Estimation of Time-Varying Heat Flux for One-Dimensional Heat Conduction Problem by Hybrid Inverse Method

2019 ◽  
pp. 215-224
Author(s):  
Sanil Shah ◽  
Ajit Kumar Parwani
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Inverse Method ◽  
Heat Conduction Problem ◽  
Time Varying ◽  
One Dimensional ◽  
Estimation Of Time

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.

An Inverse Method to Determine Boundary Temperature and Heat Flux for a 2D Steady State Heat Conduction Problem

2008 ◽  
Author(s):  
Guangxu Yu ◽  
Pihua Wen ◽  
Huasheng Wang ◽  
John W. Rose
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Inverse Method ◽  
Heat Conduction Problem ◽  
Computing Time ◽  
Principle Of Superposition ◽  
Local Boundary ◽  
Boundary Temperature ◽  
Multiple Materials ◽  
Steady State Heat

Inverse determination of temperature and heat flux on an inaccessible surface of a solid has been widely employed in engineering and research. In this paper a new inverse method was used to predict local boundary temperature and heat flux distributions for a 2D steady heat conduction problem based on temperature measurements at interior wall sample points. The method is a non-iterative meshless boundary allocation method (BAM) using the principle of superposition for linear problems. A case study showed that the BAM method predicts the boundary temperature and heat flux with about the same accuracy as Beck’s function specified method but uses less computing time. Error analysis of thermocouple position and measurement was also carried out. More difficult problems such as those with multiple materials and non-rectangular geometries can also be treated by BAM.

Comparative Assessment of the Finite Difference, Finite Element, and Finite Volume Methods for a Benchmark One-Dimensional Steady-State Heat Conduction Problem

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Energy Conservation ◽  
Heat Conduction Problem ◽  
Mesh Size ◽  
The Other ◽  
One Dimensional ◽  
Steady State Heat

The finite difference (FD), finite element (FE), and finite volume (FV) methods are critically assessed by comparing the solutions produced by the three methods for a simple one-dimensional steady-state heat conduction problem with heat generation. Three issues are assessed: (1) accuracy of temperature, (2) accuracy of heat flux, and (3) satisfaction of global energy conservation. It is found that if the order of accuracy of the numerical discretization schemes is the same (central difference for FD and FV, linear basis functions for FE), the accuracy of the temperature produced by the three methods is similar, except close to the boundaries where the FV method outshines the other two methods. Consequently, the FV method is found to predict more accurate heat fluxes at the boundaries compared to the other two methods and is found to be the only method that guarantees both local and global conservation of energy irrespective of mesh size. The FD and FE methods both violate energy conservation, and the degree to which energy conservation is violated is found to be mesh size dependent. Furthermore, it is shown that in the case of prescribed heat flux (Neumann) and Newton cooling (Robin) boundary conditions, the accuracy of the FD method depends in large part on how the boundary condition is implemented. If the boundary condition and the governing equation are both satisfied at the boundary, the predicted temperatures are more accurate than in the case where only the boundary condition is satisfied.

scholarly journals Analysis of One Dimensional Inverse Heat Conduction Problem : A Review

2012 ◽  
pp. 126-131
Author(s):  
Rakesh Kumar ◽  
Jayesh. P ◽  
Niranjan Sahoo
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Change ◽  
Surface Heat Flux ◽  
Working Condition ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Surface Heat ◽  
Inverse Heat Conduction ◽  
One Dimensional

A procedure to solve inverse heat conduction problem (IHCP) is to derive surface heat flux and temperature from temperature change inside a solid. The method proves to be very useful and powerful when a direct measurement of surface heat flux and temperature is difficult, owing to several working condition. The literature reviewed here discussion one dimensional inverse heat conduction problem. Procedure, criteria, methods and important results of other investigation are briefly discussed.

Estimation of heat flux in one-dimensional inverse heat conduction problem

2007 ◽  
Vol 2 ◽  
pp. 455-464 ◽  
Author(s):  
V. Soti ◽  
Y. Ahmadizadeh ◽  
R. Pourgholi ◽  
M. Ebrahimi
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
One Dimensional

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

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