Numerical Methods for Inverse Problem of Heat Conduction with Unknown Boundary Based on Variational Principles with Variable Domain

In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple-mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are firstestablished.Based on them,two methods of solution—generalized Ritz method and variable-domain FEM—both capable of handling problems with unknown boundaries,are suggested.Then,three sample numericalexamples have been tested.The computational process is quite stable,and the results are encouraging.Thisvariational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems inmathematical physics.     

A Novel Variational Formulation of Inverse Problem of Heat Conduction with Free Boundary on an Image

ＡＮｏｖｅｌＶａｒｉａｔｉｏｎａｌＦｏｒｍｕｌａｔｉｏｎｏｆＩｎｖｅｒｓｅＰｒｏｂｌｅｍｏｆＨｅａｔＣｏｎｄｕｃｔｉｏｎｗｉｔｈＦｒｅｅＢｏｕｎｄａｒｙｏｎａｎＩｍａｇｅＰｌａｎｅＧａｏ－ＬｉａｎＬｉｕ（ＳｈａｎｇｈａｉＩｎｓｔｉｔｕｔｅｏｆＭｅｃｈ...     

Solution of the Stationary 2D Inverse Heat Conduction Problem by Treffetz Method

The paper presents analysis of a solution of Laplace equation with the use of FEM harmonic basic functions. The essence of the problem is aimed at presenting an approximate solution based on possibly large finite element. Introduction of harmonic functions allows to reduce the order of numerical integration as compared to a classical Finite Element Method. Numerical calculations conform good efficiency of the use of basic harmonic functions for resolving direct and inverse problems of stationary heat conduction.Further part of the paper shows the use of basic harmonic functions for solving Poisson's equation and for drawing up a complete system of biharmonic and polyharmonic basic functions     

New Type of Basic Functions of FEM in Application to Solution of Inverse Heat Conduction Problem

The work presents the application of heat polynomials for solving an inverse problem. The heat polynomials form the Treffetz Method for non-stationary heat conduction problem. They have been used as base functions in Finite Element Method. Application of heat polynomials permits to reduce the order of numerical integration as compared to the classical Finite Element Method with formulation of the matrix of system of equations.     

Inverse Radiation Problem of Boundary Incident Radiation Heat Flux in Semitransparent Planar Slab with Semitransparent Boundaries

INTRODUCTI0NInverseradiati0nproblemshavedefinedasubjectofinterestf0rthepast3Oyears0nsoandthereex-istsac0nsiderablebody0fknowledgesurroundingthesubjectthathasbeenextensivelyreviewedinaseries0fpapersbyM.C.rmick[1-4].Theyarecon-cernedwiththedeterminati0noftheradiativepr0p-ertiesandthetemperaturedistributionsofmediaus-ingvari0ustypesofradiationmeasurements.Despitetherelativelylargeinterestexpressedininverseradia-tionproblems,mostoftheworkfocusedontheinverseestimati0noftemperaturedistributions…     

DPL Model Analysis of Non—Fourier Heat Conduction Restricted by Continuous Boundary Interface

IntroductionAs widely known, the hahonal Fourier law isbased on a large quantity of regular heat transfer (i.e. thethermal bine scale is comparatively lOng and the heatflux density is comparatively small) experiments and it'sjust a phenomenological descriphon of regular thermalProcesses. The Fourier law itself mpes an infinitespeed of Propagation of thermal distUrbance, indicatingthat a local change in tempera~ causes aninstantaneous per'tUrbation in the temperatore at eachPOint in the medi…     

An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

Retrieval of parameters in a non-Fourier conduction and radiation heat transfer problem is reported. The direct problem is formulated using the lattice Boltzmann method (LBM) and the finite-volume method (FVM). The divergence of radiative heat flux is computed using the FVM, and the LBM formulation is employed to obtain the temperature field. In the inverse method, this temperature field is taken as exact. Simultaneous estimation of parameters, namely, the extinction coefficient and the conduction–radiation parameter, is done by minimizing the objective function. The genetic algorithm (GA) is used for this purpose. The accuracies of the estimated parameters are studied for the effects of measurement errors and genetic parameters such as the crossover and mutation probabilities, the population size, and the number of generations. The LBM-FVM in combination with GA has been found to provide a correct estimate of parameters.     

Analytical Solution of Coupled Laminar Heat-Mass Transfer in a Tube with Uniform Heat Flux

Analytical solution is obtained of coupled laminar heat-mass transfer in a tube with uniform heat flux. This corresponds to the case when a layer of sublimable material is coated on the inner surface of a tube with its outer surface heated by uniform heat flux and this coated material will sublime as gas flows throught the tube.     

Experimental and Numerical Investigation of Enhancement of Heat and Mass Transfer in Adsorbent Beds

ＥｘｐｅｒｉｍｅｎｔａｌａｎｄＮｕｍｅｒｉｃａｌＩｎｖｅｓｔｉｇａｔｉｏｎｏｆＥｎｈａｎｃｅｍｅｎｔｏｆＨｅａｔａｎｄＭａｓｓＴｒａｎｓｆｅｒｉｎＡｄｓｏｒｂｅｎｔＢｅｄｓＬｉｕＺｈｅｎｙａｎ；ＦｕＺｈｕｍａｎ；ＧｅＸｉｎｓｈｉ；ＳｕＹｕｅｈｏｎｇ；...     

