Reconstruction of the Surface Heat Flux for a Quasi-linear System of the Hyperbolic Type Heat-Conduction Equations

2015 ◽  
pp. 49-67
Author(s):  
Valentin Borukhov ◽  
Olga Kostyukova
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Linear System ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Hyperbolic Type ◽  
Quasi Linear System

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.

Inverse Heat Flux Problem in Quenching

2000 ◽  
Author(s):  
M. Khairul Alam ◽  
Rex J. Kuriger ◽  
Rong Zhong
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Temperature Data ◽  
Surface Heat ◽  
Measured Temperature ◽  
Inverse Heat Conduction ◽  
Quenching Process

Abstract The quenching process is an important heat treatment method used to improve material properties. However, the heat transfer during quenching is particularly difficult to analyze and predict. To collect temperature data, quench probes have been used in controlled quenching experiments. The process of determination of the heat flux at the surface from the measured temperature data is the Inverse Heat Conduction Problem (IHCP), which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching which is carried out to determine the surface heat flux history during a quenching process by an IHCP algorithm. The inverse heat conduction algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve is compared with experimental results.

Dynamic Calibration of a Coaxial Thermocouples for Short Duration Transient Measurements

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Rakesh Kumar ◽  
Niranjan Sahoo
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Heat Fluxes ◽  
Dynamic Calibration ◽  
One Dimensional ◽  
Surface Heat Fluxes ◽  
Heat Loads

Coaxial thermocouple sensors are suitable for measuring highly transient surface heat fluxes because the response times of these sensors are very small (∼0.1 ms). These robust sensors have the flexibility of mounting them directly on the surface of any geometry. So, they have been routinely used in ground-based impulse facilities as temperature sensors where rapid changes in heat loads are expected on aerodynamic models. Subsequently, the surface heat fluxes are predicted from the transient temperatures by appropriate one-dimensional heat conduction modeling for semi-infinite body. In this backdrop, the purpose of this work is to design and fabricate K-type coaxial thermocouples in-house and calibrate them under similar nature of heat loads by using simple laboratory instruments. Here, two methods of dynamic calibration of coaxial thermocouples have been discussed, where the known step loads are applied through radiation and conduction modes of heat transfer. Using appropriate one dimensional heat conduction modeling, the surface heat fluxes are predicted from the measured temperature histories and subsequently compared with the input heat loads. The recovery of surface heat flux from laser based calibration experiment under-predicts by 4% from its true input heat load. Similarly, recovery of surface heat flux from the conduction mode calibration experiments under-predicts 6% from its true input value. Further, finite-element based numerical study is performed on the coaxial thermocouple model to obtain surface temperatures with same heat loads as used in the experiments. The recovery of surface temperatures from finite element simulation is achieved within an accuracy of ±0.3% from the experiment.

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.

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