Ill-posed Inverse Heat Conduction Problem Research Articles

Carbon/carbon high thickness shell for advanced space vehicles

The aim of this paper is to study a shell structure for space applications. The aim of the structure is to be reusable and thick. This first study will focus on thermal environment. Starting from a defined geometry, a prototype will be manufactured. Thermo-structural behavior of the structure will be analyzed by numerical analysis and tests. Thermal properties, such as thermal conductivity and heat capacity, will be studied by the use of the inverse method. A robust numerical approach, such as inverse method, is one of the best for this problem as many parameters concur for the determination of properties. Such approach permits to perform the parametric and structural identification of the model. These procedures are presented including both experimental investigation and methodical-numerical aspects. Special test equipment and the regularizing algorithm for solving the ill-posed inverse heat conduction problem are described. In the frame of thermal properties determination, a verification and prediction of thermocouple error will be performed. Developed in the frame of this work the experimental and theoretical methodology for complex data acquisition of unsteady thermal state of the prototype of shell structure is proposed.

Numerically solving twofold ill-posed inverse problems of heat equation by the adjoint Trefftz method

ABSTRACTThe inverse problem endowing with multiple unknown functions gradually becomes an important topic in the field of numerical heat transfer, and one fundamental problem is how to use limited minimal data to solve the inverse problem. With this in mind, in the present article we search the solution of a general inverse heat conduction problem when two boundary data on the space-time boundary are missing and recover two unknown temperature functions with the help of a few extra measurements of temperature data polluted by random noise. This twofold ill-posed inverse heat conduction problem is more difficult than the backward heat conduction problem and the sideways heat conduction problem, both with one unknown function to be recovered. Based on a stable adjoint Trefftz method, we develop a global boundary integral equation method, which together with the compatibility conditions and some measured data can be used to retrieve two unknown temperature functions. Several numerical examples demonstrate that the present method is effective and stable, even for those of strongly ill-posed ones under quite large noises.

Determination of the heat flux to the workpiece during dry turning by inverse methods

Reducing metal machining costs and harmful effects to the environment are the main benefits of dry machining compared to the application of cooling lubricants during machining processes. The abandonment of any lubricants is causing higher temperatures of workpiece, chip, and tool. Thus, the temperature gradient varies with time and space over the workpiece, causing dimensional deviations and profile defects due to thermal expansion and shrinking. The aim of this work is to determine the heat flux to the workpiece from experimental data. The temperatures of the workpiece were measured during an orthogonal turning process of carbon steel (AISI 1045). An analogous thermal model is used to solve the ill-posed inverse heat conduction problem by the sequential estimation method, introduced by Beck et al. (Inverse heat conduction, Wiley, New York, 1985) and for the evaluation of the results. The heat flux to the workpiece could be used in further work as a basic boundary condition in finite element simulations to find an alternative tool path, which compensate thermally induced deviations and profile defects of the workpiece. The heat flux to the workpiece is calculated for different cutting velocities, feed rates, and the influence of TiN-coatings on cemented carbide tools. Cutting parameters have been identified to minimize the heat load on the workpiece in general and therefore reduce errors due to dry machining.

Comparison of the Mollification and Wavelet Prefiltering of Temperature Data in an Ill-Posed Inverse Heat Conduction Problem, Application: Nonthermal Equilibrium Porous Medium

The mollification and wavelet prefiltering methods are employed in the ill-posed inverse heat conduction problem of heat flux estimation in a porous medium. The estimation of transient heat flux using the conjugate gradients method along with the adjoint differential equations has been carried out under a nonthermal equilibrium condition. The temperature sensor is located on the inactive surface of porous medium and the effects of the two already-mentioned prefiltering methods on the estimation of heat flux are studied for different noise levels. By smoothing the temperature data, the degree of difficulty of the estimation is reduced considerably. Comparison of the two filtering methods shows that a comparable improvement in performance can be achieved when using both filtering methods via mitigating the ill-posed nature of the problem. The performance of wavelet filter is somewhat superior to the mollification filter; however, the later can be implemented much more conveniently in a computer program.

