Helcio R. B. Orlande

Inverse and Optimization Problems in Heat Transfer

This paper presents basic concepts of inverse and optimization problems. Deterministic and stochastic minimization techniques in finite and infinite dimensional spaces are revised; advantages and disadvantages of each of them are discussed and a hybrid technique is introduced. Applications of the techniques discussed for inverse and optimization problems in heat transfer are presented. Keywords : Inverse problems, optimization, heat transfer

COMPARISON OF DIFFERENT VERSIONS OF THE CONJUGATE GRADIENT METHOD OF FUNCTION ESTIMATION

The inverse problem of estimating the spatial and transient variations of the heat transfer coefficient at the surface of a plate, with no information regarding its functional form, is solved by applying the conjugate gradient method with adjoint problem. Three different versions of this method, corresponding to different procedures of computing the search direction, are applied to the solution of the present inverse problem. They include the Fletcher-Reeves, Polak-Ribiere, and Powell-Beale versions. Such versions are compared for test cases involving different numbers of sensors, levels of measurement errors, and initial guesses used for the iterative procedure.

An inverse problem of parameter estimation for heat and mass transfer in capillary porous media

Abstract This work deals with the solution of an inverse problem of parameter estimation involving heat and mass transfer in capillary porous media, as described by the dimensionless linear Luikov’s equations. The physical problem under picture involves the drying of a moist porous one-dimensional medium. The main objective of this paper is to simultaneously estimate the dimensionless parameters appearing in the formulation of the physical problem by using transient temperature and moisture content measurements taken inside the medium. The inverse problem is solved by using the Levenberg–Marquardt method of minimization of the least-squares norm with simulated measurements.

Inverse Problems in Heat Transfer: New Trends on Solution Methodologies and Applications

Systematic methods for the solution of inverse problems have developed significantly during the past two decades and have become a powerful tool for analysis and design in engineering. Inverse analysis is nowadays a common practice in which teams involved with experiments and numerical simulation synergistically collaborate throughout the research work, in order to obtain the maximum of information regarding the physical problem under study. In this paper, we briefly review various approaches for the solution of inverse problems, including those based on classical regularization techniques and those based on the Bayesian statistics. Applications of inverse problems are then presented for cases of practical interest, such as the characterization of nonhomogeneous materials and the prediction of the temperature field in oil pipelines.

Estimation of dimensionless parameters of Luikov's system for heat and mass transfer in capillary porous media

Abstract This work deals with the solution of inverse problems of parameter estimation involving heat and mass transfer in capillary porous media, as described by the linear one-dimensional Luikovs equations. Our main objective is to use the D-optimum criterion to design the experiment with respect to the magnitude of the applied heat flux, heating and final experimental times, as well as the number and locations of sensors. The present parameter estimation problem is solved with Levenberg–Marquardts method of minimization of the ordinary least-squares norm, by using simulated temperature data containing random errors. Moisture content measured data is not considered available for the inverse analysis in order to avoid quite involved measurement techniques. We show that accurate estimates can be obtained for Luikov, Kossovitch and Biot numbers by using only temperature measurements in the inverse analysis. Also, the experimental time can be reduced if the body is heated during part of the total experimental time.

Recovering the source term in a linear diffusion problem by the method of fundamental solutions

This work considers the detection of the spatial source term distribution in a multidimensional linear diffusion problem with constant (and known) thermal conductivity. This work can be physically associated with the detection of non-homogeneities in a material that are inclusion sources in a heat conduction problem. The uniqueness of the inverse problem is discussed in terms of classes of identifiable sources. Numerically, we propose to solve these inverse source problems using fundamental solution-based methods, namely an extension of the method of fundamental solutions to domain problems. Several examples are presented and the numerical reconstructions are discussed.

Approximation of the likelihood function in the Bayesian technique for the solution of inverse problems

This work deals with the use of radial basis functions for the interpolation of the likelihood function in parameter estimation problems. The focus is on the use of Bayesian techniques based on Markov Chain Monte Carlo (MCMC) methods. The proposed interpolation of the likelihood function is applied to test cases of inverse problems in heat and mass transfer, solved with the Metropolis–Hastings algorithm. The use of the interpolated likelihood function reduces significantly the computational cost associated with the implementation of such Markov Chain Monte Carlo method without loss of accuracy in the estimated parameters.

Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem

This work deals with the use of the conjugate gradient method in conjunction with an adjoint problem formulation for the simultaneous estimation of the spatially varying diffusion coefficient and of the source term distribution in a one-dimensional nonlinear diffusion problem. In the present approach, no a priori assumption is required regarding the functional form of the unknowns. This work can be physically associated with the detection of material non-homogeneities, such as inclusions, obstacles or cracks, in heat conduction, groundwater flow and tomography problems. Three versions of the conjugate gradient method are compared for the solution of the present inverse problem, by using simulated measurements containing random errors in the inverse analysis. Different functional forms, including those containing sharp corners and discontinuities, are used to generate the simulated measurements and to address the accuracy of the present solution approach.

Estimation of the heat flux at the surface of ablating materials by using temperature and surface position measurements

In this article, the conjugate gradient method with adjoint problem is applied for the identification of the heat flux at the surface of ablating materials, by assuming no a priori information regarding the functional form of the unknown. Simulated measurements of the position of the ablating surface are used in the inverse analysis, together with simulated temperature measurements. The accuracy of the conjugate gradient method with adjoint problem is examined for functions containing sharp corners, by using different regularization approaches. Three different versions of the conjugate gradient method are compared, as applied to the inverse problem under observation.

Inverse analysis for estimating the timewise and spacewise variation of the wall heat flux in a parallel plate channel

Solves the inverse problem of estimating the wall heat flux in a parallel plate channel, by using the conjugate gradient method with adjoint equation. The unknown heat flux is supposed to vary in time and along the channel flow direction. Examines the accuracy of the present function estimation approach, by using transient simulated measurements of several sensors located inside the channel. The inverse problem is solved for different functional forms of the unknown wall heat flux, including those containing sharp corners and discontinuities, which are the most difficult to be recovered by an inverse analysis. Addresses the effects on the inverse problem solution of the number of sensors, as well as their locations.