Correcting lateral heat conduction effect in image-based heat flux measurements as an inverse problem

2011 ◽  
Vol 54 (5-6) ◽  
pp. 1244-1258 ◽  
Author(s):  
Tianshu Liu ◽  
Bo Wang ◽  
Justin Rubal ◽  
John P. Sullivan
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Flux Measurements ◽  
Lateral Heat

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.

scholarly journals IDENTIFICATION OF MEMORY KERNELS IN HEAT FLOW MEASURING HEAT FLUX AT THE ENDS OF THE BAR

2010 ◽  
Vol 15 (4) ◽  
pp. 473-490 ◽  
Author(s):  
Enno Pais
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Flow ◽  
Boundary Conditions ◽  
Internal Energy ◽  
Existence And Uniqueness ◽  
Financial Support ◽  
Thermal Memory ◽  
Flux Measurements ◽  
Uniqueness Of A Solution

An inverse problem to determine time‐ and space‐dependent relaxation kernels of internal energy and heat flux with first kind boundary conditions by means of heat flux measurements is considered. The case when observations of the heat flux are made at the ends of the bar with thermal memory was not studied before. Existence and uniqueness of a solution to the inverse problem are proved. The financial support of Estonian Science Foundation is gratefully acknowledged (Grant nr. 7728).

The Inverse Problem in Transient Heat Conduction

1964 ◽  
Vol 31 (3) ◽  
pp. 369-375 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh ◽  
T. S. Lundgren
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Calculation ◽  
Initial Temperature ◽  
Transient Heat Conduction ◽  
Analytical Treatment ◽  
Initial Temperature Distribution ◽  
Plane Slab ◽  
Long Cylinder

A general theory is devised for determining the temperature and heat flux at the surface of a solid when the temperature at an interior location is a prescribed function of time. The theory is able to accommodate an initial temperature distribution which varies arbitrarily with position throughout the solid. Detailed analytical treatment is extended to the sphere, the plane slab, and the long cylinder; and it is additionally shown that the semi-infinite solid is a particular case of the general formulation. The accuracy of the method is demonstrated by a numerical example. In addition, a numerical calculation procedure is devised which appears to provide smooth, nonoscillatory results.

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.

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