Investigation of local heat transfer coefficients in plate heat exchangers with temperature oscillation IR thermography and CFD

A method for the measurement of local convective heat transfer coefficients from the outside of a heat-transferring wall has been developed. This method is contact-free and fluid independent, employing radiant heating by laser or halogen spotlights and an IR camera for surface temperature measurements; it allows for the rapid evaluation of the heat transfer coefficient distribution of sizable heat exchanger areas. The technique relies first on experimental data of the phase lag of the outer surface temperature response to periodic heating, and second on a simplified numerical model of the heat exchanger wall to compute the local heat transfer coefficients from the processed data. The IR temperature data processing includes an algorithm for temperature drift compensation, phase synchronization between the periodic heat flux and the measured temperatures, and Single Frequency Discrete Fourier Transformations. The ill-posed inverse heat conduction problem of deriving a surface map of heat transfer coefficients from the phase-lag data is solved with a complex number finite-difference method applied to the heat exchanger wall. The relation between the local and the mean heat transfer coefficients is illuminated, calculation procedures based on the thermal boundary conditions are given. The results from measurements on a plate heat exchanger are presented, along with measurements conducted on pipe flow for validation. The results show high-resolution surface maps of the heat transfer coefficients for a chevron-type plate for three turbulent Reynolds numbers, including a promising approach of visualizing the flow field of the entire plate. The area-integrated values agree well with literature data. CFD calculations with an SST and an EASM–RSM were carried out on a section of a PHE channel. A comparison with the measured data indicates the shortcomings of even advanced turbulence models for the prediction of heat transfer coefficients but confirms the advantages of EASM–RSM in complex flows.

Application of Wavelet in Highly Ill-Posed Inverse Heat Conduction Problem

In this work, the prefiltering of the sensor data is taken into consideration when solving an inverse heat conduction problem. The temperature data obtained from each sensor is considered as a discrete signal, and discrete wavelet transform in a multi-resolution filter bank structure is utilized for the signal analysis, after which wavelet denoising algorithm is applied to remove noise from data signal. Subsequently, noisy and denoised temperatures are separately used as input data to an inverse heat conduction problem for comparison. The inverse heat conduction problem considered in this article is an inverse volumetric heat source problem, and it is solved using the conjugate gradient method along with the associated adjoint problem used to obtain the gradient of the objective function. Three sets of results in two case studies are compared (i.e., the result obtained from non-noisy data, noisy data, and denoised data). In the case of noisy data, iterative regularization is used to regularize the solution. The root mean square error of the estimated heat source from denoised data is reduced approximately by a factor of seven to nine as compared to those obtained from noisy data.

Removal of numerical instability in the solution of an inverse heat conduction problem

In this paper, we consider an inverse heat conduction problem (IHCP). A set of temperature measurements at a single sensor location inside the heat conduction body is required. Using a transformation, the ill-posed IHCP becomes a Cauchy problem. Since the solution of Cauchy problem, exists and is unique but not always stable, the ill-posed problem is closely approximated by a well-posed problem. For this new well-posed problem, the existence, uniqueness, and stability of the solution are proved.

Lattice-free finite difference method for numerical solution of inverse heat conduction problem

Inverse heat conduction problem consists of finding an initial temperature distribution from the knowledge of a distribution of the temperature at the present time. Here, we assume that the associated boundary conditions are known. The heat conduction problem backward in time is a typical example of ill-posed problems in the sense that the solution exists only for regular functions of some kind describing the present temperature distribution and also the solution is unstable for the present temperature distribution function. Conventional numerical methods often suffer from instability of the problem itself when high accuracy is intended in the approximation. Our aim is to create a meshless method which is applicable to the ill-posed inverse heat conduction problem. We construct a high order finite difference method in which quadrature points do not need to have a lattice structure. In order to develop our new method we show a tool in using exponential functions in Taylor's expansion. From numerical experiments we confirmed that our method is effective for solving two-dimensional inverse heat conduction problem numerically subject to mixed boundary conditions.

Numerical approximation of solution of an inverse heat conduction problem based on Legendre polynomials

In this paper, we consider an inverse heat conduction problem (IHCP). The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. Using a linear transformation, the ill-posed IHCP becomes a Cauchy problem. This problem will be solved by applying Legendre polynomials. Results show that an excellent estimation can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.

Parametric method for the solution of an ill-posed inverse heat-conduction problem in application to the optimization of thermal regimes

A method is proposed for the stable approximate solution of an ill-posed inverse heat-conduction problem, to which the investigated problem of optimal control of the thermal regime of a rigid body is reduced.

Analysis and solution of the ill-posed inverse heat conduction problem

The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature and heat flux values on the surface. The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. A special solution procedure is developed for the one-dimensional case which replaces the heat conduction equation with an approximating hyperbolic equation. If viewed from a new perspective, where the roles of the spatial and time variables are interchanged, then an initial value problem for the damped wave equation is obtained. Since the formulation is well-posed, both analytic and numerical solution procedures are readily available. Sample calculations confirm that this approach produces consistent, reliable results for both linear and nonlinear problems.