Heat Transfer Characteristics of Laminar Flow in Internally Finned Tubes under Various Boundary Conditions

ＨｅａｔＴｒａｎｓｆｅｒＣｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＬａｍｉｎａｒＦｌｏｗｉｎＩｎｔｅｒｎａｌｌｙＦｉｎｎｅｄＴｕｂｅｓｕｎｄｅｒＶａｒｉｏｕｓＢｏｕｎｄａｒｙＣｏｎｄｉｔｉｏｎｓ￥Ｚｅ－ＮｉｎｇＷａｎｇ；Ｑｉａｎｇ－ＴａｉＺｈｏｕ（Ｄｅｐａｒ...     

A solution to the two‐dimensional inverse heat conduction problem

A simple method is developed in this paper to solve two‐dimensional nonlinear steady inverse heat conduction problems. The unknown boundary conditions can be numerically obtained by using the iteration and modification method. The effect of measurement errors of the wall temperature on the algorithm is numerically tested. The results prove that this method has the advantages of fast convergence, high precision, and good stability. The method is successfully applied to estimate the convective heat transfer coefficient in the case of a fluid flowing in an electrically heated helically coiled tube. © 2000 Scripta Technica, Heat Trans Asian Res, 29(2): 113–119, 2000     

Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction

This work presents an improved apparatus and a numerical approach to obtain the estimate of thermal diffusivity of complex materials. Transient thermal response at the axis of cylindrical sample is measured when boundary temperature is suddenly changed. Instead of assuming an ideal step temperature excitement, a measured temperature of a material boundary was employed. An iterative procedure, based on minimizing a sum of squares function with the Levenberg–Marquardt method, is used to solve the inverse problem. A graphical user interface is built to enable easy use of the inverse thermal diffusivity estimation method. The reference materials used to evaluate the method are Agar water gel, glycerol and Ottawa quartz sand.     

Application of the homotopy perturbation method for the solution of inverse heat conduction problem

This paper deals with an application of the homotopy perturbation method for the solution of inverse heat conduction problem. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of functions describing the temperature and heat flux on the boundary, when the temperature measurements in the domain are known. Examples illustrating discussed application and confirming utility of this method in such a type of problem was also presented.     

Analytical solution of the inverse unsteady wall heat conduction problem and experimental application

Based on the analytical solution of the unsteady heat conduction differential equation, a solution procedure is presented for the inverse unsteady wall heat conduction problem, i.e. for the calculation of the thermal properties of structural elements of existing buildings under real transient conditions, using on-site temperature measurements. Previous procedures, which were based on the finite-difference method, required a considerable number of temperature measurements in space and time within the wall. The advantage of the present analytical procedure is that it requires only two temperature measurements, apart from some information on the outdoor and indoor temperature variations. The two temperature measurements may be taken on the outdoor and indoor wall surfaces at the same time level, or on one of these surfaces at two different time levels. The proposed analytical procedure provides the values of the thermal conductivity and heat capacity of structural elements, and therefore it may be used in practice for ex post checking of the materials used by the constructor, or for load calculation when heating or cooling systems are to be installed in old buildings of unknown wall properties. Experimental examples are presented which show that the proposed analytical procedure may be applied in practice with very good accuracy.     

共轭梯度法求解竖直环隙间多孔介质的传热反问题

提出一种反演多孔介质热物性参数的一般数值模式。采用有限体积法对竖直环隙间多孔介质模型进行离散化,通过SIMPLE算法获得竖直环隙间多孔介质传热系统的温度场和流体的速度场。通过构建误差信息最小化函数,建立反演模型。利用共轭梯度法对单宗量和多宗量的多孔介质热物性参数进行了反演,并讨论了待反演参数的初始猜测值、温度测点数、温度测量误差等对反演结果的影响。     

Integral transform methods for inverse problem of heat conduction with known boundary of a thin rectangular object and its stresses

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D: a≤x≤a; b≤y≤b; 0≤z≤h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.     

Application of inverse solution in two‐dimensional heat conduction problem using Laplace transformation

An inverse solution has been explicitly derived for two‐dimensional heat conduction in cylindrical coordinates using the Laplace transformation. The applicability of the inverse solution is checked using the numerical temperatures with a normal random error calculated from the corresponding direct solution. For a gradual temperature change in a solid, the surface heat flux and temperature can be satisfactorily predicted, while for a rapid change in the temperature this method needs the help of a time partition method, in which the entire measurement time is split into several partitions. The solution with the time partitions is found to make an improvement in the prediction of the surface heat flux and temperature. It is found that the solution can be applied to experimental data, leading to good prediction. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 602–617, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10115     

Analysis and solution of the ill-posed inverse heat conduction problem

The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature and heat flux values on the surface. The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. A special solution procedure is developed for the one-dimensional case which replaces the heat conduction equation with an approximating hyperbolic equation. If viewed from a new perspective, where the roles of the spatial and time variables are interchanged, then an initial value problem for the damped wave equation is obtained. Since the formulation is well-posed, both analytic and numerical solution procedures are readily available. Sample calculations confirm that this approach produces consistent, reliable results for both linear and nonlinear problems.