scholarly journals Stability and Resolution in Thermal Imaging

1995 ◽  
Author(s):  
Kurt Bryan ◽  
Lester F. Caudill
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Thermal Imaging ◽  
Exterior Boundary ◽  
Inversion Procedure ◽  
Material Sample ◽  
The Stability

Abstract This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample’s exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type

2020 ◽  
Vol 28 (1) ◽  
pp. 43-52
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
Zhanna Dmitrievna Totieva
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equations ◽  
Stability Estimate ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Weighted Norms ◽  
The Stability ◽  
The One ◽  
Global Unique Solvability

AbstractThe integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained.

scholarly journals Solution of inverse heat conduction equation with the use of Chebyshev polynomials

2016 ◽  
Vol 37 (4) ◽  
pp. 73-88 ◽  
Author(s):  
Magda Joachimiak ◽  
Andrzej Frąckowiak ◽  
Michał Ciałkowski
Keyword(s):  
Inverse Problem ◽  
Chebyshev Polynomials ◽  
Direct Problem ◽  
Least Square Method ◽  
Least Square ◽  
Random Disturbance ◽  
Inverse Heat Conduction ◽  
Chebyshev Nodes ◽  
The Difference ◽  
The Stability

AbstractA direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.

Stability and Enhancement of Boiling in Microchannels

2011 ◽  
Author(s):  
A. E. Bergles
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Critical Heat Flux ◽  
High Heat ◽  
Heat Fluxes ◽  
Transfer Enhancement ◽  
The Past ◽  
The Stability ◽  
Saturated Boiling ◽  
Microelectronic Components

During the past 20 years, there has been intense worldwide interest in microchannel heat exchangers, particularly for cooling of microelectronic components. Saturated boiling of the coolant is usually indicated in order to accommodate high heat fluxes and to have uniformity of temperature. However, boiling is accompanied by several instabilities, the most severe of which can sharply limit the maximum, or critical, heat flux. These stability phenomena are reviewed, and recent studies will be discussed. Elevation of the critical heat flux will be discussed within the context of heat transfer enhancement. Means to improve the stability of boiling and the enhancement of boiling heat transfer, in general, are discussed.

An Inverse Determination of Unsteady Heat Fluxes Using a Network Simulation Method

2003 ◽  
Vol 125 (6) ◽  
pp. 1178-1183 ◽  
Author(s):  
F. Alhama ◽  
J. Zueco and ◽  
C. F. Gonza´lez Ferna´ndez
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Input Data ◽  
Heat Conduction Problem ◽  
Network Simulation ◽  
Simulation Method ◽  
Heat Fluxes ◽  
Incident Heat Flux ◽  
Network Simulation Method

This work addresses unsteady heat conduction in a plane wall subjected to a time-variable incident heat flux. Three different types of flux are studied (sinusoidal, triangular and step waveforms) and constant thermal properties are assumed for simplicity. First, the direct heat conduction problem is solved using the Network Simulation Method (NSM) and the collection of temperatures obtained at given instants is modified by introducing a random error. The resulting temperatures act as the input data for the inverse problem, which is also solved by a sequential approach using the NSM in a simple way. The solution is a continuous piece-wise function obtained step by step by minimizing the classical functional that compares the above input data with those obtained from the solution of the inverse problem. No prior information is used for the functional forms of the unknown heat flux. A piece-wise linear stretches of variable slope and length is used for each of the stretches of the solution. The sensitivity of the functional versus the slope of the line, at each step, is acceptable and the complete piece-wise solution is very close to the exact incident heat flux in all of the mentioned waveforms.

Sign in / Sign up

Export Citation Format

Share Document