early time steps.

An improved lumped analysis for transient heat conduction in different geometries with heat generation

This article deals with the analysis of transient one-dimensional heat conduction in both Cartesian and cylindrical geometry by employing the polynomial approximation method (PAM). Four different models such as specified heat flux for both slab and tube and heat generation in both slab and tube have been analyzed. The transient temperature is found to depend on various model parameters, namely, Biot number, heat source parameter and time. With the use of PAM, it has been possible to derive a unified relation for the transient thermal behavior of solid (slab and tube) with both internal generation and boundary heat flux. Present prediction is found to be in good agreement with other analytical results reported in the literature.

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB

Diffusion only, two dimensional heat conduction has been described on partial differential equation. Based on Finite Volume Method, Discretized algebraic Equation of partial differential equation have been deduced. different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulated.. Transient heat conduction analysis of infinite plate with uniform thickness and two dimensional rectangle region are realized by programming using MATLAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression, feasibility and stability of numerical method have been demonstrated by running result.

Two-Dimensional Inverse Transient Heat Conduction Analysis of Laminated Functionally Graded Circular Plates

A two-dimensional inverse transient heat conduction algorithm is developed to estimate the heat flux and convection heat transfer coefficient on the bottom (top) surface of the multilayered functionally graded (FG) circular plates using the measured temperature on their top (bottom) surface. The non-Fourier heat transfer, in conjunction with the layerwise-incremental differential quadrature method (LW-IDQM), is employed to accurately model the problem. The conjugate gradient method (CGM), coupled with the sensitivity and adjoint problems, are employed for the optimization procedure. The reliability and robustness of the presented approach is demonstrated by simulating the exact and noisy data through different examples.

Analysis of Transient Heat Conduction in a Hollow Sphere Using Duhamel Theorem

Analysis of Transient Heat Conduction in a Hollow Sphere Using Duhamel Theorem