Exact Solution of Heat Conduction in Composite Materials and Application to Inverse Problems

1998 ◽  
Vol 120 (3) ◽  
pp. 592-599 ◽  
Author(s):  
C. Aviles-Ramos ◽  
A. Haji-Sheikh ◽  
J. V. Beck
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Composite Materials ◽  
High Speed ◽  
Series Solution ◽  
Auxiliary Function ◽  
Inverse Heat Conduction ◽  
High Temperature Materials ◽  
Nonhomogeneous Boundary ◽  
High Mach

Calculation of temperature in high-temperature materials is of current interest to engineers, e.g., the aerospace industry encounters cooling problems in aircraft skins during the flight of high-speed air vehicles and in high-Mach-number reentry of spacecraft. In general, numerical techniques are used to deal with conduction in composite materials. This study uses the exact series solution to predict the temperature distribution in a two-layer body: one orthotropic and one isotropic. Often the exact series solution contains an inherent singularity at the surface that makes the computation of the heat flux difficult. This singularity is removed by introducing a differentiable auxiliary function that satisfies the nonhomogeneous boundary conditions, Finally, an inverse heat conduction technique is used to predict surface temperature and/or heat flux.

Efficient Numerical Solution of Inverse Heat Conduction Problems

1995 ◽  
Author(s):  
Hans-Jürgen Reinhardt ◽  
Dinh Nho Hao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Stationary Point ◽  
Forthcoming Paper ◽  
Inverse Heat Conduction ◽  
Piecewise Constant ◽  
Numerical Tests ◽  
Inverse Heat Conduction Problems ◽  
Special Case

Abstract In this contribution we propose new numerical methods for solving inverse heat conduction problems. The methods are constructed by considering the desired heat flux at the boundary as piecewise constant (in time) and then deriving an explicit expression for the solution of the equation for a stationary point of the minimizing functional. In a very special case the well-known Beck method is obtained. For the time being, numerical tests could not be included in this contribution but will be presented in a forthcoming paper.

A New Integral Equation for Heat Flux in Inverse Heat Conduction

1966 ◽  
Vol 88 (3) ◽  
pp. 327-328 ◽  
Author(s):  
L. I. Deverall ◽  
R. S. Channapragada
Keyword(s):  
Heat Flux ◽  
Integral Equation ◽  
Heat Conduction ◽  
Inverse Heat Conduction

Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Discrete Point ◽  
Element Algorithm

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.

Inverse heat conduction modeling to predict heat flux in a hollow cylindrical tube having irregular cross-sections

2018 ◽  
Vol 128 ◽  
pp. 1310-1321 ◽  
Author(s):  
Jung-Hun Noh ◽  
Dong-Bin Kwak ◽  
Ki-Beom Kim ◽  
Ki-Up Cha ◽  
Se-Jin Yook
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cross Sections ◽  
Cylindrical Tube ◽  
Inverse Heat Conduction

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

Applying Neural Networks to the Solution of the Inverse Heat Conduction Problem in a Gun Barrel

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Y. Hwang ◽  
S. Deng
Keyword(s):  
Neural Network ◽  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Nonlinear Function ◽  
Inverse Heat Conduction ◽  
Unknown Parameters ◽  
Acceptable Error ◽  
Gun Barrel ◽  
Inverse Heat Conduction Problems

The primary cause of gun barrel erosion is the heat generated by the shell as its travels along the barrel. Therefore, calculating the heat flux input to the gun bore is very important when investigating wear problems in the gun barrel and examining its thermomechanical properties. This paper employs the continuous-time analog Hopfield neural network (CHNN) to compute the temperature distribution in various forward heat conduction problems. An efficient technique is then proposed for the solution of inverse heat conduction problems using a three-layered backpropagation neural network (BPN). The weak generalization capacity of BPN networks when applied to the solution of nonlinear function approximations is improved by employing the Bayesian regularization algorithm. The CHNN scheme is used to calculate the temperature in a 155mm gun barrel and the trained BPN is then used to estimate the heat flux of the inner surface of the barrel. The results show that the proposed neural network analysis method successfully solves forward heat conduction problems and is capable of predicting the unknown parameters in inverse problems with an acceptable error.

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