SOLUTION OF AN INVERSE PROBLEM TO DETERMINE HEAT SOURCE STRENGTH AND LOCATION

2017 ◽  
Author(s):  
Ardeshir Bangian Tabrizi ◽  
Yogesh Jaluria
Keyword(s):  
Inverse Problem ◽  
Heat Source ◽  
Source Strength

scholarly journals Determination of a time-dependent heat source under not strengthened regular boundary and integral overdetermination conditions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 809-814 ◽  
Author(s):  
Makhmud Sadybekov ◽  
Gulaiym Oralsyn ◽  
Mansur Ismailov
Keyword(s):  
Inverse Problem ◽  
Heat Source ◽  
Input Data ◽  
Nonlocal Boundary ◽  
Fourier Method ◽  
Time Dependent ◽  
Regular Boundary ◽  
Associated Functions ◽  
Integral Overdetermination

We investigate an inverse problem of finding a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is not complete. But the system of eigen- and associated functions forming a basis. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method.

Inverse Heat Transfer Study of a Power Transmission Line Tower Foundation

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Daqian Zhang ◽  
Xili Duan
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Thermal Effect ◽  
Power Transmission ◽  
Temperature Fields ◽  
Heat Transfer Analysis ◽  
Source Strength ◽  
Inverse Heat Transfer ◽  
Tower Foundation ◽  
Transfer Models

Abstract In some northern regions, power transmission lines are built with metal tower footings buried in the permafrost. With a high thermal conductivity, the tower footing has a significant thermal effect on the foundation and the nearby permafrost. Heat transfer models were previously developed to predict the thermal effect with line heat source assumptions, without knowing the exact spatial distribution and temporal variation of the heat source strength. This limited the accuracy of these heat transfer models. In this work, an inverse heat transfer method (IHTM) based on dynamic matrix control (DMC) theory is developed to better estimate the heat source strength representing the tower footing. The methodology is validated with numerical simulations and experimental data. It is found that the distribution of heat source varies spatially and temporally in a more complicated way than what was assumed in previous studies. The inversed heat source is then used to reconstruct the temperature fields in a tower foundation, which provides more accurate heat transfer analysis for design and maintenance of the foundation.

Identification of thermal conductivities by temperature gradient profiles: One‐dimensional steady flow

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 643-653 ◽  
Author(s):  
G. Ponzini ◽  
G. Crosta ◽  
M. Giudici
Keyword(s):  
Inverse Problem ◽  
Temperature Gradient ◽  
Heat Source ◽  
Multiplicative Noise ◽  
Central Italy ◽  
Admissible Solution ◽  
Stability Estimates ◽  
Source Terms ◽  
One Dimensional ◽  
Thermal Conductivities

The comparison model method (CMM) is applied to the identification of spatially varying thermal conductivity in a one‐dimensional domain. This method deals with the discretized steady‐state heat equation written at the nodes of a lattice, a lattice which models a stack of plane parallel layers. The required data are temperature gradient and heat source (or sink) values. The unknowns of this inverse problem are not nodal values but internode thermal conductivities, which appear in the node heat balance equation. The conductivities, e.g., the solutions to the inverse problem obtained by the CMM, are a one‐parameter family. In order to achieve uniqueness (which coincides with identifiability in this case), a suitable value of this parameter must be found. To this end we consider (1) parameterization, i.e., introducing equality constraints between the unknown coefficients, (2) the use of two data sets at least in a subdomain, and (3) self‐identifiability. Each of these items formally translates the available a priori information about the system, e.g., geophysical properties of the layers. Under the assumption that an admissible solution exists, we evaluate the effects on the solution of two types of data noise: additive noise affecting temperature and a kind of multiplicative noise affecting heat‐source terms. In the numerical examples we provide, parameterization is combined with the CMM in order to obtain the unique solution to a test inverse problem, the geophysical data of which come from a well drilled across Tertiary layers in central Italy. Finally, we consider data perturbed by pseudorandom noise. More precisely, we add noise to temperature gradients and obtain stability estimates which correctly predict the numerical results. In particular, if the layers where the parameterization constraint applies contain a strong source term (e.g., due to flowing water), the solution is relatively insensitive to noise. Also, for multiplicative noise affecting heat‐source terms, theoretical stability predictions are confirmed numerically. The main advantage of the CMM is its simple algebraic formulation. Its implementation in the field by means of a pocket calculator allows both a consistency check on the data being collected and estimates of the unknown values of conductivity.

scholarly journals Thermal control system based on ant colony algorithm

2021 ◽  
Vol 25 (4 Part B) ◽  
pp. 3179-3189
Author(s):  
Ran Zhang ◽  
Yan Zhou
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Source ◽  
Ant Colony Algorithm ◽  
Temperature Curve ◽  
Information Value ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Measuring Point ◽  
Source Seeking

In order to improve the accuracy and speed of solving the inverse problem of source-seeking heat conduction, the paper proposes a correlation-based ant colony optimization algorithm for the inverse problem of source-seeking heat conduction based on the characteristics of the influence of the heat source position on the boundary temperature distribution in the heat conduction problem. This method is used to construct the corresponding heuristic information value for each co-ordinate of the heat source location, which can reflect the degree of similarity between the temperature curve of the calculated measuring point and the temperature curve of the real measuring point, namely the correlation degree. The ant colony optimization algorithm the medium path selection mechanism and the structure of the objective function have been improved. The paper replaces the actual experiment with numerical calculation obtain the temperature of the measuring point, and performs computer programming experiment on the inverse problem. The calculation results show that the calibration method of this heuristic information value and the objective function the construction method can distinguish the quality of the path well, thereby increasing the speed of the ant colony converging to the best path. The computational efficiency is improved by 18-60% compared with the ant colony algorithm that does not consider the correlation.

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