Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes

1960 ◽  
Vol 82 (1) ◽  
pp. 20-25 ◽  
Author(s):  
G. Stolz
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Surface Heat Flux ◽  
Direct Problem ◽  
Numerical Solutions ◽  
Superposition Principle ◽  
Surface Heat ◽  
Numerical Inversion

Numerical methods are presented for solving an inverse problem of heat conduction: Given an interior temperature versus time, find the surface heat flux versus time. The analysis is developed specifically for spheres; it applies to other simple shapes. The system is treated as linear, permitting use of the superposition principle. The essence of the method is the numerical inversion of a suitable direct problem: Given a surface heat flux versus time, find an interior temperature versus time. Care is required in selecting a time spacing for, if it is chosen too small in relation to the conditions, undesirable oscillation results. Simplifying suggestions are presented, and the use of the methods are illustrated by examples.

scholarly journals Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Beck’s Second Method

1980 ◽  
Vol 102 (2) ◽  
pp. 168-176 ◽  
Author(s):  
B. R. Bass
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Finite Element ◽  
Heat Conduction ◽  
Interior Point ◽  
Surface Heat Flux ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Surface Heat ◽  
Inverse Heat Conduction

The calculation of the surface temperature and surface heat flux from a measured temperature history at an interior point of a body is identified in the literature as the inverse heat conduction problem. This paper presents, to the author’s knowledge, the first application of a solution technique for the inverse problem that utilizes a finite element heat conduction model and Beck’s nonlinear estimation procedure. The technique is applicable to the one-dimensional nonlinear model with temperature-dependent thermophysical properties. The formulation is applied first to a numerical example with a known solution. The example treated is that of a periodic heat flux imposed on the surface of a rod. The computed surface heat flux is compared with the imposed heat flux to evaluate the performance of the technique in solving the inverse problem. Finally, the technique is applied to an experimentally determined temperature transient taken from an interior point of an electrically-heated composite rod. The results are compared with those obtained by applying a finite difference inverse technique to the same data.

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.

A Near Real-Time Solution Approach for Surface Heat Flux Estimation in One Dimensional Inverse Heat Conduction Problems With Moving Boundary

2019 ◽  
Author(s):  
Obinna Uyanna ◽  
Hamidreza Najafi
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Real Time ◽  
Surface Heat Flux ◽  
Moving Boundary ◽  
Surface Heat ◽  
Inverse Heat Conduction ◽  
Heat Flux Estimation ◽  
Flux Estimation ◽  
Inverse Heat Conduction Problems

Abstract Developing accurate and efficient solutions for inverse heat conduction problems allows advancements in the heat flux measurement techniques for many applications. In the present paper, a one-dimensional medium with a moving boundary is considered. It is assumed that two thermocouples are used to measure temperature at two locations within the medium while the front boundary is moving towards the back surface. Determining surface heat flux using measured temperature data is an inverse heat conduction problem. A filter based Tikhonov regularization method is used to develop a solution for this problem. Filter coefficients are calculated for various thicknesses of the medium. It is demonstrated that the filter coefficients can be interpolated to calculate the appropriate values for each thickness while it is continuously moving at a known rate. The use of filter method allows near real-time heat flux estimation. The developed solution is validated through several numerical test cases including a test case for a moving boundary in a medium modeled in COMSOL. It is shown that the proposed solution can effectively estimate the surface heat flux on the moving boundary in a near real-time fashion.

Surface heat transfer coefficient measurement by immersed temperature sensor and inverse modelling

2016 ◽  
Vol 83 (11) ◽  
Author(s):  
Mirko Javurek ◽  
Andreas Mittermair
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Flux Density ◽  
Temperature Sensor ◽  
Surface Heat Flux ◽  
Heat Flux Density ◽  
Surface Heat ◽  
Problem Solution ◽  
Inverse Problem Solution

AbstractA transient surface heating or cooling process of a solid is considered. A procedure for the determination of surface temperature and surface heat flux density during such a process is presented using a submersed temperature sensor in the solid. From this measured temperature the surface temperature and surface heat flux density are calculated by inverse process modelling. This method is prone to errors since measurement errors are amplified in the inverse process modelling and can thus easily become unacceptably large. The LSQR regularisation algorithm is optimised for fast performance as well as less memory requirement and applied to the inverse problem solution. The proposed method allows to simulate an experimental setup and to determine the accuracy of the results gained from the simulated experiment. This is essential for the determination of the accuracy of a planned or existing test facility. The influence of process parameters like sensor depth, sensor noise level, sampling rate, heat flux density amplitude and cooling/heating process duration is investigated. In most cases it is very important to carefully adjust the process parameters in order to obtain reliable and accurate results. Additionally the proper selection of the regularisation parameter required for the inverse problem solution is analysed.

scholarly journals A note on the free convection boundary layer on a vertical surface with prescribed heat flux at small Prandtl number

1992 ◽  
Vol 15 (3) ◽  
pp. 605-608
Author(s):  
J. H. Merkin ◽  
V. Kumaran
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Heat Flux ◽  
Numerical Solutions ◽  
Vertical Surface ◽  
Surface Heat ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Free Convection Boundary Layer

It is shown that for a particular case of the surface heat flux the equations for small Prandtl number have simple analytical solutions. These are presented and compared with numerical solutions of the general equations.

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